An Evolutionary Goal-Programming Approach Towards ... - IEEE Xplore

An Evolutionary Goal-Programming Approach Towards Scenario Design for Air-Traffic Human-Performance Experiments Rubai Amin∗ , Jiangjun Tang∗ , Mohamed Ellejmi† , Stephen Kirby† and Hussein A. Abbass∗ ∗ School of Engineering and Information Technology University of New South Wales at Canberra, Canberra, Australia Email: [email protected],[email protected],[email protected] † EUROCONTROL Cooperative Network Division (CND) at Brtigny-sur-Orge, Paris, France Email: [email protected],[email protected]

Abstract—Air traffic controllers are responsible for maintaining a safe and efficient flow of air traffic in controlled airspace. Many aspects of air traffic control are impacted by the performance of air traffic controllers such as separation assurance tasks. In order to design more advanced air traffic management systems, there is a need for more experiments to be conducted which evaluate the impact of human performance on the system. The design of scenarios that satisfy/meet specific traffic characteristics needed by the analyst is a daunting task. For example, it is often required to design scenarios for a specific sector that have a specific number of conflicts to evaluate human task load. To schedule the aircraft within the time specified for the experiment, and given all the constraints imposed by the route structure and airspace design parameters for the sector in question, are far from trivial problems. In this paper, an evolutionary goal programming approach has been presented which generates a set of scenarios for use in these experiments. The evolutionary goal programming system aimed to generate scenarios meeting the criteria of a set number of conflicts in each of four conflict angle groups. Differential evolution was employed in addition to three modified methods for the optimization of the problem. It was found that the three modified methods outperformed the standard method by producing a greater number of scenarios meeting the set criteria.

I. I NTRODUCTION The International Civil Aviation Organization (ICAO) predict that scheduled passenger air traffic are likely to grow by 4.4% per year between 2002 and 2015 [1]. In order to accommodate this growth in aircraft movements, there is a growing effort to introduce new concepts, new air traffic management systems and/or adaptations of existing airspace designs and procedures [2], such as dynamic sectorization and user preferred trajectory. Air traffic controllers (ATC) are an integral element of the air traffic management system. In order to design these advanced air traffic control systems there is a need to understand the factors which effect an ATC’s mental workload and other cognitive processes [2], [3] and to develop systems with which to evaluate human performance. ATCs are responsible for maintaining a safe and efficient flow of air traffic in controlled airspace which often consists of a large number

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of aircraft travelling from different directions, with different speeds and altitudes; and heading to different destinations. An ATC has several roles which include ensuring separation between aircraft and avoiding many hazards; providing flight information services, such as weather and airport conditions; and managing congestion in and around airports and airspace [4]. At a given time, an ATC could be responsible for simultaneously managing multiple aircraft, and therefore the safety of hundreds of people. The complex processes of air traffic control rely significantly on and are limited by human performance [3]. Like many complex and dynamic systems, the air traffic system cannot be temporarily paused while the ATC takes a break. Studies focusing on human performance require the design and use of scenarios in order to evaluate the effects of different factors on the system. In the ATC context, these scenarios involve simulating air traffic in an airspace. For the purposes of these studies, there is a need for a system which can easily generate a set of scenarios meeting a certain criteria. For example, the analyst need to generate scenarios with a specific number of conflicts to evaluate human cognitive load. Controlling the number of conflicts in a scenario is a daunting design exercise and as the complexity of the sector increases, the complexity of the design increases exponentially. In this paper we present an approach which has been devised to generate a set of scenarios which can be used in human performance experiments. The number of conflicts within a sector in normal operations relies on the arrival time of a flight to the sector boundary. On the contrary to traditional flight scheduling [5], [6] which aims at eliminating conflicts, our objective here is equivalent to scheduling flights to generate a target number of conflicts. Goal programming is a common technique in scheduling and is particularly useful when it is required to simultaneously consider multiple criteria for stratifying a solution. Goal programming allows for the setting of target values for each criterion and then optimizing for the sum of the deviations of each criterion from the respective aspiration level. Goal

