Group Elevator Control Optimization using Artificial

Group Elevator Control Optimization using Artificial Atom Algorithm Ayse ERDOGAN YILDIRIM

Ali KARCI

Computer Engineering Department University of Firat Elazig, Turkey [email protected]

Computer Engineering Department University of Inonu Malatya, Turkey [email protected]

Abstract— With the applications of artificial intelligence, it is possible to produce accurate and effective solutions for many problems encountered in daily life. In this study, Artificial Atom Algorithm, which is a topical algorithm, is used for optimum routing in group elevator control. The Artificial Atom Algorithm is a meta-heuristic algorithm that was improved by inspired the compounding process of atoms. With the application, it is aimed that is responded to hall calls in the most effective way by working 7 elevators in 16-storey building. The system which is designed for this purpose, offers optimum control for elevators. The total elapsed time to answer the hall calls has been minimized with the study. Index Terms—Elevator control optimization, Artificial atom algorithm, Meta-heuristic algorithm, Artificial intelligence applications

I. INTRODUCTION The elevator is a type of vertical transportation that is very convenient for people to carry cargo and passengers, especially in high-rise and crowded buildings. However, over time, it has become important that the elevators respond to the hall calls and carry out the transportation as soon as possible. According to the size of the buildings, the number of elevators also varies. For this reason, it is critical to provide group elevator control for buildings where multiple elevators work in. It is possible to provide group elevator control in the most convenient way, especially in places with intensity and urgency such as hospital, by means of a suitable control algorithm [1]. Artificial intelligence optimization algorithms are effective methods that used to optimally solve many problems in daily life. It is also expected to give effective results for group elevator control problems. In the literature, different artificial intelligence optimization algorithms are used to solve group elevator optimization problems. For example, fuzzy logics, genetic algorithms, DNA computing, particle swarm optimization, adaptive artificial immune systems, ant colony optimization, reinforcement learning [2-11]. In this paper, the Artificial Atom Algorithm-A3, improved recently and giving successful results in the optimization problems, has been used to solve the group elevator control optimization problem [12-16]. In this study, A3 was applied to group elevator control optimization and its performance was compared with adaptive artificial immune systems [9]. We implemented A3 using

MATLAB 2013a on an Intel Core-i3 3.3 GHz PC to the group elevator control optimization problem of a 16-storey building which had 7 elevators. We aimed to provide optimum result for this group elevator control optimization problem. This paper is organized as follow. Section 2 briefly describes group elevator control optimization. Section 3 describes a new nature-inspired meta-heuristic algorithm Artificial Atom Algorithm (A3). Section 4 explains the method which is used in the solution of group elevator control optimization with A3. Section 5 illustrates the experimental results and compares with the adaptive artificial immune system and finally Section 6 concludes this paper. II. GROUP ELEVATOR CONTROL OPTIMIZATION Elevators are the systems that perform transportation in the vertical direction. They are used in the most building for different purposes such as cargo and passenger transport. Nowadays, it becomes important that the service quality of elevator. The physical conditions of the elevator affect the quality of this service. For example, the conditions such as the load-carrying capacity according to the size of the building, the inter-floor transition speed, the opening/closing speed of the door determine the service quality of the elevator. Passenger elevators are usually hydraulic or electrical in the 8-storey or less buildings. Hydraulic elevators speed up to 1 m/sec. Electrical elevators also speed up to 2.5 m/sec. Elevators are electrical and gearless until the 10-storey buildings. Those elevators also speed up to 2.5 m/sec. In the higher building from 10-storey, the elevators speed up between 2.5 m/sec and 10 m/sec. [1, 17, 18]. The physical characteristics of the elevator get to the forefront in buildings with a single elevator. In addition, the call aggregation strategies are important in the single elevated systems of low rise buildings. For this, four basic methods are used. These are simple aggregation, upward call aggregation, downward call aggregation, double direction call aggregation. In these methods, the call answering strategy is determined according to the direction in which traffic is intense [19]. Many elevators serve in the buildings of high-rise like skyscrapers, in the crowded places like shopping malls and in the places with urgency like hospitals at the same time. In crowded and high-rise buildings where there is more than one elevator, in addition to the physical conditions of the elevators,

