Exploiting the Imperialist Competition Algorithm to ...

Simulation

Exploiting the Imperialist Competition Algorithm to determine exit door efficacy for public buildings

Simulation: Transactions of the Society for Modeling and Simulation International 2014, Vol. 90(1) 24–51 Ó 2013 The Society for Modeling and Simulation International DOI: 10.1177/0037549713509416 sim.sagepub.com

Pejman Kamkarian1 and Henry Hexmoor2

Abstract The Imperialist Competition Algorithm has recently shown superior performance in optimizing goals. This algorithm has inspired us to apply it to exit doors. The Imperialist Competition Algorithm is applied to an environment to find the best possible locations for exit doors and also to estimate the minimum required width for each door in order to be able to rapidly evacuate a crowd out of danger in emergency situations. The results of our system are applied to a few prototypical scenarios that have demonstrated that the location of each exit door in an indoor space can play a significant role in the evacuation of a crowd out of an emergency situation. Our results thus far are promising and future work will account for more complex floor layouts.

Keywords Exit door safety, human behavior representation, expert systems, modeling and simulation environments, agent-based systems, artificial intelligence

1. Introduction In developed countries, people spend most of their lives in indoor spaces. Often, large groups of people are gathered at the same location for leisure or work purposes. We will consider these groups to be crowds. Generally, a crowd is defined as a set of agents who are gathered at one physical location who share and follow some common objectives.1 If a life-threatening emergency, such as fire or earthquake, occurs, there should be efficient and reliable ways available for people to rapidly evacuate buildings. Evacuation becomes proportionally more urgent with rises in population sizes and lengths of times that occupants need to remain at the location. Pedestrian traffic outside buildings is beyond our scope. Our focus on architectural issues is strictly limited to passageways colloquially known as exit doors intended for use for evacuation. However, our observations are strictly technical and aesthetic. We will focus more closely on characteristics of a crowd in the context of an emergency that requires evacuation. Although each group has a shared set of goals among its members, individuals do not necessarily share similar actions. This is especially true when they encounter dangerous situations such as fire. In such cases, because of fear and natural instincts for survival, individuals will take separate, individualistic actions to address their own needs for survival. They will not follow group

patterns for action selection. The characteristics of this situation are described in numerous reports including Villamil et al.2 and Heı¨geas et al.3 We give a brief summary of key observations as follows. • • • •

Regardless of the crowd, each individual will attempt to keep himself/herself out of danger as quickly as possible. Every person looks around to find the quickest way out. Having more knowledge about the environment and layout helps each individual to better escape. Increasing fear and chaos among agents will make the exit doors crowded and an ‘‘arch phenomenon’’ emerges. This situation leads to decreased movement flow and eventually perpetuates the notion that the rate of increased frantic pace proportionally lowers overall evacuation speed.

1

Electrical and Computer Engineering Department, Southern Illinois University, USA 2 Computer Science Department, Southern Illinois University, USA Corresponding author: Pejman Kamkarian, Southern Illinois University, USA.

Downloaded from sim.sagepub.com by guest on January 13, 2016

Kamkarian and Hexmoor • • •

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Because of herding behavior, weaker individuals will stumble and fall down. Therefore, the escape speed becomes even slower. Typically, the frightened crowd will congregate at one exit door and ignore all other exits. Due to excessive crowding, it is possible that a nearby wall will collapse and it will cause injuries.4

In such circumstances of anxiety, if an effective evacuation strategy does not exist, we may encounter catastrophic scenarios with lives lost. One of the most important solutions that should be explored for evacuating people in emergency situations is to study exit door specifications. We need to consider some important key features of environments that assist in evacuating crowds away from danger using the safest routes in the least amounts of time. We can study evacuation processes by modeling crowd dynamics. Existing models of crowd behavior during evacuations can be classified into two broad categories: topdown and bottom-up models. Top-down models describe macroscopic crowd behavior and lack explanatory power for individual actions. Bottom-up models start from individual behaviors and attempt to scale them up to crowds. Our own approach is a bottom-up model. The most commonly reported types of bottom-up crowd models are queuing and network models.5,6 A possible flaw with bottom-up models is a lack of ability to account for serendipity and the chaos of interaction in the crowd. Our model strives to account for a few key crowd interaction properties, but surely it will need to be extended in future for better realism. The idea of evacuating a crowd is not limited to humans: it pertains to all other types of animals. The safest exit doors should be able to evacuate not only humans but all kinds of animals that might be present in indoor spaces. This urges us to consider appropriate designs for exit doors. Buildings must adhere to an acceptable standard to be able to evacuate people who are inside it in an emergency. In most cases, such standards must account for combinations of exit doors, including stairs and ladders. Emergency evacuation conditions of a crowd and simulation of real crowds are modeled by Still7 and Bandini et al.8 The required number of exit doors will vary based on the size and architecture of each environment. One of the most important considerations about locating the exit doors is the evacuation rate. We must evacuate the most number of people in the least amount of time. Lacking such a standard will lead us to have problems in emergency situations, even if exit doors themselves are built and located in safe and reliable places. To make this clear, we point to stampeding events, which are one of the most common occurrences during an emergency. A stampede can occur due to human reaction to unexpected sets of events. People will

herd and push each other in competition to reach the exit doors. People who are in emergencies often behave irrationally, largely based on reactions to the information available to them at the time. For instance, studies of evacuations in fires such as in Sime9 and in Canter10 indicate that people tend to leave gathering venues through the original pathways they entered. This offers people better solutions in terms of the availability of closer, more accessible exit doors. This can be seen as irrational behavior. In a fire, the smoke and heat create limited visibility, which may cause people to seek escape through an exit door that they already know exists if they are unfamiliar with other possible choices. Most often during such situations, we observe a great deal of panic among people. Although the predominance of mass panic that occurs during emergency situations is widely understood by academic societies, people in practice still do not integrate it in their considerations for addressing solutions.11–13 Implications of overlooking crowd mentality in emergency situations continue to plague us with problems. Studies of the impact of environmental/perceptual information on crowd behaviors are conducted by environmental psychologists. The results indicate that perceived threats such as fire or smoke can stress crowds, whereas clear and precise information can calm them down and reduce risks of disorder or blocking.14,15 Dynamics of how people interact and how inherent properties of crowds could affect their behaviors is explored by social psychologists. According to recent studies, the society’s view of crowd behavior and management often rely wrongly on early reactionary accounts of crowd psychology, such as Le Bon’s (1895/1947) commentary on the crowds of the Paris Commune during 1870–1871.16,17 This view attempts to ascribe an individual mind to the group. This is misleading. Although crowds may appear to act in unison, they do not meld their minds into one; rather, they behave as a collective while each person maintains their broad action autonomy. Individuals flexibly enter behaviors that are compatible with others but also choose behaviors to serve their own well-being. As an example of crowd behavior, we can point out the 2003 station nightclub fire that was the fourth deadliest nightclub fire in the American history. Located at 211 Cowesett Ave. in West Warwick, Rhode Island, it killed 100 people at 11:07 PM EST, on Thursday, February 20, 2003. Firing of pyrotechnics, set off by the tour manager of the evening’s headlining band, ignited flammable sound insulation foam in the walls and ceilings surrounding the stage. The fire quickly moved all around and engulfed the club in less than six minutes. Of the 462 people who were in attendance during the event, about 230 people were injured and another 132 escaped uninjured.18Figure 1 shows the floor plan for the station nightclub and its exit door locations, as well as fire locations.


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Simulation: Transactions of the Society for Modeling and Simulation International 90(1)

Figure 1. Station nightclub exit doors and fire positions (adapted from http://www.nist.gov/public_affairs/factsheet/ mar_3_rifindings.cfm).

Figure 2. The victims’ locations by their numbers (adapted from http://en.wikipedia.org/wiki/The_Station_nightclub_fire).