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programming has been applied to problems in a wide range of areas such as the selection of airports for an airline’s network [7], the scheduling of aircraft landing on a runway [8], the selection of suppliers based on multiple factors [9], such as price, production time and product quality; job shop scheduling [10] and the scheduling of shifts for ground staff at airports [11]. There are several methods available for optimizing problems using goal programming. One of these methods is the weighted sum goal programming method where the optimization is done by assigning weights to each goal and then minimizing the weighted sum of the deviations from targets [12]. Several alternative goal programming optimization methods include the MINMAX and Lexicographic methods [13]. In the MINMAX method, the maximum deviation from the target is minimized instead of minimizing the weighted sum of the deviations. This method also makes use of weight factors. The lexicographic method assigns priorities for different goals and goals with the highest priority are are considered first [13]. All three of these goal programming methods rely on the use of user defined factors which are subjective to the user [13]–[15]. For this reason it has been suggested that evolutionary algorithms are more flexible for the optimization phase of the problem [15]. Evolutionary algorithms are a desirable method of solving optimization problems as the algorithms simultaneously work with a set of possible optimal solutions in a single run instead of a series of separate runs as required by some other methods [16]. Using evolutionary algorithms for optimization also has the potential to produce multiple solutions in one run. Differential evolution (DE) [17] is an evolutionary algorithm that leverages direction information to guide the search [18]. DE compares the fitness of an offspring directly to the fitness of the corresponding parent which results in faster convergence speeds than other EAs [18]. In addition DE is also easy to use and requires fewer control parameters and can find near optimal solutions regardless of the initial parameter values [19]. DE has been applied to a range of topics in science, engineering and management, such as logistics [20], [21] and crew rostering for airlines [22]. In this paper we present an approach which has been devised to generate a set of scenarios for use in human factors experiments using evolutionary goal programming and in particular with the use of differential evolution. The aim is to generate a set of scenarios which consist of a set number of conflicts in each of four different conflict groups defined by the angle between the two aircraft concerned in the conflict. In the following section we present definition of the problem, followed by the methodology used to produce this system, a section detailing the setup used to test the system and in the final section we analyse the results from the system. II. P ROBLEM D EFINITION For the generation of scenarios using this evolutionary goal programming system we require an input of an airspace consisting of a set of routes, R = {ri }N i=1 , where ri = W1 , W2 , ..., Wj

ri is a unidirectional route consisting of j waypoints (W), each with x and y coordinates, which must be visited by every aircraft travelling on route ri in sequential order. Waypoint W1 is the activation point for the aircraft and Wj is the deactivation or final point. We also require an input of a set of aircraft A = {ai }N i=1 where ai = (r, T, S, δ) The input information for each aircraft includes its route number (r), activation time (T), speed (S), and navigational error (δ). The navigational error is a deviation of the aircraft from the great circle path between two waypoints. This deviation distance is a random number selected from a normal distribution with a mean of zero and a standard deviation of δ. Conflicts among aircraft are a necessary design-element when designing human performance experiments for ATC. In our study a conflict is defined as the distance between two aircraft being less than or equal to 5NM. The conflict can be grouped in one of four categories, as shown in Table I, based on the difference of the heading angles of the two aircraft concerned in the conflict. The conflict types require different actions to be taken by air traffic controllers, which can lead to wider and deeper exploration of human factors experiments. TABLE I C LASSIFICATION OF CONFLICTS BASED ON THE ANGLE OF CONFLICT Group 1 2 3 4

Description In-Tail Crossing Narrow Crossing Wide Head-on

Criteria θ ≤ 0◦ + tolerance 0◦ + tolerance < θ ≤ 90◦ + tolerance 90◦ + tolerance < θ ≤ 180◦ - tolerance 180◦ - tolerance < θ ≤ 180◦

The aim of this study is to schedule the aircraft in such a way that a certain number of conflicts occur and are divided evenly between the four conflict types. To determine if the number of conflicts in a group has met the target for that group we use Equation 1 where xn is the number of conflicts in group n and T is the target number of conflicts for each group. −1 xn − d+ =T i + di

(1)

To determine if all four groups consist of the target number of conflicts we use Equation 2 where f, the objective, is the sum of the deviations of the number of conflicts in each group from the target for that group. The target is for this objective to equal zero and the aircraft scheduling is optimized at this value. f=

N  i=1

− d+ i + di

(2)

In order to calculate the fitness value and to continue to optimize the fitness towards the target, we require a simulation system for the input route structure and aircraft; and an optimization system, both of which are further discussed in the following section.