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it is also important that the elevators work together in coordination. That is, in the group elevator control, it gains significance to share the calls that elevators will answer to. In this decision mechanism, the use of a control method provides to increase the service speed of the elevators without improving the physical conditions [17]. Various control algorithms have been developed to work those elevators together in the most efficient way. The many artificial intelligence optimization methods as fuzzy logics, genetic algorithms, DNA computing, particle swarm optimization, adaptive artificial immune systems, ant colony algorithm, reinforcement learning are also used in group elevator control optimization problems [2-11]. By applying artificial intelligence approaches to elevator traffic control, effective call answering ratios have increased considerably [19].

III. ARTIFICIAL ATOM ALGORITHM (A3) A3 has emerged as a new meta-heuristic approach as a result of the designing of covalent bond process and ionic bond process in chemistry as algorithmic operators. The most important feature of A3 is the calculation of the effect of each parameter value on the objective function. After the effects of parameter values on the objective function have been determined, it is easily decided which parameter values are modified in the solution set. Thus, A3 offers fast and effective solutions for optimization problems. A3 has three basic concepts. These are electron, atom and atom set. The electron is the parameter value of having effect on the solution at atom set which initially generated randomly. Electrons form atom that leads to meaningful solution as a vector. The number of atoms is determined according to the size of the problem and atoms form atom set as a matrix. Figure 1 shows an atom set, covalent region and ionic region.

Fig. 1 Representation of atom set, covalent region (CR) and ionic region (IR)

If it is assumed that there are 𝑛 electrons in each atom in a randomly determined atom set and β indicates covalent rate, α also indicates ionic rate, there are β𝑛 electrons in covalent region (CR) which is the area of application of the covalent bond operator, there are αn electrons in ionic region (IR) which is the area of application of the ionic bond operator, and α+β=1. A3 uses two basic operators. These are ionic bond operator and covalent bond operator. Ionic bond is the process of randomly assigning new electrons instead of electrons whose effect value is low in the atoms ranked according to electron effects. Covalent bond is the process of comparing the effect values of the electrons in order in two selected atoms and copying the electron which has larger effect value, instead of the other one [12, 15, 16]. A. Covalent Bond In chemistry, covalent bond is common usage of electrons to form compound. In A3, covalent bond is sharing better electron values among two atoms. Assume that 𝐴𝑗 and 𝐴𝑟 are two atoms

in atom set. There are 𝑛 electrons in each atom. 𝐴𝑗 (𝑘) is the 𝑘 𝑡ℎ electron of 𝐴𝑗 and 𝐴𝑟 (𝑘) is the 𝑘 𝑡ℎ electron of 𝐴𝑟 . If the effect value of 𝐴𝑗 (𝑘) (𝐸[𝐴𝑗 (𝑘)]) is better than effect value of 𝐴𝑟 (𝑘) (𝐸[𝐴𝑟 (𝑘)]), 𝐴𝑗 (𝑘) is copied to 𝐴𝑟 (𝑘), otherwise 𝐴𝑟 (𝑘) is copied to 𝐴𝑗 (𝑘). 𝑘1,2, … , β𝑛 // 𝑘 ≤ β𝑛 if 𝐸[𝐴𝑗 (𝑘)] is better than 𝐸[𝐴𝑟 (𝑘)] Copy value of 𝐴𝑗 (𝑘) to 𝐴𝑟 (𝑘) else Copy value of 𝐴𝑟 (𝑘) to 𝐴𝑗 (𝑘) Figure 2 illustrates the operation of covalent bond. Implementation of covalent bond operator is too easy for nonpermutational problems [16].