Based on the video footage of the fire, when it started to grow, it made a billow of smoke, which quickly made escape impossible. The exit blockage by smoke further hindered evacuation. Although there were four exit doors located around the club, most people naturally headed for the front door through which they had entered earlier. The ensuing stampede led to crushing people in the narrow hallway leading to that exit door. The stampede quickly blocked the exit door completely and resulted in numerous

deaths and injuries among the patrons and staff. Of the all people who were inside, 100 lost their lives, and about half were injured, either from burns, smoke inhalation, or trampling. Among those who perished in the fire are Great White’s lead guitarist, Ty Longley, and the show’s emcee, WHJY DJ Mike. As another example, we highlight the Santika Club fire that occurred on January 1, 2009, in Watthana, Bangkok, Thailand near Thong Lo Road. Figure 2 shows that floor


Kamkarian and Hexmoor

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plan. Of the attending people, 66 people were killed and 222 people were injured when fire broke out during the New Year’s celebration while the band named Burn was playing.19–21 The fire started just after the new year in Thailand, at 12:35 AM.22,23 There were 35 foreigners from Australia, Belgium, Canada,24 France, Finland, Japan, Nepal, the Netherlands, Singapore, South Korea, Switzerland, and the United Kingdom.24 Foreigners, including those from the United States, were among the injured.20,22,23,25 The official reason for the fire has not been concluded by investigators. Many eyewitnesses suggested that the fire was caused by fireworks that lit a second-story ceiling on fire, or by sparklers inside the nightclub.20 Other sources suggested an electrical explosion was at fault and eventually caused the fire.25 Based on what an eyewitness stated, there were no pyrotechnics in the club at all.21 Another eyewitness reported seeing flames on the roof of the building after going outside to watch the midnight fireworks display. The recorded videotapes of the indoor stage event, including the countdown, show that only sparklers were used. Furthermore, the fire only became visible indoors approximately 10 minutes after midnight. This strongly suggests that the fire originated inside the ceiling space or on the roof, allowing it to grow in intensity while going unnoticed for some time. Due to the tropical, wet climate and lax enforcement of building codes, tar paper and various plastics are often used as waterproofing materials. There were about 1000 people in attendance at the club when it ignited, and the deaths occurred from smoke inhalation and burns, as well as from stampedes.21 Fainting after a short time because of release of fumes from burning plastics was another reason for deaths announced by doctors. The club only had one main exit, with an additional staff exit,26 unknown to clubbers, and a third door that was locked to prevent burglars.27 To summarize, lack of a suitable number and correct locations for exit doors are among chief reasons for preventing the crowd from evacuating in an emergency. The time of evacuation is also another important factor that should be accounted for while designing and placing exit doors. As is highlighted in the second example, breathing poisoned air, which emanated from the plastic fume fire, caused people to faint and eventually lose their lives. In this paper, we will focus on the most important attributes and specifications that the exit doors should meet in order to be able to keep the crowd out of danger in the most reliable and safe manner.

2. The main attributes for exit doors As one of the most important steps to study and design exit doors, we have to consider salient attributes that can directly or indirectly affect exit doors designs. In the following we outline several of these key attributes.

2.1 Occupant species Considering different groups of living beings that can be present at a certain place can be useful while designing exit doors. For example, locating small doors at the bottoms of exit doors can help smaller pets to evacuate during an emergency situation, whereas people need larger exits. If there is a mix of people and pets, we need both kinds of exits. If we consider only human in our environment, we can use particle systems that were proposed by Bouvier et al.28 to simulate human behaviors. Based on particle swarms theory, each agent is considered to be a particle, augmented with a state and a feedback function to dominate its behavior. All agents’ behaviors constitute the whole system’s performance. Particle systems are also used for modeling the motion of groups with significant models of physics.28,29

2.2 Occupant headcount Considering the number of individuals includes counting all types of living beings, including the number of pets. Having an accurate estimate is an important factor that should be considered while deciding widths and locations for exit doors. As we highlighted in the previous examples, absence of these attributes was the main reasons for injuries and deaths. The width of exit doors should be determined relative to the proportion of the crowd.

2.3 Time Time is another important attribute that should be accounted for while designing and placing exit doors. On the other hand, exit doors should be able to service evacuation of the crowd through them in the minimum possible time. This will reduce the number of people who lose their lives due to breathing poisoned air or stampeding of herding behavior.

3. Calculating to find the optimal values for the main attributes We use the optimized Imperialist Competition Algorithm (ICA) in order to find the values and proportions for the attributes mentioned for exit doors. The ICA is a particle swarm optimization (PSO) algorithm. These algorithms help us simulate a real space that is occupied with the crowd in order to mimic and analyze their behavior in order to find better ways in terms of seeking exit doors without injury and other undesirable events in the real world. By applying the optimized ICA we are able to simulate crowd movements toward the environment’s exit doors, hence we will satisfy the mentioned key features for exit doors.


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4. Particle swarm optimization PSO is a population-based stochastic optimization technique for performing numerical optimization without explicit knowledge of the gradient of the problem to be optimized. PSO was originally developed by Kennedy, Eberhart and Shi in 199530–33 and was first intended for simulating social behavior of organisms, such as bird flocking and fish schooling.34,35 The algorithm was simplified and it was not only a tool for optimization, but also a tool for representing socio-cognition of human and artificial agents, based on principles of social psychology32 PSO optimizes a problem by maintaining a population of candidate solutions called particles and moving these particles around in the search-space according to simple models. A complex system is modeled as a large collection of different constituents. These particles interact among themselves, with other particle sources, and also with surrounding surfaces or obstacles. They can be subject to external forces and particles can also be coupled with the surrounding environment.28 The movements of the particles are guided by the best found positions in the searchspace, which are continually updated as better positions are found by the particles. On the other hand, each particle adjusts its position according to its own experience, and according to the experience of a neighboring particle, making use of the best position encountered by itself and by its neighbor. Whenever particles interact they become more similar. As they influence and imitate one another they teach and learn from each other and eventually lead and follow each other.36 Thus, as in modern mimetic algorithms, a PSO system attempts to balance exploration and exploitation by a combination of local search methods with global search methods.37 Based on the experiments reported by Shi and Eberhart,38 having the mentioned balance is generally controlled by the inertia weights.

5. Exit door locator algorithm Finding the best positions for each exit door and also obtaining the best mentioned feature values for them in order to be able to evacuate a crowd in a reasonable time is the most important objective that must be considered while designing public spaces. The exit door locator algorithm is a population-based method. The best locations for exit doors will be determined by the best values obtained from applying the ICA in an agent population. Also the results in each cycle of experiments will determine the appropriate width for each exit door.

6. An overview of the Imperialist Competition Algorithm The ICA is a relatively new evolutionary optimization method, which is based on inspiration from natural

processes.39 Our brief summary is adapted from AtashpazGargari and Lucas39 and is included here so we may assume reader familiarity and brevity for discussing our application. Ant colony optimization is an example based on modeling each ant to find the shortest possible path to the food source. With the case of having a large-scale problem such as a population in a closed space, the ICA is able to rapidly find the optimized solution. Evolutionary optimization algorithms are developed based on observing and modeling natural processes and other properties of evolution, especially human evolution. However, the ICA uses socio-political evolution of humans as a source of inspiration for developing a strong optimization strategy. In particular, this algorithm considers imperialism as a level of human social evolution and using mathematical modeling this complicated political and historical process, it arrives at a tool for evolutionary optimization. Since its inception, this novel method has been widely adopted by researchers to solve different optimization tasks. It is used to design optimal layout for factories, adaptive antenna arrays, intelligent recommender systems, and optimal controllers for industrial and chemical possesses. Imperialism is the strategy of extending the power and rule of a government beyond its own territory. A country may attempt to dominate others by direct rule or by less obvious means, such as a control of markets for goods or raw materials. The ICA is a novel global search heuristic that uses imperialism and imperialistic competition process as a source of inspiration. Like other evolutionary algorithms, the proposed algorithm starts with an initial population that is countries in the world. Based on the power that initially each country possesses, a few of the best ones in the population are selected to be the imperialists and the remainders are classified as colonies for imperialists.39 All colonies of initial population are divided among the imperialists based on their power. After dividing all colonies among imperialists, the colonies start moving toward their relevant imperialist country. The total powers of an empire depend both on the power of the imperialist country itself and sum of powers of its respective colonies. This model defines the total power of an empire by the power of an imperialist country plus a percentage of mean power of its colonies. Then the imperialistic competition begins among all empires. Any empire that is not able to succeed in this competition and increase or prevent decreasing its power will be replaced,40 and eventually eliminated from the competition. The imperialistic competition will gradually result in an increase in the power of powerful empires and a decrease in the power of weaker ones. Weak empires will lose their power and ultimately they will collapse. The movement of colonies toward their relevant imperialists along with competition among empires and also the collapse mechanism will hopefully cause all the countries to converge to a state in



