A Hybrid Multi-Objective Chicken Swarm Optimization and Teaching Learning Based Algorithm for Charging Station Placement Problem

A new hybrid multi-objective evolutionary algorithm is developed and deployed in the present work for the optimal allocation of Electric Vehicle (EV) charging stations. The charging stations must be positioned on the road in such a way that they are easily accessible to the EV drivers and the electric power grid is not overloaded. The optimization framework aims at simultaneously reducing the cost, guaranteeing sufﬁcient grid stability and feasible charging station accessibility. The grid stability is measured by a composite index consisting of Voltage stability, Reliability, and Power loss (VRP index). A Pareto dominance based hybrid Chicken Swarm Optimization and Teaching Learning Based Optimization (CSO TLBO) algorithm is utilized to obtain the Pareto optimal solution. It amalgamates swarm intelligence with teaching-learning process and inherits the strengths of CSO and TLBO. The two level algorithm has been validated on the multi-objective benchmark problems as well as EV charging station placement. The performance of the Pareto dominance based CSO TLBO is compared with that of other state-of-the-art algorithms. Furthermore, a fuzzy decision making is used to extract the best solution from the non dominated set of solutions. The combination of CSO and TLBO can yield promising results, which is found to be efﬁcient in dealing with the practical charging station placement problem