Fig. 2 Covalent bond operator

B. Ionic Bond In chemistry, ionic bond is the exchange of electrons to form compound. In A3, ionic bond is the removal of worse electrons from atom and instead of addition of new electrons randomly. 𝑘 ← β𝑛 + 1, β𝑛 + 2, … , 𝑛 //  is covalent rate,(1 − )𝑛 = 𝛼𝑛 𝐴𝑟 [𝑘] ← 𝐿𝑘 +  ∗ (𝑈𝑘 − 𝐿𝑘 ) //𝐿𝑘 is lower bound for 𝑘 𝑡ℎ attribute //𝑈𝑘 is upper bound for 𝑘 𝑡ℎ attribute where  is a random number in interval (0,1). The ionic bond operator is applied to the ionic region of atoms. After the applied of ionic bond operator, the effect value of each electrons are computed [16]. C. Algorithmic Steps of A3 A3 which is a computational intelligence algorithm is developed by inspired basically chemical processes such as covalent bond and ionic bond. It starts with creating random atom set. And it continues with computing of electron effects and objective function for each atom. Then, the atom set is sorted according to the objective function values of atoms. The following steps repeat the number of iterations or until stopping criterion met. 1) Covalent bond operator is applied to covalent region. 2) Ionic bond operator is applied to ionic region. 3) The effect values of electrons in ionic region are computed. 4) The value of objective function for each atom is computed. 5) The atom set is sorted according to the objective function values of atoms. The ionic rate is 0.4; covalent rate is 0.6 for benchmark problems [12]. The ionic and covalent rates are more appropriate to be 0.5 for travelling salesman problems [16]. The algorithmic steps of A3 are shown in the flowchart in Fig. 3 [16].

Fig. 3 Flowchart of A3

IV. APPLICATION OF GROUP ELEVATOR CONTROL WITH A3 In the application of group elevator control with A3, elevator and buildings features were considered fixed in the group elevator control optimization problem, since they would not affect the success of the optimization algorithm. The number of floors and the number of elevators in the building, the average transition time between floors and the average waiting time for opening and closing the elevator door, which are physical characteristics of the building and the elevators, are given in Table I [9]. TABLE I. ELEVATOR AND BUILDING FEATURES Feature

Value

Number of floors

16

Number of elevators

7

Average door opening/closing time (sec)

4

Average floor transition time (sec)

3

There are two kinds of elevator calls. These are hall calls and cabin calls. In this application, hall calls are taken into account. The floors where elevator cabins are located at the beginning of application and hall calls which are made by passengers are given in Fig. 4 [9].

Fig. 4 First position of cabins of elevators and hall calls

For the optimization algorithm, the electron effects and objective function are calculated with following formulas. Electron Effect: 𝐸[𝐴(𝑘)] = [| 𝑐𝑝 (i) - 𝑐𝑡 (i) |] * 𝑡𝑇 * 𝛼1 + 𝑡𝐷 * 𝛼2

𝑘 = {1, 2 … 𝑛} 𝑖 = {1, 2 … 𝑚} 𝑛 𝑚 𝑐𝑝 𝑐𝑡 𝑡𝑇 𝒕𝑫

: Number of hall calls : Number of elevators : Position of the cabin : Target floor of the cabin : Average of cabin’s floor transition time : Average of cabin’s door opening/closing time

TABLE II. THE PARAMETER SETTINGS OF A3 Parameter

10

Number of atoms

100

Covalent rate (β)

0.5

Ionic rate (α)

0.5

Iteration times

1000

In Table II, it is shown the parameter settings of A3 for group elevator control optimization. The number of electrons was determined as much as the number of hall calls. The atom set was created randomly and atoms had indicated elevators that would respond to the call in turn. As a result of optimization of the atom set with A3, it was tried to obtain the most suitable elevator list to answer the call. In the application of the optimization algorithm, the position of elevator cabin had updated when the elevator reached the floor of hall call. Thus, the objective function was computed correctly. Unlike the standard A3, after applying the covalent bond operator, it was checked whether the value of the objective function improved. When the result was worse, change did not apply. For the group elevator control optimization with A3, the following algorithmic steps were used. 1- Create the random atom set. (Electrons are show elevator numbers and can repeat in atom) 2- Calculate electron effects for each electron and objective functions for each atom. 3- Repeat the following steps as much as the number of iteration. a) Apply the ionic bond operator. b) Calculate electron effects for each electron and objective functions for each atom. c) Apply the covalent bond operator. d) Sort the atom set by the value of the objective function. V. EXPERIMENTAL RESULTS 3