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which there exists just one empire in the world and all the other countries are colonies of that empire. In this ideal new world, colonies have the same position and power as the imperialist. The steps of the ICA are as follows.

6.1 Generating initial empires The goal of optimization is to find an optimal solution in terms of problem variables. Initially, we form an array of variables to be optimized. The basic variable unit is called a ‘‘country’’. In an Nvar dimensional optimization problem, a country is an Nvar × 1 array, defined by Equation (1): country = ½p1 , p2 , p3 , . . . , pNvar

ð1Þ

The variable values in the country are represented as floating point numbers. The cost of a country is found by evaluating the cost function f at the variables (p1 , p2 , p3 , . . . , pNvar ), shown in Equation (2): costi = f ðcountryi Þ = f ðp1 , p2 , p3 , . . . , pNvar Þ

ð2Þ

To start the optimization, we generate the initial population of size Ncountry . We select Nimp of the most powerful countries to form the empires. The remaining Ncol of the population will be the colonies each of which belongs to a distinct empire. Then we have two types of countries: imperialists and colonies. To form the initial empires, we divide the colonies among imperialists based on their power. That is, the initial number of colonies of an empire should be directly proportional to its power. To divide the colonies among imperialists proportionally, we define the normalized cost of an imperialist by costi = cn maxi fci g

ð3Þ

Here, cn is the cost of nth imperialist and Cn is its normalized cost. Having the normalized cost of all imperialists, the normalized power of each imperialist is defined by C n pn = PNimp i = 1 Ci

ð4Þ

From another point of view, the normalized power of an imperialist is determined by the proportion of colonies under possession of that imperialist. Then, the initial number of colonies of an empire will be in Equation (5): N × Cn = round fpn × Ncol g

ð5Þ

Here, N × Cn is the initial number of colonies of nth empire and Ncol is the number of all colonies. To divide the colonies among imperialists we choose randomly N × Cn colonies and assign them to each imperialist. The colonies together with the imperialist will form the nth empire.

Figure 3. Moving colonies toward empires.

6.2 Moving the colonies of an empire toward the imperialist As mentioned earlier, imperialist countries start to improve their colonies. We have modeled this by moving all colonies toward the imperialist. This movement is shown in Figure 3 in which a colony moves toward an imperialist by x units. The new position of the colony is shown in a darker color. The direction of the movement is shown by the arrow extending from a colony to an imperialist. In this figure x is a random variable with uniform (or any proper) distribution. Then for x we have x ∼ U ð0, β × d Þ

ð6Þ

Here, β is a number greater than 1 and d is the distance between a colony and an imperialist. A ðβ > 1Þ causes the colonies to get closer to the imperialist state from both sides. To explore variations around an imperialist, we allow for deviations from the direction of the movement in a random manner. Figure 3 shows the new direction. In this figure, θ is a random number with uniform (or any proper) distribution so that θ ∼ U ðγ, γ Þ

ð7Þ

γ is a parameter that adjusts the deviation from the original direction. The values of β and γ are chosen arbitrarily. In most cases a value of about 2 for β and about π=4 (Rad) for γ have resulted in good convergence of countries to the global minimum. While moving toward an imperialist, a colony may reach a position with lower cost than that of the imperialist. In such a case, the imperialist moves to the position of that colony and vice versa. Then an imperialist will follow the algorithm in the new position and colonies start moving toward that position.


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6.3 The total power of an empire The total power of an empire is mainly affected by the power of the imperialist country, but the power of the colonies of an empire has an effect, albeit negligible, on the total power of that empire. We have modeled this fact by defining the total cost by T × Cn = Costðimperialistn Þ + ξmeanfCostðcolonies of empiren Þg

ð8Þ

Here, T × Cn is the total cost of the nth empire and ξ is a positive number that is considered to be less than 1. A small value for ξ implies that the total power of an empire is determined by just the imperialist; a large value implies an increasing role for the colonies in determining the total power of an empire.

6.4 Imperialistic competition All empires try to take possession of colonies of other empires and control them. This imperialistic competition gradually brings about a decrease in the power of weaker empires and an increase in the power of more powerful ones. We model this competition by choosing a number (e.g., usually one) of the weakest colonies of the weakest empires and allow for the empires to compete for acquiring the chosen colonies (or the colony). To start the competition, firstly, we calculate the probability of each empire succeeding to acquire colonies in lieu of its total power. The normalized total cost simply is obtained by Equation (9): N × T × Cn = T × Cn maxi fT × Ci g

ð9Þ

Here, T × Cn and N × T × Cn are, respectively, total cost and normalized total cost of nth empire. Having the normalized total cost, the possession probability of each empire is given by N ×T ×C n ð10Þ ppn = PNimp N × T × Ci i=1

To divide colonies among empires using the probability of acquisition as a guide, we form the vector P as h i P = pp1 , pp2 , pp3 , . . . , ppNimp

ð11Þ

Then we create a vector of size P with elements as uniformly distributed random numbers as R = r1 , r2 , r3 , . . . , rNimp

ð12Þ

Next we form vector D by simply subtracting R from P as D = P R = D1 , D2 , D3 , . . . , DNimp = ½pp1 r1 , pp2 r2 , pp3 r3 , . . . , ppNimp rnimp

Referring to vector, we will assign the colonies to the empire whose relevant index in D is a maximum number. At the end, powerless empires will disintegrate in the imperialistic competition and their colonies will be divided among other empires. The criteria used in modeling the disintegration mechanism vary. In most of our model executions, a disintegrated empire is one that loses all of its colonies.

ð13Þ

6.5 Convergence After a while all empires except the most powerful one will collapse and all the colonies will be under the control of this unique empire. In this ideal new world all the colonies will have the same positions and same costs and they will be controlled by an imperialist with the same position and cost as themselves. In this ideal world, there is no difference not only among colonies, but also between colonies and the imperialist. In such a condition, we put an end to the imperialistic competition and stop the algorithm. Later in this paper, we will apply the proposed algorithm to some of benchmark problems in the realm of optimization. The outline of main steps in the algorithm is summarized in the pseudo code is as follows. Initialization state •

Select some random points on the function and initialize the empires.

Process • • •

Assimilation of moving the colonies toward their relevant imperialist. If there is a colony in an empire that has lower cost than that of imperialist, exchange the positions of the colony with the imperialist. Compute the total cost of all empires (related to the power of both imperialist and its colonies).

Elimination •

Choose the weakest colonies from the weakest empires and assign the colonies to the empire with the highest probability of acquisition potential, which is called imperialistic competition.

7. Application of the optimized Imperialist Competition Algorithm In this section, we demonstrate and apply the optimized ICA to our particles as agents in order to find the best possible placements for exit doors. Our experimental



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environment consists of three different kinds of entities: exit doors, obstacles, and people. In an indoor place, there are two kinds of obstacles. The first kind is placed based on a plan such as chairs, trash cans, tables, etc., whereas the second kind is any other object present that is usually a result of some event, such as earthquake or fire. Smoke, debris, and the wall or cell parts are as an also instances of the second type of obstacle.