I. INTRODUCTION
Road transportation sector is one of the major emitters of greenhouse gases [1]. EVs have emerged as an environmentally friendly alternative to traditional Internal Combustion Engine (ICE) driven vehicles, because they have the potential to reduce greenhouse gas emissions. However, the large-scale deployment of EVs may be a major threat to electric power grid, due to increase and variance in power demand by the charging stations of EVs. Actually, the degradation of voltage The associate editor coordinating the review of this manuscript and approving it for publication was Hongwei Du. stability and reliability indices, reduced reserve margin, and increased power losses are the consequences of improper positioning of EV charging stations in the electric power distribution network [2]- [4].
In [5], a sketchy overview of the latest drift in charging infrastructure planning problem was given thereby elaborating modelling approaches, objective functions, and constraints of the placement problem. In [6], a comprehensive survey of the optimization and control aspects of EV fleet management was provided. In [7], an overview on the computational scheduling methods for integrating EVs with power grid is given. In [8], charging station placement problem was formulated under a single objective framework with cost as the objective function. The candidate sites for charging stations were identified based on service radius, environmental factors and the optimization problem was attacked by using Modified Primal-Dual-Interior Point Algorithm (MPDIPA). In [9], the placement problem was framed with the considering of the EV flow, voltage deviation, and power loss as objective functions.A Cross-Entropy (CE) method was used for obtaining the Pareto front, and Data Envelopment Analysis (DEA) was applied for the final decision-making. In [10], the problem was modelled with cost, annualized traffic flow, and energy losses as objective functions. A Multi-Objective Evolutionary Algorithm (MOEA) was utilized for obtaining the Pareto optima, and the final planning scheme was decided by fuzzy logic. In [11], cost was considered as the main objective function of the placement problem, and the placement problem was solved by using Binary Firefly Algorithm (BFA). In [12], the authors proposed a placement scheme for public charging stations with cost as the objective function. A Varonoi diagram based technique was employed to decide the service region, and Particle Swarm Optimization (PSO) algorithm was applied to cope with the non-linear optimization problem. In [13], cost and utilization rate of chargers were considered as objective functions in problem modelling. Moreover, a novel Strengthened Pareto Evolutionary Algorithm II (SPEA II) was used for obtaining the best locations for placing the charging stations. In [14], the authors modelled the placement problem under a multi-objective framework with cost, real power loss reduction index, reactive power loss reduction index, and voltage profile improvement index as the objective functions. A hybrid GA PSO algorithm was deployed to handle this problem. In [15], the authors presented an optimal placement scheme for charging stations considering stochastic charging. In [16], [17], the authors provided an optimal planning scheme for EV charging stations based on voltage sensitivity indices. In [18], the authors presented an optimal placement and charging scheme for EV charging stations under contingent conditions in smart distribution grid. In [19], the authors presented a scenario based planning model of charging station placement with the network reconfiguration being taken into account, and solved this problem using a coevolutionary approach. In [20], the authors proposed a multiobjective framework of charging station placement with the voltage deviation, power losses, and EV flow. The Multiobjective Grey Wolf Optimization (MOGWA) was further developed in their work. In [21], the authors investigated a robust chance constrained model for the similar charging station placement problem.
Literature [8]- [21] reveals that the charging station placement is a complex and demanding problem involving a number of objective functions and constraints. However, the reliability of the power grid network is neglected in most of the formulations of charging station placement. Exclusion of reliability indices while formulating the charging station placement problem is a major research gap. Hence, in this paper, we strategically address the charging station placement problem by giving the due consideration to the reliability indices simultaneously considering other planning objectives like cost, power loss, voltage deviation, and accessibility. Table 1 highlights the differences between the proposed formulation of charging station placement problem and the formulations of charging station placement problem present in the existing literature. From Table 1 it is clear that the proposed formulation of charging station problem is superior to the existing formulations as it has the capacity of addressing economic factors, security of the power grid as well as EV driver's convenience. The current study does not focus on the home charging of EVs, because the authors find public charging infrastructure vital for large penetration of EVs in metropolitan cities. Moreover, from [8]- [21], it is clear that researchers have applied a large variety of meta-heuristics and classical optimization algorithms for coping with the charging station placement problem. The existing methodologies in handling the placement problem are summarized and given in Table 2. Heuristics or meta-heuristics can give near-optimal solutions in lesser time as compared to analytical methods in handling complex non-linear problems like the charging station placement problem [5]. Hence, the need for developing efficient and fast meta-heuristics remains. CSO and TLBO are the two state-of-the-art nature-inspired algorithms successfully applied by researchers for complex engineering optimization problems. In [22], the authors have reviewed different variants, applications of CSO as well as efficacy of CSO in solving different real-world problems. For example, CSO is applied for solving economic load dispatch [23], fault diagnosis of pumping wells [24], ascent trajectory optimization [25], train energy saving [26], robot path planning [27] etc. Similarly, TLBO is successfully used to cope with parameter optimization of machining process [28], transmission expansion planning [29], economic load dispatch problem [30], optimization of heat exchangers [31], optimal configuration of microgrid [32], optimization of space trusses [33], groundwater prediction [34], energy demand estimation [35], parameter extraction of photovoltaic models [36], glazing system design [37], PID controller design [38], wind speed forecasting [39], energy performance assessment of buildings [40], etc. CSO is a popular evolutionary algorithm, in which the search space can be effectively explored. The features of CSO are its powerful utilization of population and efficient exploration of search space. However, in some cases, it is observed that CSO gets stuck in the local optima. Actually, TLBO may be combined with CSO to combat with this drawback. Therefore, the synergy of CSO and TLBO can enhance the overall search capability and avoid premature convergence.
The contribution of our work is threefold: 1. A new multi-objective formulation of charging station placement problem is proposed. The formulation strategically addresses the charging station placement problem considering cost, operating parameters of the power grid as well as EV user's convenience. 2. A novel Pareto dominance based CSO TLBO algorithm for the charging station placement problem is proposed. 3. A number of multi-objective benchmark problems and the problem to locate electric vehicle charging stations areattacked by CSO TLBO, and the performance of the proposed algorithm is statistically weighted against the up-to-date algorithms.

II. PROBLEM FORMULATION
The charging station placement is a multifaceted problem involving multiple decision variables, objective functions, and constraints. A schematic overview of the charging station placement problem is shown in Fig.1. In the present work, the charging station placement is formulated as a multi-variable, multi-objective, and non-linear optimization problem. One of the salient features of the charging station placement problem presented here is multi-objective formulation of the problem with cost, VRP index, and accessibility index as the objective functions. Thus, we consider economic objectives, driver's convenience as well as safety limits of the distribution network parameters in modelling the charging station placement problem. However, we do not convert reliability indices and power loss to their equivalent cost, since conversion of reliability indices and power loss to their equivalent cost is an approximate method. Large investments associated with the establishment of charging stations give motivation for careful optimization of the charging infrastructure with respect to the traffic and electric grid [41]. The three prime factors: cost, VRP index, and accessibility index must be considered in the formulation of the charging station placement problem. Therefore, the objective function is expressed as The explanation of these three objective functions is presented below.