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III. M ETHODOLOGY Our approach consisted of two components: simulation and optimisation. The simulation component was used to evaluate the flight plans while the optimisation component generated the flight plans. The simulation component returned a fitness value for each flight plan based on the desired scenario design criteria after simulating the flight plan. This fitness value was then used by the optimisation component to generate flight plans by optimising the plans in order to better meet the desired criteria. The two components will be furthered discussed in the following sections. A. Simulation

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A multi-agent system was developed to simulate an airspace based on an input flight plan. The multi-agent approach was used as it allows for the mapping of an environment to individual agents capable of autonomous action in the environment to meet design objectives [23]. The information extracted from the flight plan was used to construct a number of routes in the airspace. The agents in this system were individual aircraft and the flight plan included information about each of the aircraft’s route and speed. The agents were simulated to travel based on their selected routes and the movement of the aircraft was based on the equations of motion. In the real world, aircraft do not always travel in a perfect great circle route between two points due to factors such as error in the navigational system. In order to account for this error, several additional intermediate waypoints are added by the system to slightly deviate the aircraft from the straight line path between two points. These additional waypoints are placed at a point perpendicular to the original path between two consecutive waypoints for a route at 5 minute intervals. As the location of the deviation is dependent on time required for travel along the original path, the location varies with different aircraft speeds. The distance of the additional waypoint from the original path is a random distance selected using a normal distribution where the mean is zero and the standard deviation, δ, which is a fixed a number for each aircraft obtained from the flight plan. An example of the implementation of the deviation can be seen in Figure 1. This figure shows two waypoints (circles) which are 250km apart. If an aircraft is travelling at 800km/h between these waypoints then it will cover around 66km every 5 minutes and it can be seen from the figure that at every 66km along the great circle path between the two waypoint, the route deviates from the path. The deviation point is equally as likely to be on either side of the original path.

NP

NP

Fig. 1. Example of potential navigational error for an aircraft travelling at 800km/h between two waypoints with δ equal to 4km

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Each aircraft in the flight plan is simulated in one second time steps. In each time step the aircraft was moved towards the next waypoint in aircraft’s designated route, or if all the waypoints had been visited, the deactivation point. The direction of travel is determined using the heading angle to the the next point. The simulation continues until all of the aircraft have reached their deactivation point. At the end of the simulation the total number of conflicts between the aircraft are counted and the details of the conflicts are recorded in a file. B. Differential Evolution Differential evolution, in conjunction with the multi-agent simulation systems, was used to generate scenarios for a given criterion. Data contained within the chromosomes used for the DE process were used to generate flight plans. Each of the flights plans were simulated using the multi-agent simulation system and were then evaluated using the goal-programming technique to determine the fitness of each flight plan based on a given criteria. The aim of the DE was to minimise the fitness of the flight plans in order to generate a number of flight plans, and therefore a number of scenarios, meeting a certain criteria. 1) Chromosome Encoding: For solving problems with DE it is usual to represent each individual with just one chromosome which contains a chain of integer parameters each representing real world objects or systems, in this case each aircraft and/or route. The chromosome used in this system included chains of three parameters representing each aircraft, which can be seen in Figure 2. Each of the chains of parameters were grouped in such a way that aircraft assigned to the same route appear consecutively in the chromosome. The parameters for each aircraft include the aircraft’s speed, S, standard deviation of the aircraft’s deviation from the route, δ, and either the activation time for the route, A, or separation time from the previous aircraft on the route, T. A1,1

S1,1

δ1,1

First aircraft on the 1st route

T1,2

S1,2

δ1,2

Second aircraft on the 1st route

…

…

…

Ti,j

Si,j

δi,j

Last aircraft on the last route

Fig. 2. Chromosome representation for fixed route simulations where A is the activation time for the route, T is the gap between the aircraft and the previous aircraft in the route, S is the aircraft’s speed, δ is the aircraft’s maximum deviation from the route, i is the number of routes and j is the number of aircraft per route

The activation time for each route was assigned to the first aircraft (represented by the first group of three parameters from left to right) for each route. The activation time represents a time, in seconds, for when the first aircraft on a route will become active in the simulated airspace after the start of the simulation. The remaining aircraft were assigned a value for separation time which represents a time lag, in seconds, of the activation time for that aircraft relative to the previous aircraft in the list. These time lags represent the inter-activation time. Each of the parameters in the chromosome were initialized