7.1 Generating initialization for the environment

Figure 4. The distances of each agent from exit doors.

The goal of optimization is to find an optimal solution in terms of the variables of the problem. The ICA requires an array of variable values to be optimized. Here we form the array ED for this array. In a Nvar dimensional optimization problem, an ED array is shown as a (1 × Nvar ) array: ED = fed1 , ed2 ed3 , . . . , edNvar g

ð14Þ

The variable values in exit doors are represented as floating point numbers. The cost of an exit door is determined by the number of people who are trying to evacuate through that exit door and the rate of evacuation in each time period. This is shown by Equation (15): Cost(edn ) = Cost(ERedn ) = f (edn ) = f (ERedn )

ð15Þ

where ERedn represents the evacuation rate of the nth exit door. To start the optimization algorithm we generate the initial population of size Npop in our indoor space. We place Ned exit doors on each valid region. A valid region on a wall is one that permits the same distance among doors and to the end of each wall corner. The number of exit doors in each a given valid region is obtained by Equation (16): Ned =

WVR (Wini × 2) Wini × 2

ð16Þ

Ned is the total number of exit doors for each valid region, WVR is the width of the jth valid region and the Wini is the initial value of the width of each exit doors. TheNpop of the population will be the people that are randomly placed in our environment. The obstacles will be chosen and placed based on the environment’s design.

7.2 Forming the initial zones To form the initial zones, we divide the people among exit doors based on their distances. We have three different sizes, which belong to three different groups of agents who are present in our environment, made up of adult males, adult females, and children. We consider Fruin classifications to determining each group’s size. Equation (17) is an adaptation of Fruin’s principle:41,42

Velocityðpn Þ = f ðpn Þ = f ðswn Þ + f (bdn )

ð17Þ

swn is the shoulder width of the nth person and bdn is the body length (i.e., body depth) of the same person. Each exit door has an initial number as a constant. We define the initial constant with Equation (18): Init Cost(ed1 ) = Init Cost(ed2 ) = . . . = Init Costðedn Þ = m ð18Þ

Here, m is the cost of each exit door at the initialization state. In our paper, we assume three different types of body sizes for males, females, and children. Having the velocity and the distance of each exit door, each person picks the exit door that meet the best exit conditions:

Pfpn ∈ edn g ≡ max Velocitypn , minðDistanceedn Þ ð19Þ

Velocitypn is the velocity for the nth person and Distanceedn is the nearest exit door. Figure 4 shows the different distances relative to different exit doors that an agent has at the beginning. Each agent then picks the shortest path to the nearest exit door. To choose the best possible exit door, each agent measures its distance from all exit doors and picks the closest exit door, shown in Figure 4 and Equations (20) and (21): D = Dist(Ax )ed1 , D0 = Dist(Ax )ed2

ð20Þ

if D0 > D \ ed2 ∈ Exit PathðAx Þ

ð21Þ

Figure 5 shows the initial population at each zone. As shown in this figure, larger zones have greater number of people, while weaker ones have fewer. In this figure, exit door 1 has formed the most powerful zone and has the greatest number of people. In order to remain as the powerful exit door among all exit doors in the same valid region, exit door 1 should be able to evacuate all agents belonging to it in the shortest time.


VR = fVR1 , VR2 , . . . , VRn g

ð22Þ

Z = fZ1 , Z2 , . . . , Zn g

ð23Þ

fed1 , ed2 , . . . , edn g ∈ VRn

ð24Þ

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Figure 5. Generating the initial zones (the more people an exit door possess, the larger is its relevant zone).

fA1 , A2 , . . . , An g ∈ edn ∈ Zn

ð25Þ

Am = fDed1 , Ded2 , . . . , Dedn g

ð26Þ

if An ∈ Zn \ min D = Dedn

ð27Þ

Here, Dedn is the distance from the nth agent to the nth exit door and Z is the list of all zones in the environment. Figure 6. Moving people toward exit doors.

7.3 Moving people in a zone toward exit doors People of each zone start improving their place by moving toward the exit door to which they belong. We have modeled this idea by moving individuals by x units. We define the normalized x units of the nth person in Equation (28): Xn = xn maxi fXi g

ð28Þ

xn is the unit of the nth person and Xn is the same as a normalized unit. Having the normalized unit of all people, the normalized unit of each person is identified by Equation (29): x i pn = PNx i = 1 xi

ð29Þ

From another point of view, the normalized unit of a person is the portion of movement that should be possessed by that person. Then the initial number of units of people will be as follows:

N × Xn = round pn × Npep

ð30Þ

N × Xn is the initial movement unit of the nth person and Npep is the total unit of all people. This movement is shown in Figure 6 in which the person moves toward the exit door by x units based on their movements’ proportions. The new position of the person is shown in a darker color. The direction of the movement is the vector from the person to the exit door: x ∼ U ð0, β × d Þ

ð31Þ

β is a number greater than 1 and d is the distance between the person and the exit door. When (β > 1), people get closer to the exit door state from both sides.

7.4 Moving a person around obstacles While each person is moving toward an exit door that he is drawn toward, there are two different kinds of obstacle that might be in his way. The first type of obstacle is that placed in the environment constantly, such as rows of chairs in a theater. We call such obstacles static obstacles. Moving around such obstacles is shown by the following relation:



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Figure 7. Moving around a static obstacle.

if dn ≤ y then P

v v0

≡ minðdistedm Þ

ð32Þ

dn is the distance between the nth person and the obstacle, y is the minimum needed distance to making a decision about moving around the obstacle, vand v0 are possible ways that the nth person can choose and distedm is the distance of the nth person to the mth exit door. The possible ways for a static obstacle are shown in Figure 7. As is shown in Figure 7, if obstacle O1 is formed accidentally, the agent must either choose to move around it to continue moving toward his current zone, or find another alternative way. In this case, the possible routes to move around obstacle O1 are V = a + b + c,V 0 = a0 + b0 . If there was another exit, say exit door 2, located at a close distance to such a person, the distance from it is calculated based on V 00 = a00 . Considering that exit is capable of accepting more people to evacuate, Figure 8 is a decision flowchart which may apply to a particle as a person, in order to continue staying at the current zone, or changing it to exit door 2. A second kind of obstacle is the other people who might be between the person and the exit door. We call them dynamic obstacles. Choosing the way is identified by the following relation and is shown in Figure 9: if dn ≤ z then PðvÞ = pðv0 Þ; Path = Rand fv, v0 g

One other possibility is facing another agent who is trying to go in the opposite direction. If there were no free rooms around such an agent, it will swap its place with the agent who is trying to move in the opposite direction.

7.5 Eliminating the exit doors based on the results After each cycle of evacuation, based on the total number of people that each exit door has evacuated thus far and also considering the door’s evacuation rate, the weakest exit door in terms of evacuating is eliminated. The first step to finding the weakest door is to have a list of all environments’ valid regions. The valid region list is identified by the following relation: VR = fVReg1 , VReg2 , . . . , VRegn g

VR is the valid region list and VRegn is the nth valid region. We start the experiments with a number n exit doors that is in excess of what we expect to be needed at each valid region. After each experiment period of evacuation and door competitions, one of the exit doors at each valid region will eliminated. We then continue this process until all excess exit doors are eliminated. The exit doors at each valid region are identified by the following relation: VRn = fed1 , ed2 , . . . , edt g

ð33Þ

z is the distance between the nth person and the mth person and v, v0 are the possible ways that the nth person can choose.

ð34Þ

ð35Þ

VRn is the nth valid region and edt is the tth exit door on the nth valid region. We define ET as the total number of experiments based on Equation (36):


34


Figure 8. Decision flowchart to decide about staying or leaving zones.