1) COST
The optimization is concerned with the minimization of the overall cost. The installation cost is the monetary investment associated with the construction of charging stations. The land cost, building cost, labour cost, and charger cost are all included in the installation cost. The operation cost is the cost of the electric power for imparting the service of charging to the EVs.
The total cost function includes: As given in Eqs. (3) and (4),the installation and operating costs are only dependent on the number of fast and slow charging stations, and are independent of the location of charging stations, because of the assumption that the land, building, labour, charger, and electricity cost are the same for all the nodes of the entire network.

2) VRP INDEX
The VRP index is recently formulated by Deb et al. [2] with the voltage stability, reliability, and power loss considered together. Moreover, both the frequency based and duration based reliability indices are taken into account. Charging stations increase the load demand of the power grid, and possibly result in the deterioration of voltage profile, reliability, and increase in power loss. Hence, in our work, the impact of EV charging stations on the power grid is considered by regarding the minimization of the VRP index as one of the objective functions. The VRP index and terms associated are where V = VSI base VSI l ,

3) ACCESSIBILITY INDEX
The charging stations must be easily accessible to the EV drivers to reduce the driving range anxiety. The placement of charging stations needs to be optimized with the routes followed by the EVs and charging point demand. If the locations of the charging stations are too far away from the charging demand points, additional charge will be wasted to travel that distance, and in the worst condition, the battery may run short of charge. Thus, in our work, the accessibility index is considered as the third objective function: where d is the distance between the charging demand points and charging stations.
For a road network having q charging demand locations and m charging stations, the computation of the accessibility index is a tedious task. The distance matrix D and reduced distance matrix DD need to be first calculated. Distance matrix represents the distance between the charging demand locations and charging stations. The reduced distance matrix, DD, identifies the nearest charging stations for each of the charging demand locations, and gives the distance between the charging demand locations and its nearest charging station. D, DD, and d are: The optimization is carried out with a number of equality and inequality constraints given by Eqs. (17)- (21).
The constraints depicted by Eqs. (17) and (18) consider the maximum and minimum number of fast and slow charging stations placed at the candidate locations. Eqs. (19) and (20) are related to the safety limit of the active and reactive power, respectively. The amount of the generated power at all the buses must satisfy the load demand and losses. Thus, the power balance equations given in Eqs. (21) and (21) are considered as the equality constraints in this charging station placement problem.

III. OVERVIEW OF MULTI-OBJECTIVE OPTIMIZATION
The result of multi-objective optimization is usually a set of solutions providing the best trade-off amongst the objectives that are conflicting in nature. The multi-objective optimization problem yields As we know that finding the best compromise solution in presence of conflicting objectives is a complex task. The best compromise solution is found by evaluating the ranks assigned to the solutions based on the nondominance or Pareto optimality concept and the crowding distance value. In multi-objective optimization problems, a set of optimal solutions called non-dominated solution or Pareto optimal solution exist [42], [43]. The boundary defined by the Pareto optimal solutions is called Pareto front [42], [43].
A solution x 1 is said to dominate solution x 2 ,if the following two conditions are satisfied [44] • The solution x 1 is no worse than x 2 in all objectives, • The solution x 1 is strictly better than x 2 in at least one objective. There are numerous techniques for finding the Pareto optimal solution, e.g., Kung's algorithm [44] and Ding's algorithm [44]. In this paper, the method proposed by Mishra and Harit [44] is utilized to identify the Pareto optimal solution due to its simplicity, which can be elaborated by Algorithm 1. The Pareto optimal solution obtained by the aforementioned algorithm is assigned rank one, put in the first front, and removed from the set P. The algorithm for finding the Pareto optimal solution is similar. The second Pareto front is assigned rank two. The same procedure is repeated until set P becomes an empty set [42], [43]. For obtaining a well-spread Pareto front, the concept of crowding distance is introduced [42], [43]. The crowding distance of a solution is an estimation of the density of solutions neighboring that solution. Algorithm 2 follows the solution procedure according to [42].