2013 IEEE Symposium on Computational Intelligence in Vehicles and Transportation Systems (CIVTS)

with a random number within a predefined range. As there are a fixed number of aircraft assigned to each route, there was no need for the inclusion of additional parameters to signify the start of each route. In order to make use of the DE system, we are required to generate a population of individuals, or candidate solutions. Each of the individuals in this population are represented by the chromosomes discussed in this section. We will use the notation shown in Equation 3 to represent the chromosome in further DE operations. In this notation i is the individual number, j is the parameter number, G is the generation number and N is the total number of parameters. Each parameter is initialized with a random number within the range minj ≤ xj,i,1 ≤ maxj where minj and maxj are predefined ranges for each parameter type.

may be responsible for. A potential conflict occurs when two active aircraft are separated by a distance less than 5NM horizontally and 2000ft vertically. These separation distances are required for aircraft flying under the instrument flying rules for altitudes above 18,000 feet and 29,000 feet respectively [24]. When a conflict occurs between two aircraft the position of the two aircraft are recorded along with the angle between the two aircraft at the beginning of the conflict period. The angle between the two aircraft is determined using Equation 6 where α and β are the heading angles of the two aircraft. The resulting angle between the aircraft will always be less than or equal to 180◦ . The conflict is then classified based on the angle into one of four groups, as shown in Table I where θ is the angle from Equation 6 and the tolerance is set to 5◦ by default.

xi,G = [x1,i,G , x2,i,G , ..., xj,i,G ], j = 1, ..., N

angle = min ((|α − β|), (360 − |α − β|))

(3)

2) Mutation, Recombination and Selection: At each generation, for each individual in the population three different individuals, xi,r1 , xi,r2 , xi,r3 ; are randomly selected from the population and are treated as vectors. The weighted difference of two of the selected vectors is summed with the remaining vector, as shown in Equation 4, to produce a donor vector. In this equation vi,G+1 is the donor vector corresponding to the individual xi,G and F is the scaling factor, a number between 0 and 2. vi,G+1 = xi,r1 + F (xi,r2 − xi,r3 )

(4)

The system includes two different options for the implementation of the scaling factor. The first option is to use a fixed value for the scaling factor for all individuals for all generations while the second option uses a different scaling factor for each generation which is randomly generated at the start of each generation. Equation 4 is the most basic version of the DE mutation strategies and is also the most commonly used strategy. Once the donor vector, vi,G+1 , has been generated a trial vector, ui,G+1 , is generated by combining elements from both the donor vector and the target vector, xi,G , based on Equation 5. Element j in the trial vector is equal to the element j of the donor vector if a random number between 0 and 1 is less than or equal to the crossover rate, CR. If the random number is greater than CR then element j in the trial vector is equal to element j in the target vector.  rand([0,1]) ≤ CR vj,i,G+1 uj,i,G+1 = (5) xj,i,G rand([0,1]) > CR Next the fitness of the trial vector is determined by simulating the vector. The trial vector is used to generate a flight plan and used as an input to the simulation program, as discussed above. Checks for potential conflicts are conducted at the end of each time step in the simulation between every active aircraft inside a selected sector of the airspace. This sector represents a region of airspace which an air traffic controller

(6)

The fitness of the trial vector is determined by Equation 2 − where d+ i and di are the difference of the number of conflicts whose angles are categorized into group i and the target number of conflicts for that group. The target number of conflicts for all four groups were set to the same value, 5, in an attempt to generate solutions where the number of conflicts in each group were evenly distributed. If the fitness of the trial vector is less than the fitness of the target vector then the trial vector is selected to appear in the next generation, otherwise the target vector is selected. 3) Diversity: The system provides an option of an additional measure if the fitness of both the trial vector and the target vector are equal. This measure is referred to as the diversity which aims to prevent the potential population of the next generation from becoming too similar. If this option is enabled, then whenever there is a pair of trail vectors and target vectors with the same fitness they are recorded. Once all trial vectors have been generated for each of the individuals in a population and either each of the trial vectors have been selected for the next generation, the corresponding target vectors have been selected for the next generation or both vectors have been determined to have equal fitness, the calculation of the diversity begins for each of the pairs of trial and target vectors with equal fitness. To calculate the diversity of a vector, the vector is subtracted from an individual in the already selected population for the next generation, the values are normalized based on the data type represented by the parameter and then the individual values are summed together. Equation 7 shows the equation for the calculation of diversity for two individuals. In this equation the x1 , k represents parameter k of the vector which is being tested, x2 , k represents parameter k of a vector in the already selected population for the following generation and is the number of parameters. The two parameters are then normalised with the maximum and minimum possible values for the corresponding parameter type. The sum of differences continues for all of the individuals in the selected population and all other pairs of trial and target vectors whose finesses were also equal. The