RedET =

ð40Þ

R is the list of all exit doors rates, RedET is the rate for the ETth exit door, TedET is the evacuation time for the ETth exit door, and PopedET is the total number of people who choose the ETth exit door for evacuation. The final step of each experiment period is to find the weakest exit door in terms of the exit door that evacuates the least people using the longest time. We identified the relation for door elimination using Equation (41):

Figure 9. Moving around a dynamic obstacle.

ET = fTED TNDg

ð36Þ

Here, TED is the total exit doors at the start of experiments and TND is the total needed exit doors. We are interested in two different values after each experimental cycle that are (a) the number of people who decided to evacuate through each exit door and (b) the time that they needed to evacuate through a given exit door: EET = fEV1 , EV2 , . . . , EVET g

ð37Þ

EV = f(T1 , Pop1 ), (T2 , Pop2 ), . . . , (TET , PopET )g ð38Þ

EET is the evacuation experiment time interval, EVET is the pair of values in each experiment period, EV is the list of the pairs for each pair of values in each experiment, and (TET , PopET ) is the pair of the evacuation time for the ETth time and the number of people who evacuated at that time. The list of rates and also the rate of each exit door will be identified by the Equations (39) and (40): R = fRed1 , Red2 , . . . RedET g

TedET PopedET

ð39Þ

E = max (Redn )

ð41Þ

E is the elimination finder and Redn is the rate of the nth exit door that has the maximum value among the list of rates.

7.6 Continuing optimization process The experiment will continue with the same number of people and initializing the values until we reach the minimum required exit doors.

7.7 Adding a proper value to the width of the final exit doors The process of evacuation continues until all particles as people evacuate through available exit doors. Based on the number of people who could evacuate successfully, using Equation (42), the application determines the best possible width of each exit:



35

Figure 10. A view of the simulated environment.

Wi =

"P

# Popi × ∂ (in) PSi

ð42Þ

Here, Wi is the suggested width obtained from the experiment cycle for exit door, i. Si is the number of people who changed their zones during the experiment for any reasons. ∂ is a constant that can vary based on the examined public space and the native architecture standards. Here, we assumed ∂ = 10 as the default value. Each exit door, based on its status during the experiment, may have a different W. Based on this value, the amount that should be added to each exit is obtained. To increase the accuracy, we can repeat the experiment until the W becomes either minimum or very close to its previous value in the last experiment. At the end of the process, the total amount of value that should be added to each exit is determined by Equation (43): Ci =

X

Wi + γ i

ð43Þ

Ci is the total optimized amount in inches that should be added to exit door i. γ i is the first initialization value that the ith exit door had at the beginning of the first period of experiments, and Wi is the total value that was earned during the experimental processes.

8. Simulator, concepts, and rules As a step toward validation, we fully implemented a simulation for the nightclub scenario we offered at the opening of this paper. We scaled the floor plan of the environment in order to increase the population and enhance accuracy. We also assumed that the area consists of two valid regions

that divide the whole area into the left-hand side and the right-hand side. Using initial markings, we considered three exit doors in each side that are located at the top, middle, and lower portions of each valid region. The goal for performing our sets of experiments is to discover and eliminate the weakest functioning exit door in each side and extending door widths appropriately. At the end of each set of experiments, based on the final results, we are able to determine the best location for exit doors, including the best possible width for each.

8.1 Simulator The simulator consists of two general modules: the simulated environment site and results page. Figure 10 shows the simulated environment. The results panel consists of eight different panel segments: the left-hand panel, the right-hand panel, doors status, interaction buttons, proportions, variables, population, and swaps.

8.2 The left-hand panel The left-hand panel consists of three different subsections, which are dependents to pertinent data derived from the left-hand valid regions, which are closest the left-hand wall. It consists of upper door status, middle door status, lower door status, graph, the best exit door result, and the worst exit door result. The upper exit door status consists of two components. It depicts the total number of people who chose the lefthand upper exit door as their favorite path to exit from the environment. The time shows the total amount of time that


36


Figure 12. The right-hand panel.

Figure 11. The left-hand panel.

the attending people used to evacuate through that exit door. The graph draws the number of people who are still inside the environment during running of the experiment. At the end of each cycle of experiment, after all people have evacuated through all exit doors, based on the results, the best exit door, the worst exit door, and their rates reflect values based on the efficacy of the most powerful exit door, the worst exit door, and the rates for each one. Figure 11 shows the left-hand panel and its mentioned corresponding constituent components.

8.3 The right-hand panel The right-hand panel consists of three different components, which are dependent on the data from the rightmost valid regions, which are closest to the right wall. It consists of upper door status, middle door status, lower door status, graph, the best exit door result and the worst exit door result. The upper exit door status consists of two components. It shows the total number of people who chose the righthand upper exit door as their favorite path to exit from the environment. The time shows the total amount of time that the mentioned people spent to evacuate through that exit door. The graph displays the number of people who are still inside the environment based on the time during running the experiment. At the end of each cycle of experiment, after all people evacuated through all exit doors, based on the results, the best exit door, the worst exit door

and their rates will reflect values based on the most powerful exit door, the worst exit door, and the rates for each one. Figure 12 shows the left-hand panel and its mentioned relative components.

8.4 The left-hand exit doors activator/deactivator In order to be able to deactivate the worst performing exit door at the end of each cycle, we envisaged this component. This component consists of three activate/deactivate buttons for the left-hand upper exit door, left-hand middle exit door, and left-hand lower exit door. Figure 13 shows the left-hand door actions for the left-hand valid region, which is the left-hand wall.

8.5 The right-hand exit doors activator/deactivator In order to be able to deactivate the worst performing exit door at the end of each cycle, we included this component. This component consists of three active/deactivate buttons for the right-hand upper exit door, right-hand middle exit door, and right-hand lower exit door. Figure 14 shows the right-hand door actions for the right-hand valid region, which is the right-hand wall.

8.6 The control buttons This module consists of two user-controlled buttons for initialization and start. In order to erase all previous results



37

Figure 13. Left-hand doors activator/de-activator.

Figure 17. The settings component.

Figure 14. Right-hand door actions for the right-hand panel.

Figure 18. The people panel. Figure 15. The main user control buttons.

Figure 19. The swap counter.

times of experiments, we should be able to enter the duration of the experiments. Also we can select the kinds of agents using the agent shape parameter. Figure 17 shows the settings component.

Figure 16. The proportions component.

and put all agents in their new positions, we use the initialization button. To start animating agents toward their favorite exit doors we use the start button. Figure 15 shows these buttons.

8.9 The people count The people count component shows the total number of people who are inside the environment at the initialization time. Figure 18 shows this component with a value of 275.

8.7 Proportions selection In order to specify the population proportion for each group of males, females, and children used for a given experiment, we used this module. In this component, we also introduced the number of people that we need to have in available spaces in percentages. We can also define the percentage of obstacles that should exist inside the environment. In the real world, there should be some situations in that because of events such as explosion, the vision range will be limited because of smoke or so on. In such situations, there will be many agents who will not be able to choose the right exit door in terms of the closest one and, therefore, they will choose an exit door randomly. By enabling random exit, we are able to model agents who will pick an exit door randomly. Figure 16 shows the proportions component.

8.8 The settings The settings component consists of two different parts for agent shape and times of experiments. To determine the

8.10 The Swaps Swaps represents possibilities of exchanging places between two agents who are trying to cross each other’s paths in terms of proceeding toward their favorite exit doors in the case that there are no empty spaces around them. This component shows the total number of swaps that may occurs during a run. Figure 19 shows the swap counter component with a 0 value shown.