IV. OPTIMIZATION ALGORITHMS
Heuristics or meta-heuristics can give near-optimal solutions in less time as compared to analytical methods for dealing with complex non-linear problems. Hence, Pareto dominance based multi-CSO TLBO is employed in this paper to handle the charging station placement problem. TLBO is free from any algorithm-specific control parameters, and has a fairly good convergence property. It is expected that when the grading mechanism of CSO is combined with TLBO, the rate of utilization of the population can improve, and a faster convergence towards the optimal solution is favoured. An overview of these algorithms is given in this section.

A. MULTI-OBJECTIVE CSO
CSO mimics the behaviour of the chicken swarm and the food searching procedure of the swarm [22], [45]. The group is divided into the dominant rooster, hens, and chicks on the VOLUME 8, 2020 Algorithm 1 Pseudo Code for Finding Pareto Optimal Solution Put Forwarded by Deb [42] Sort P in descending order based on f 1 basis of the rank of the chickens. Roosters have the highest rank, hens the intermediate, and chicks the lowest. The random assignment of the mother-child relationship in the swarm is also a salient feature of the algorithm. After every G steps, the hierarchal order and mother-child relationship is updated. The algorithm efficiently uses the biological behaviors of hens to follow their group mate rooster and chicks to follow their mother in the search of food. This algorithm also assumes that the chickens may try to steal the food found by others resulting in a competition for food in the group.
In the initialization phase, the general and algorithmspecific parameters of CSO are defined. In multi-objective CSO, the division of the population into rooster, hen, and chick is based on the rank instead of fitness value as in the single-objective CSO [45]. The rank of all the individuals of the population is obtained by the idea mentioned in Section 3, and a hierarchal order is established according to the rank of the individuals in the population. The mother hen selection is made randomly. The algorithm assumes that the number of chicks is smaller than that of hens, and hens are the largest in the group [22]. There aresome differences in the food searching process of roosters, hens, and chicks. The update or food searching process of roosters is: where randn (0,σ 2 ) represents a Gaussian distribution with the mean and standard deviation equal to 0 and σ 2 , respectively. The variable f is the normalized fitness value of the corresponding x, k is the randomly selected rooster's index. is a small constant used to avoid division by zero. f is calculated by the weighted sum method [46].
Hens follow the path of their group roosters in food searching. Additionally, chickens may steal food found by other chickens. Their update strategy is: where rand is a randomly generated number between in [0,1]. r1 ∈ [1, N ] is an index of the rooster, the i th hen's group mate. r2 ∈ [1, N ] is an index of the rooster or hen, a random number such that r1 = r2. The inherent tendency of chicks to follow their mother is expressed as: where x t m,j represents the position of the i th chick's mother. FL is a parameter signifying that the chick would follow its mother. FL is generally chosen between 0 and 2.
The pseudo code of multi-objective CSO is given in Algorithm 3.

B. MULTI-OBJECTIVE TLBO
TLBO is a population-based evolutionary algorithm inspired from the interactive process of teaching and learning [47], [48]. In TLBO, learners constitute the population. The teacher is an erudite scholar, and he transfers his knowledge to the learners. The performance of the learners is dependent of the knowledge and teaching ability of the teacher. The algorithm is divided into two parts: Teacher phase, where the students learn from the teacher and Learner phase, where the students learn from each other by mutual interaction [47], [48].
In multi-objective TLBO, the learner having the best ranking a randomly generated population is generally assigned the role of teacher. Each learner learns from the teacher as follows: The learner learns by mutual interaction among themselves. For each learner Z i , any learner Z j is arbitrarily chosen from the learner matrix. The objective function values are arbitrarily compared for the two selected learners. If the value of the objective function of Z i is lower than the objective function of Z j , the i th learner is modified: Otherwise, the learner is modified as follows: The pseudo code of multi-objective TLBO is given in Algorithm 4.

C. MULTI-OBJECTIVE CSO TLBO
A multi-objective version of the hybrid CSO-TLBO presented by Deb et al. [49] is developed in this paper. The mechanism of grading prevalent in CSO, when combined with TLBO, can improve the utilization rate of the population and lead to a faster convergence towards the optimal solution. The hybridization of CSO and TLBO is expected to reduce the probability of premature convergence of CSO for computationally expensive problems. In the hybridization scheme, TLBO is performed for all the generation, and CSO is invoked Selecting the best compromise solution from the set of Pareto optimal solution is always tricky and difficult. The final decision making is performed by the fuzzy evaluation system [50]- [52]. In the fuzzy evaluation framework, each objective function is represented by a scaled membership function in the range of 1-10 given by Eq. (35). The range of objective function associated with all the membership functions or scores can be found by the back calculation in Eq. (35).
In a word, the net score for all the Pareto optimal solutions are evaluated, and the Pareto optimal solution having the highest score is preferred.