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smallest summed value is chosen and this value becomes the diversity of this vector. If the diversity of the trial vector is greater than the diversity of the corresponding target vector, then the trial vector is selected to be represented in the next generation, otherwise the target vector is selected.

D=(

n  k=1

x1,k − minx1,k x2,k − minx2,k − )2 (7) maxx1,k − minx1,k maxx2,k − minx2,k

The mutation, recombination and selection cycle continues until a target number of generations is reached. The chromosomes for each of the individuals in the last generation were recorded and then converted to flight plans representing a scenario. IV. E XPERIMENT D ESIGN

TABLE II O UTLINE OF WAYPOINTS AND ELEVATIONS FOR ROUTES Route 1 2 3 4 5 6

Waypoints 7 → 13 → 11 → 4 2 → 9 → 10 → 12 3 → 11 → 12 1 → 10 → 11 → 5 6 → 12 → 13 → 8 → 1 6 → 12 → 9 → 8 → 1

Elevation (ft) 30,000 30,000 30,000 30,000 29,000 29,000

flight level and also maintained the same speed throughout the entire simulation. From Figure 3 we can see that there is significantly higher chance of conflicts occurring in groups 2 and 3 shown in Table I when two route cross each other. More conflicts may occur in the other two groups as several portions of some of the routes come into close proximity without crossing, for example the segment between waypoints 12 and 8 for routes 5 and 6 or around waypoint 9 for routes 2 and 6. A total of four different experiments were conducted by varying one or both of two different components. The two components were the population diversity check and the variable mutation factor. An outline of the experiments conducted can be seen in Table III. TABLE III O UTLINE OF EXPERIMENTS CONDUCTED Experiment 1 2 3 4

Fig. 3. The route structure used in all experiments. Circles represent each waypoint and box signifies the sector of interest

Before any experiments could take place, a route structure was first defined consisting of 6 routes connected by the waypoints as shown in Figure 3. The sector is based on a realistic sector design. This figure shows each waypoint (circles) in the airspace and also the sector of interest (the box). Each route consists of a start point, several waypoints and an end point. Some of the waypoints were assigned to multiple routes and each of the points have an x and y coordinate while the z coordinate is determine by the flight level of the aircraft. The routes were designed for travel on one of two different flight levels, 2 routes at 29,000ft and 4 routes on 30,000ft. The combination of waypoints for each route can be seen in Table II. The use of two flights levels also follows a common ATC method of flight level allocations for flights travelling in opposite directions. The sequence of waypoints visited is fixed for each route and the position of each waypoint is also fixed for all simulations. All aircraft remained on the same

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Route Fixed Fixed Fixed Fixed

Diversity No Yes No Yes

Mutation Factor Fixed Fixed Variable Variable

Code SNN SYN SNY SYY

An option was also available to execute the additional check for diversity when the fitness of two individuals were equal. Another option was also available to select which implementation of the mutation factor was used. If the fixed mutation factor was selected, then a value of 0.3 for the mutation factor, F, was used for all runs, generations and individuals. If the variable mutation factor option was selected then a random mutation factor was selected at the start of each generation. This random number was between 0.1 and 0.5 and selected from a normal distribution with a mean of 0.3 and standard deviation of 0.1. A. Parameters Every experiment consisted of twenty runs with a population size of 100 individuals with 60 aircraft each (10 per route) and the run was conducted for 200 generations. Each run for an experiment used a different seed for the random number generator. A crossover rate of 0.3 was used for all runs. The chromosomes in DE process were initialized with random numbers within the ranges shown in Table IV. V. R ESULTS A NALYSIS Each of the scenarios generated in each of the twenty runs for the four experiments were analyzed. A plot of the best fitness from all individuals for each generation for each run in

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TABLE IV M INIMUM AND M AXIMUM VALUES FOR EACH PARAMETER IN THE Parameter Activation Time (sec) Separation Time (sec) Speed (m/s) Deviation (m)