8.11 Summary of overall, simulated concepts A crowd consists of people who are placed inside an available space between obstacles. We have three different groups of agents in our space, namely males, females, and children. We used the term ‘‘crowd’’ to demonstrate a mass term for a gathering of a mix of the group types at the same time in an environment. In each indoor space, there are some limitations in terms of placing exit doors. In other words, we are able to locate the exit doors on certain locations. We call such


38


Figure 20. Different zones, with people who are differently shaded in each zone.

locations ‘‘valid regions’’. The valid regions are different from one environment to the next, depending on the building map and some other facilities, such as stairs and so on. There are three kinds of people who exist inside an environment. By default, we assumed children have the smallest size, males the largest and females a medium size or average. As mentioned, we can have a crowd at one time that is a population with a mix of children, males, and females at the same time and at the same location. There are two general kinds of obstacles that exist in the environment. Firstly, there are normal obstacles like rows of chairs, trash cans, etc. Secondly, there are random obstacles that may appear suddenly due to an event such as an explosion. In the real world, when people face an emergency situation and need to make a quick decision in terms of evacuating form a place that they are in, in some cases they might choose the wrong exit door to evacuate through by mistake. In other words, when there are distracting elements in the environment such as smoke that limit vision or pushing or herding behavior, it will cause people to make the wrong decision about their preferred exit door. The simulator is able to model a certain percentage of the crowd making wrong decisions in terms of choosing their favorite exit doors. We refer to this situation as the percentage of wrong decisions. 8.11.1 Traps. In the real world, an emergency situation may consist of explosions or similar events. In such situations, some obstacles may block all possible paths to exit doors for some of the agents. We call such obstacles ‘‘traps’’. 8.11.2 Crowd density (%). The crowd density percentage is the percentage of the people who can be placed between normal obstacles at initial locations.

8.12 Rules After all initial variables in terms of crowd density, people proportions, and percentage of wrong decisions are determined, they will be placed randomly among obstacles inside available spaces. With the next step, each particle consists of people determining the closest exit door as their evacuation path. Each simulated agent shows its preferences for exit doors it chooses by its color, which matches the exit door color. Figure 20 shows the agents after they have picked their favorite exit doors by their colors. As shown in Figure 20, there are six exit doors. There are distinct shades for each door and corresponding client agents. After deciding to evacuate through a door, the agent inherits the same exit door shade. There might be many agents who make wrong decisions about picking their exit doors. White shaded zones are samples of such agents. In this case, we assumed having 25% of available space occupied by agents and 10% of them having made a wrong door decision. After the start button is pressed by the user, each particle depicting an agent starts moving toward the closest exit door for one step. The process of movement continues until all agents have evacuated through exit doors. The path that each agent chooses depends on the situations and is different from one situation to another. For each step, if there is nothing between the agent and the exit doors in terms of obstacles or other agents, then the agent will choose a straight line that is the closest path between him and his favorite exit door and then move one step toward it at each cycle. Otherwise, if there are any other agents or obstacles between the agent and his favorite exit door, then before moving, the agent will look around and find an empty space to go around that object. If there is no empty space available, then the agent will wait until another



39

agent around him moves and some of space around him becomes empty. Then the agent will move to get closer to his favorite exit door. There are several peculiar possibilities that may occur during this process that are outlined next. 8.12.1 Queuing. If there are many agents who are staying behind an exit door, the other agents who are trying to get to that door will wait and let the agent in front to proceed to the door first. Soon after they find empty space around themselves, they quickly move to that empty space in terms of progressing toward the exit door. 8.12.2 Swapping. In some cases it is possible that two different agents who are aiming toward different exit doors come face to face with each other such that they will be opposite each other and there are no empty spaces available around them. In such cases they will change their positions as swapping in order to find a solution to continue their path to their respective exit door. 8.12.3 Trapping. If we randomly place obstacles, there may be some situations where agents become trapped among obstacles. In the real world, we can observe this situation when an explosion suddenly happens and some obstacles such as walls block some people behind them. In such cases, since there may not be a path to an exit door, people who are trapped among such obstacles may have to wait and remain in their places forever, adding to casualties. For a simplification of measurements, we assume that we do not have traps. After placing the crowd and starting to move them, we wait until all agents are evacuated from the environment. We gather two important values from each exit door after each cycle of experiment. The number of people who chose each exit door as their favorite one and also the time that it took for that amount of people to be evacuated through that exit door. We will classify each exit door having these two values. In other words, if an exit door could evacuate more people in a shorter time, it means that the door is more powerful and should be

retained for the next experiment cycle. To reach a value, after each cycle of experiment, we divide the number of people to the evacuation time for each exit door. We do an ascending sort of the result and then consider, between two exit doors, which has the smaller values and is the weaker exit door, which means evacuating fewer people in longer duration. These doors will be removed for the next cycle of experiment. In each cycle, the weakest exit door is removed in terms of having the smallest value. We continue the experiment until all but one exit door is removed from each valid region. To have a suitable width for the remaining exit door, for the final period of experiment we add a number to the width of the final remaining exit door in centimeters that compensates for the total number of people who could have evacuated through the removed exit doors on the previous experiments.

9. Experimental setup 1 In this section we report on three general sets of experiments. As the first set, we assumed having 40% of the available spaces to be occupied with people. Furthermore, there are no traps. The only obstacles are walls. The proportions of the populations of females and males remain to be randomly selected. Since we assumed our experiment space to be a nightclub, we considered having no children present inside the environment. We also assumed that 10% of the crowd will choose their favorite exit doors randomly. The number of people in this situation is 1437. We repeat this set five times and at the end of each cycle show them as one table of results. After each cycle of experiments, based on the results, we removed one of the weakest exit doors from each valid region. Table 1 shows the results for the first cycle of experiments. Table 2 shows the overall result based on the results of the first round of experiments. As shown, for the first period of experiments, the middle left-hand exit door received the worst rate of 3.214 and needs to be removed for the next cycle. The lower righthand exit door with the rate of 1.426 has the same

Table 1. The result for the first round of experiments. Exit Doors Left-hand side

1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People

Middle Middle Middle Middle Middle

2.455 2.628 3.512 4.642 2.833

88 94 84 81 90

Lower Lower Lower Lower Lower

1.555 1.456 1.538 1.93 1.532

146 147 143 115 139


40


Table 2. The overall results based on the Table 1 results. Exit Doors Left-hand side

Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Middle

3.214

87

Lower

1.426

138

Table 3. The result for the first round of experiments. Exit doors Left-hand side

1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People

Upper Upper Upper Upper Upper

0.723 0.744 0.767 0.735 0.702

423 434 455 434 436


0.866 0.883 0.907 1.011 0.943

298 309 301 273 279

Table 4. The overall results based on the Table 3 results. Exit doors Left-hand side

Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Upper

0.734

436

Upper

0.922

292

situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 112 centimeters. For this level of experiments we observed five swaps on average. Table 3 shows the results for the second cycle of experiments. Table 4 shows the overall results based on the results of the first round of experiments. As shown, for the first period of experiments, the upper left-hand exit door got the worst rate at 0.734 and should be removed for the next cycle. The upper right-hand exit door with the rate of 0.922 has the same situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 364 centimeters. For this level of experiments we observed a similar five swaps on average. For the second set, we assumed having 60% of the available spaces occupied by people. We also assumed that we do not have traps. The same as the previous set of experiments, the only obstacles are walls. The proportion of males and females is select randomly. We also assumed that 10% of the crowd will choose their favorite exit doors randomly. The number of people in this situation is 2875

people. We repeated this set five times and at the end of each cycle show them as one table of results. After each cycle of experiments, based on the results, we removed one of the weakest exit doors from each valid region. Table 5 shows the results for the first cycle of experiments. Table 6 shows the overall result based on the results of the first round of experiments. As shown, for the first period of experiments, the middle left-hand exit door got the worst rate at 3.288 and should be removed for the next cycle. The lower righthand exit door with the rate of 0.954 has the same situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 583 centimeters. For this level of experiments we observed 47 swaps on average. Table 7 shows the results for the second cycle of experiments. Table 8 shows the overall results based on the results of the first round of experiments. As shown, for the first period of experiments, the upper left-hand exit door got the worst rate of 0.719 and should be removed for the next cycle. The upper right-hand exit door with the rate of 0.713 has the same situation. If we