(2)

Value

Number of electrons

(1)

Objective Function: min ∑𝑚 𝑖=1([| 𝑐𝑝 (i) − 𝑐𝑡 (i) |] ∗ 𝑡𝑇 ∗ 𝛼1 + 𝑡𝐷 ∗ 𝛼2 )

𝜶𝟏 : Weight coefficient (0.8) 𝜶𝟐 : Weight coefficient (0.2)

A was applied to the group elevator control optimization problem of a 16-storey building which had 7 elevators. It was used MATLAB 2013a on an Intel Core-i3 3.3 GHz PC for the group elevator control optimization with A3. Then, the success of this algorithm was compared with adaptive artificial immune systems. For the group elevator control optimization problem, the experimental results of obtained by the proposed method are shown in Fig. 5 and Fig. 6.

In Table III, the following path of elevator without optimization, the following path of elevator with the optimization of the adaptive artificial immune system and the following path of elevator with the optimization of A3 was compared [9]. TABLE IV. THE COMPARISON OF THE WAITING TIME OF PASSENGERS FOR ELEVATOR SERVICE

The Waiting Time (sec)

Fig. 5 The optimization of atom set with A3 for the group elevator control problem

Without optimization

Adaptive Artificial Immune System

Artificial Atom Algorithm (A3)

326.4

246.4

22.4

In the group elevator control without optimization, the average waiting time of passengers for elevator service was 326.4 seconds. In application of the group elevator control optimization using the adaptive artificial immune system, the average waiting time of passengers for elevator service was 246.4 seconds. Whereas, in application of the group elevator control optimization using A3, the average waiting time of passengers for elevator service was 22.4 seconds. It was observed that the result of the application of performed with A3 was rather better than the compared methods (Table IV) [9]. The average computational time of the application of the group elevator control optimization with A3 was 0.96 sec. when the algorithm ran 20 times. VI. CONCLUSIONS

Fig. 6 The average waiting time of passengers for atom set

As shown in the graphs of Figure 5 and 6, in the shortest time, the best scheduling that elevators could respond to hall calls, had been reached. TABLE III. THE COMPARISON OF PATHS

Elevator

Path without optimization

Adaptive Artificial Immune System’s Path

1

Floor 3

Floors 3-5

Floor 1

2

Floor 6

Floor 6

Floors 5-6

3

Floor 9

Floor 9

Floors 8-9

4

Floors 8-13-14-16

Floors 13-14-16

Floor 11

5

Floor 5

Floor 1

Floors 13-14

6

-

-

Floor 3

7

Floors 1-11

Floors 8-11

Floor 16

Artificial Atom Algorithm (A3)’s Path

The elevator is an important technological machine that facilitates the human life using to carry cargo and passenger in daily life. In particular, in recent years, it has become indispensable for busy person’s life. In this busy life, as much as possible shortening the waiting time to benefit from the elevator service has also gained importance. For the buildings that have more than one elevator depending on their size and crowd, the control of elevator from a center can reduce the waiting times of passengers for elevator. Of course, it will be an advantage, if this control is done with an optimization algorithm. A3 is a new nature-inspired optimization algorithm based on process of compound formation of atoms. It uses two operators called as ionic bond and covalent bond. It takes into account the effect of parameter values on the solution unlike the other heuristic methods. In this paper, we carried out the group elevator control with a new meta-heuristic method, A3. This control had previously made by an adaptive artificial immune system. The performance of A3 and the adaptive artificial immune system was compared for the group elevator control optimization of a 16-storey building which had 7 elevators [9]. Consequently, it was observed that the A3 achieved the optimum result for the group elevator control optimization problem. And when it was compared with adaptive artificial immune systems, it seems to be quite successful in terms of waiting times of passengers to benefit from elevator service [9]. The computational time performance of the algorithm for this problem is at a reasonable level.

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