Maximum 1200 600 250 10000

an experiment can be seen in Figure 4. If the best fitness for a particular run at a generation is zero, then there is at least one individual (ie. one scenario generated) in the population for that generation which meets the target criterion of having the total number of conflicts evenly distributed among the four groups show in Table I. From Figure 4 we see that both experiments with additional diversity checks had a greater number of runs which had at least one individual with a fitness value of zero. The total number of scenarios generated from each experiment which meet the target criteria can be seen in Table V. From this table we can see that experiments with additional diversity checks produced the greatest number of suitable scenarios which is consistent with results shown in Figure 4. Table V shows that on average experiments SYY and SNY produced 4 suitable scenario for every 5 runs, but if we apply a tolerance of 1 conflict (that is, a fitness value of 1 as

TABLE V T OTAL NUMBER OF SUITABLE SCENARIOS GENERATED BY EACH EXPERIMENT FOR 20 RUNS Experiment SNN SYN SNY SYY

Suitable Scenarios 12 16 14 16

± 1 fitness 102 115 119 111

calculated using Equation 2), we are able to obtain in excess of 100 scenarios from the twenty runs for experiment SYY. The distribution of the fitness values from all of the scenarios produced in experiment SYY can be seen in Figure 5 and the total number of scenarios generated within this tolerance for each experiment can be seen in Table V. The fitness values in Figure 5 have been modified slightly for this figure such that the original fitness value is displayed as a negative value if the scenario produced less than 20 conflicts and as a positive value if the scenario produced 20 of more conflicts. The absolute value of the fitness values are still the same as those calculated using Equation 2. A fitness value of 1 or -1 in Figure 5 for a scenario means that are three the conflict angle groups which meet the target while the remaining group has one more or one less conflict that the target, respectively. A fitness value of zero represents scenarios which meet the target number of conflicts in each of the four conflict angle groups. Similar plots

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for other experiments show the same general trend. The large number of scenarios which are being generated with a fitness of 1 or -1, as shown in Figure 5, suggests that the fixed nature of the route structure and the configuration of the routes and waypoints is the cause of so many scenarios not being able to meet the target criteria. This is clear when we see Table VII which shows the distribution of the conflicts in each group from every scenario generated in experiment SYY. It is clear from this table that there is a larger number of conflicts in group 2 compared to the remaining groups. In Table VII we can see also see the number intersection points between routes which are categorised into each of the four groups. We see that there are more intersection points categorised into group 2 than all other groups combined and this the main cause for so many conflicts occurring in this group.  

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Fig. 5. Distribution of individual’s fitness for experiment SYY for 20 runs with 100 individuals each TABLE VII D ISTRIBUTION OF CONFLICT ANGLES FOR ALL SCENARIOS GENERATED IN EXPERIMENT SYY FOR 20 RUNS WITH 100 INDIVIDUALS EACH AND THE NUMBER OF CROSSINGS BETWEEN ROUTES WHICH FALL INTO EACH OF THE FOUR GROUPS

Group In-Tail Crossing Narrow Crossing Wide Head-On

Total Number of Conflicts 8524 13108 8349 9483

Crossings 2 8 4 1

All of the experiments undertaken achieved the goal of producing a set of scenarios consisting of five conflicts in each of the four conflict angle groups, but some produced more conflicts than others. From Table V we see that experiments SYN and SNY produced a greater number of suitable scenarios than experiment SNN. This shows that enabling the options of diversity checks and variable scaling factor individually led to better results than when neither of these options were enabled in experiment SNN. Enabling the diversity checks resulted in better results as this method produced a more

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diverse population of individuals which were available for selection in the next generation. The variable scaling factor allowed for a wider set of potential search moves and therefore improved the chance of obtaining new high quality solutions. Table V also shows that simultaneously enabling both of these options resulted in a similar number of suitable scenarios being generated as the experiment with just the diversity checks enabled. This suggests that for this particular system that the effect of the diversity checks is stronger than that of the variable scaling factor. To verify that the generated scenarios were different we have chosen three scenarios generated from the same run for one experiment which met the target criteria and presented the details of the conflicts in these scenarios in Table VI. The conflicts shown in this table were sorted by the conflict angle and also shows the time of the start of the conflict in seconds after the start of the simulation and the route that the two concerned aircraft were travelling on. The route pairings shown in the table further confirms that the conflicts produced were limited by the route structure. Although all three scenarios contained a large proportion of conflicts between the same route parings, we can see that the angle of conflicts and the time at which these conflicts occur are different and therefore provide a set of different scenarios while still maintaining five conflicts in each of the four conflict angle groups.