41


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


3.397 3.671 3.017 3.306 3.05

179 158 181 180 200


1.028 0.894 0.797 1.106 0.949

252 284 300 246 256


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Middle

3.288

898

Lower

0.954

268


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


0.72 0.732 0.723 0.697 0.724

874 865 819 842 855


0.695 0.7 0.717 0.71 0.743

600 587 597 599 619


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Upper

0.719

851

Upper

0.713

600

stopped the experiments at this level, the width value that should be added to all other exit doors would be 726 centimeters. For this level of experiments we observed 74 swaps between agents on average. For the third set, we assumed having 80% of the available spaces occupied by people. We assumed that we do not have traps. Walls are the only obstacles that are considered. The proportion of males and females will be selected randomly. We also assumed that 10% of the crowd will

choose their favorite exit doors randomly. The number of people in this situation is 4312. We repeated this set five times and at the end of each cycle show them as one table of results. After each cycle of experiments, based on the results, we will remove one of the weakest exit doors from each valid region. Table 9 shows the results for the first cycle of experiments. Table 10 shows the overall results based on the results of the first round of experiments.


42



1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


3.728 3.154 3.352 3.627 3.39

265 286 267 284 269


0.72 0.694 0.678 0.703 0.715

397 889 945 505 917


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Middle

3.450

274

Upper

0.702

730


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


0.73 0.736 0.733 0.74 0.726

1386 1328 1297 1298 1322


0.827 0.82 0.808 0.826 0.82

846 851 919 828 869


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Upper

0.733

1326

Lower

0.820

863

As shown, for the first period of experiments, the middle left-hand exit door got the worst rate of 3.450 and should be removed for the next cycle. The upper righthand exit door with the rate of 0.702 has the same situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 502 centimeters. For this level of experiments we observed 172 swaps among particles on the average. Table 11 shows the results for the second cycle of experiments.

Table 12 shows the overall result based on the results of the first round of experiments. As shown, for the first period of experiments, the upper left-hand exit door got the worst rate of 0.733 and should be removed for the next cycle. The lower right-hand exit door with the rate of 0.820 has the same situation. If we stopped the experiments at this level, the value that should be added to all other exit doors would be 1096 centimeters. For this level of experiments we observed 176



43

Figure 21. A view of the simulated environment with the screen on top and people scattered on rows.

Figure 22. Different zones, which are differently shaded.

swaps between people on the average. In the following section we discuss a second set of experiments for further corroboration and validation of our methodology.

10. Experimental setup 2 For our second set of experiments, we duplicated a local movie theater. This theater has two valid regions on the left-hand wall and the right-hand wall. We are allowed to place only one exit door on each valid region at conclusion. We start our experiments with having three exit doors at each valid region. At the end of each cycle of

experiment run, the weakest exit door at each valid region was removed. We continued the set of experiments until reaching one exit door on each valid region. We also assumed having three different kinds of objects: people, obstacles, and exit doors. The simulator consists of two general modules: a simulated environment site and results page. Figure 21 shows the simulated environment. The results panel consists of eight different panels: the left-hand panel, right-hand panel, doors status, buttons, proportions, variables, population, and swaps. The simulator concepts for these sets of experiments follow the ones that are indicated for the last experimental setup. After all initial variables in terms of crowd density, people proportions, and percentage of wrong decisions are determined, they will be placed randomly among obstacles inside available spaces. With the next step, each particle consists of people determining the closest exit door as their evacuation path. Each simulated agent shows its preferences for an exit door it chooses to by its color that matches the exit door color. Figure 22 shows the agents after they picked their favorite exit doors by their colors. As shown in Figure 22, there are six exit doors. There are distinct shades for each door and corresponding client agents. After deciding to evacuate through a door, the agent inherits the same exit door shade. There might be many agents who make wrong decisions about picking their exit doors. White shaded zones are samples of such agents. In this case, we assumed having 25% of available space occupied by agents and 10% of them having made a wrong door decision. As the first set, we assume having 75% of the available spaces occupied with people. Furthermore, there are no traps. The only obstacles are either walls or rows of chairs. The proportion of the populations of children, female and males will select randomly. We also assumed that 10% of the crowd will choose their favorite exit doors randomly. The number of people in this situation is 1031. We repeat this set five times and at the end of each cycle show them as one table of results. After each cycle of experiments, based on the results, we removed one of the weakest exit doors from each valid region. Table 13 shows the results for the first cycle of experiments.


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.686 1.426 1.486 1.22 1.295

140 148 142 150 146


1.333 1.522 1.418 1.503 1.355

141 136 158 147 152


44


Table 14. The overall results based on the Table 1 result. Exit doors Left-hand side

Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.423

145

Lower

1.426

147


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.64 1.658 1.608 1.605 1.423

200 196 209 200 201


1.536 1.512 1.456 1.525 1.796

220 217 226 217 196


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.587

201

Lower

1.565

215

Table 14 shows the overall result based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door received the worst rate of 1.423 and needs to be removed for the next cycle. The lower righthand exit door with the rate of 1.426 has the same situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 146 centimeters. For this level of experiments we observed 455 swapping actions on average. Table 15 shows the results for the second cycle of experiments. Table 16 shows the overall results based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.587 and should be removed for the next cycle. The lower right-hand exit door with the rate of 1.565 has the same situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 208 centimeters. For this level of experiments we observed 331 swapping actions on average.

For the second set, we assumed having 80% of the available spaces occupied by people. We also assumed that we do not have traps. The only obstacles are either walls or rows of chairs. The proportion of children, females, and males will be selected randomly. We also assumed that 10% of the crowd will choose their favorite exit doors randomly. The number of people in this situation is 1100. We repeated this set five times and at the end of each cycle show them as one table of results. After each cycle of experiments, based on the results, we removed one of the weakest exit doors from each valid region. Table 17 shows the results for the first cycle of experiments. Table 18 shows the overall result based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.492 and should be removed for the next cycle. The lower right-hand exit door with the rate of 1.427 has the same situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 156 centimeters. For this level of experiments we observed 517



45


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.391 1.434 1.456 1.51 1.671

169 152 160 157 143


1.487 1.435 1.404 1.414 1.349

150 154 151 152 166


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.492

156

Lower

1.427

155


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.568 1.659 1.513 1.631 1.661

220 217 226 217 218


1.612 1.606 1.618 1.648 1.66

219 221 225 213 215


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.606

220

Lower

1.629

219

swapping actions on average. Table 19 shows the results for the second cycle of experiments. Table 20 shows the overall results based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.606 and should be removed for the next cycle. The lower right-hand exit door with the rate of 1.629 has the same situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 220

centimeters. For this level of experiments we observed 382 swapping actions on average. For the third set, we assumed having 85% of the available spaces occupied by people. We assumed that we do not have traps. The only obstacles are either walls or rows of chairs. The proportion of children, females, and males will be selected randomly. We also assumed that 10% of the crowd will choose their favorite exit doors randomly. The number of people in this situation is 1168. We repeated this set five times and at the end of each cycle


46



1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.491 1.349 1.465 1.42 1.534

165 166 157 169 163


1.5 1.54 1.331 1.469 1.533

162 176 169 160 165


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.452

164

Lower

1.475

166


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.507 1.671 1.613 1.5 1.578

227 234 230 248 237


1.394 1.545 1.575 1.483 1.51

241 244 233 232 247


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.574

235

Lower

1.501

239

show them as one table of results. After each cycle of experiments, based on the results, we will remove one of the weakest exit doors from each valid region. Table 21 shows the results for the first cycle of experiments. Table 22 shows the overall results based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.452 and should be removed for the next cycle. The lower right-hand exit door with the rate of 1.475 has the same situation. If we

stopped the experiments at this level, the width value that should be added to all other exit doors would be 165 centimeters. For this level of experiments we observed 594 swapping actions on average. Table 23 shows the results for the second cycle of experiments. Table 24 shows the overall result based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.574 and should be removed for the next cycle. The lower right-hand exit