In this paper we presented an evolutionary goal programming approach to generating scenarios for use in human performance experiments in the air traffic control domain. Three modified differential evolution methods were used in addition to the standard differential evolution method. The modified methods produced a greater number of scenarios meeting the target of five conflicts in each of the four conflict angle groups. The route structure constrained the number of conflicts that were generated, which is the typical problem that faces an analyst when designing such scenarios. Our future work will investigate further experiments which incorporate different fleet mix and an allowance for aircraft to perform more manoeuvres. R EFERENCES [1] ICAO, “Outlook for Air Transport to the Year 2015,” International Civil Aviation Organisation, Montreal, Canada, Tech. Rep. Cir 304 AT/127, 2004. [2] S. Loft, P. Sanderson, A. Neal, and M. Mooij, “Modeling and predicting mental workload in en route air traffic control: Critical review and broader implications,” Human Factors: The Journal of the Human Factors and Ergonomics Society, vol. 49, no. 3, pp. 376–399, 2007. [3] S. Inoue, K. Furuta, K. Nakata, T. Kanno, H. Aoyama, and M. Brown, “Cognitive process modelling of controllers in en route air traffic control,” Ergonomics, vol. 55, no. 4, pp. 450–464, 2012. [4] P. Belobaba, A. Odoni, and C. Barnhart, The Global Airline Industry, ser. Aerospace Series. Wiley, 2009. [Online]. Available: http://books.google.com.au/books?id=BRtDl0CJpQIC [5] E. K. Burke, P. D. Causmaecker, G. D. Maere, J. Mulder, M. Paelinck, and G. V. Berghe, “A multi-objective approach for robust airline scheduling,” Computers & Operations Research, vol. 37, no. 5, pp. 822 – 832, 2010, disruption Management. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0305054809000896

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TABLE VI C OMPARISON OF CONFLICT ANGLES , THE START TIME OF THE FIRST CONFLICT AND ROUTES OF THE AIRCRAFT CONCERNED FOR THREE SCENARIOS GENERATED FROM ONE RUN

Angle group

In-Tail

Crossing Narrow

Crossing Wide

Head-On

Scenario 1 0.00 0.01 1.13 2.23 4.75 6.83 19.80 68.90 78.79 82.43 107.63 113.17 122.28 136.52 142.41 175.38 175.38 175.40 175.40 177.28

Angle Scenario 2 0.01 1.30 3.13 3.15 3.47 5.97 6.83 23.56 38.82 43.08 107.72 115.20 119.11 170.11 172.48 175.35 175.39 175.40 175.44 176.64

Scenario 3 0.01 0.01 0.01 1.39 1.85 13.40 25.03 38.87 41.23 53.96 90.68 96.44 107.88 139.51 141.63 175.29 175.45 176.19 178.21 178.33

Conflict Start Time (sec) Scenario 1 Scenario 2 Scenario 3 8505 9587 7806 10189 6237 8604 7076 6319 11085 7294 5849 5877 6357 6863 9365 5726 8162 7785 10012 5968 9056 4433 9484 5598 9425 4918 8930 9425 5680 8397 2508 3949 1948 9057 9383 4055 8586 9375 4603 5564 6176 3193 5180 6246 3209 5812 6031 6411 5851 6179 5828 6030 6396 6249 6081 6583 6331 8877 6631 6426

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Scenario 1 5-6 5-6 5-6 5-6 5-6 5-6 5-6 1-3 4-6 4-6 1-2 4-5 4-5 3-5 1-2 2-5 2-5 2-5 2-5 5-6

Route Pair Scenario 2 5-6 5-6 5-6 5-6 5-6 5-6 2-6 5-6 2-3 2-6 1-2 4-5 4-5 2-6 2-6 2-6 2-5 2-5 2-5 2-5

Scenario 3 5-6 5-6 5-6 5-6 5-6 5-6 5-6 2-3 4-6 4-6 1-3 1-3 1-2 1-2 1-2 2-5 2-5 2-5 2-5 2-5

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