47


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.293 1.649 1.465 1.383 1.301

174 168 172 188 183


1.311 1.214 1.406 1.305 1.285

180 182 170 174 172


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.419

177

Lower

1.304

176


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.516 1.675 1.633 1.447 1.407

248 240 245 253 263


1.446 1.474 1.625 1.514 1.528

251 253 248 253 250

door with the rate of 1.501 has the same situation. If we stopped the experiments at this level, the value that should be added to all other exit doors would be 237 centimeters. For this level of experiments we observed 489 swapping actions on average. As the fourth set, we assumed having 90% of the available spaces occupied by people. We also assume that there are no traps. The only obstacles are either walls or rows of chairs. The proportion of children, females, and males will select randomly. We also assumed that 10% of the crowd will choose their favorite exit doors randomly. The number of people in this situation is 1237. We repeat this set five times and at the end of each cycle show them as one table of results. After each cycle of experiments, based on the results, we will remove one of the weakest exit doors from each valid region. Table 25 shows the results for the first cycle of experiments. Table 26 shows the overall results based on the results of the first round of experiments.

As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.419 and should be removed for the next cycle. The lower right-hand exit door with the rate of 1.304 has the same situation. If we stopped the experiments at this level, the value that should be added to all other exit doors would be 177 centimeters. For this level of experiments we observed 656 swapping actions on average. Table 27 shows the results for the second cycle of experiments. Table 28 shows the overall results based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.536 and should be removed for the next cycle. The lower right-hand exit door with the rate of 1.517 has the same situation. If we stopped the experiments at this level, the value that should be added to all other exit doors would be 251 centimeters. For this level of experiments we observed 505 swapping actions on average.


48



Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.536

250

Lower

1.517

251


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.314 1.282 1.458 1.592 1.271

185 195 190 184 199


1.572 1.665 1.452 1.643 1.497

187 173 186 182 183


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.383

191

Lower

1.566

182

As the fifth set, we assume having 95% of the available spaces occupied by people. We also assume that there are no traps. The only obstacles are either walls or rows of chairs. The proportion of children, females, and males will be selected randomly. We also assumed that 10% of the crowd will choose their favorite exit doors randomly. The number of people in this situation is 1306. We repeat this set five times and at the end of each cycle show them as one table of results. After each cycle of experiments, based on the results, we will remove one of the weakest exit doors from each valid region. Table 29 shows the results for the first cycle of experiments. Table 30 shows the overall results based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.383 and should be removed for the next cycle. The lower right-hand exit door with the rate of 1.566 has the same situation. If we stopped the experiments at this level, the value that should be added to all other exit doors would be 187 centimeters. For this level of experiments we observed 814 swapping actions on average. Table 31 shows the results for the second cycle of experiments.

Table 32 shows the overall based on the results of the first round of experiments. As shown, for the first period of experiments, the lower left-hand exit door got the worst rate of 1.507 and should be removed for the next cycle. The lower right-hand exit door with the rate of 1.538 has the same situation. If we stopped the experiments at this level, the width value that should be added to all other exit doors would be 265 centimeters. For this level of experiments we observed 515 swapping actions on average.

11. Related work Anyone living in a populated, gregarious world has experienced the effects of crowds. Crowds exert an invisible force on individuals. Directly, movements of an individual’s crowd neighbors will physically propel the individual in the direction of a crowd’s general moving trajectory. Indirectly, in order to maintain personal space, the individual will experience social forces to accommodate for the crowd movement.43 Derived from safety concerns in indoor spaces, there is a force that propels people toward exit openings. This has



49


1 2 3 4 5

Right-hand side

Location

Rate

People

Location

Rate

People


1.48 1.48 1.44 1.631 1.502

277 269 266 260 267


1.603 1.431 1.651 1.513 1.491

262 260 261 261 267


Overall

Right-hand side

Location

Rate

Width

Location

Rate

Width

Lower

1.507

268

Lower

1.538

262

best been modeled in terms of a game among members of a crowd.44 Game theory modeling and analysis, as well as an extensively validated fire evacuation simulator, are reported from a Finish research center.44 There have been attempts to learn human movement from animal behaviors. Argentine ants have been studied as test organisms to explore their natural evacuation processes in response to fire. It was observed that any movement in response to citronella does not necessarily follow a simple set of rules. As citronella is repellent to ants, they showed negative taxis, moving away from the stimulus toward the exit. This is similar to what one can expect when a crowd of people runs away from a source of danger (e.g., a fire) toward a safe place.45 This demonstrated how such empirical data from non-human organisms, such as ants, can overcome the shortage of human panic data for model calibration and validation, something that has intrigued researchers for decades. Experiments with ants were used to model the consideration of both attractive and repulsive forces under panic condition to maintain the coherence of collective dynamics. Ant models are in the class of microscopic models where individual behaviors are modeled. However, people are not like homogeneous, interchangeable, non-rational, non-cognitive entities. We must incorporate human factors into the microscopic models in Henein and White.46 Navigation fields were introduced in order to direct virtual crowds using goal-directed navigation functions. Macroscopic behavior is generated by microscopic modeling methods.47 A force-enabled version of the floor field pedestrian is presented by Henein and White46 where a building is treated as an information system through which people move. Using Henein and White’s model, communication

agents update and maintain multiple perspectives of their environment. Recently, there has been an increasing interest in pedestrian traffic.48 For instance, a method for determining density using Voronoi cells is found in Steffen and Seyfried.49 A survey of mathematical modeling techniques for traffic flow and crowd models are also available.50 Common methodological approaches for crowd evacuation are reviewed by Zheng and Cheng.51 Macroscopic models are computationally less expensive because they consider less detailed interactions between people and their environment. Instead, mathematical models are used to describe crowd movements as liquid flows.52–54

12. Conclusion This paper has explored the implementation and adaption of the optimized ICA to a sample indoor layout to demonstrate a solution for optimizing the best exit door locations. The results of our implemented system applied to prototypical scenarios have demonstrated that the location of each exit door in an indoor space can affect significantly the evacuation of a crowd in emergency situations. Future work will account for complex floor plans. We will also apply our assumptions about traps so we can add to the realism of evacuation chaos with unexpected clutter and debris. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.


50


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Author biographies Pejman Kamkarian received his BS degree in computer software engineering in 2004 from the University of UAE, Dubai, United Arab Emirates, and his MS degree in computer science from Southern Illinois University, Carbondale, in 2009. He is currently working toward his PhD in computer engineering at Southern Illinois University, Carbondale. He has been the Network Administrator and LAN systems specialist for the College of Education and Human Services at Southern Illinois University, Carbondale. Also, he served as Local Area Network Administrator and IT Specialist for Southern Illinois Airport and served as LAN Administrator and IT Specialist for the Neuroscience lab in the Life Science Department at Southern Illinois University, Carbondale. His research interests include artificial intelligence, humanoid, robot mind, operating systems, and network technologies, including design, security, and analysis. Henry Hexmoor received his MS degree from Georgia Tech, Atlanta, and his PhD degree in computer science from the State University of New York, Buffalo, in 1996. He is an IEEE senior member. He taught at the University of North Dakota before a stint at the University of Arkansas. Currently, he is an associate professor with the Computer Science Department, Southern Illinois University, Carbondale. He has published widely in artificial intelligence and multiagent systems. His research interests include multiagent systems, artificial intelligence, cognitive science, mobile robotics, and predictive models for transportation systems.


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