VI. SOLUTION METHODOLOGY OF CHARGING STATION PLACEMENT PROBLEM
In this paper, multi-objective CSO TLBO is employed to handle the charging station placement problem elaborated in Section 2. The systematic step-by-step procedure is as follows [50]: Step 1: Initialization Step 1.1: Initialize algorithm settings. Set the road network, distribution network data, upper and lower limits of different constraints, and set the different control parameters of CSO TLBO, such as gen , PN, RN, CN, HN A randomly generated initial solution is feasible, if it satisfies all the constraints explained in Section 2.3.
Step 1.3: Evaluate the three objective functions cost, VRP index and accessibility index for the initial population. Compute the rank and crowding distance by the methodology elaborated in Section 3. The first Pareto front with rank one is designated as T k .
Step 2.1: Run TLBO, and update the solution based on rank and crowding distance. Step 2.2: If the elements B pop exceed n fastp , element is made equal to n fastp . If the elements of C pop exceed n slowp , element is made equal to n slowp .
Step 2.3: Check feasibility of the solution. If the solution is infeasible, repeat Steps 2.1 and 2.2 until a feasible solution is obtained.
Step 3: Check whether the iteration count t is divisible by INV. If yes, go to Step 3.1. Otherwise, go to Step 3.5.
Step 3.1: If t is divisible by INV, run CSO.
Step 3.2: Run CSO, and update the solution based on ranking and crowding distance.
Step 3.3: If the elements B pop exceed n fastp , element is made equal to n fastp . If the elements of C pop exceed n slowp , element is made equal to n slowp .
Step 3.4: Check feasibility of the solution. If the solution is infeasible, repeat Steps 3.2 and 3.3until a feasible solution is obtained.
Step 3.5: Update the iteration count.
Step 4: Check whether the maximum generation count is reached. If the maximum generation count is reached, obtain the Pareto front. Otherwise, repeat Step 2 to Step 4.
Step 5: Selection of the best compromise solution from the set of non dominated solution is made by using the fuzzy decision making explained in Section 5.

VII. PERFORMANCE OF PARETO DOMINANCE BASED CSO TLBO ON MULTI-OBJECTIVE BENCHMARK PROBLEMS
The proposed Pareto dominance based CSO TLBO algorithm was first tested on some basic multi-objective benchmark functions. The algorithm-specific parameters of CSO TLBO were tuned as in Table 3. Moreover, the performance of the proposed algorithm in attacking the benchmark problems was compared with NSGA II and other hybrid algorithms like multi-objective DE PSO, multi-objective cultural PSO, and its variants. The aforesaid algorithms were statistically compared by on the basis of the hypervolume, which is a metric proposed by Zitzler [53] used to analyze the distribution of Pareto optimal solutions. Hypervolume physically signifies the volume occupied by the non dominated solution set. It is concluded in [54] that maximizing hypervolume is equivalent to producing a well distributed Pareto front.

A. COMPARISON OF PARETO DOMINANCE BASED CSO TLBO WITH DE PSO AND NSGA II
The performance of Pareto dominance based CSO TLBO algorithm was compared with that of DE PSO and NSGA II on two objective ZDT [55] and three objective DTLZ [56] benchmark problems. The three algorithms were statistically compared by computing hypervolume for a total of 50 independent trials. The results of DE PSO and NSGA II were directly taken from [57]. For a fair comparison, the population size (PN) and generation (gen) of CSO TLBO were kept the same as in [57]. Each benchmark problem was examined by CSO TLBO with the values of PN and gen as 200 and 750, respectively. The test problems were compared based on the normalized hypevolume (Table 4). It was observed that CSO TLBO performed better than DE PSO and NSGA II on ZDT4, DTLZ1, and DTLZ6. The performance of CSO TLBO was equivalent to that of DE PSO on DTLZ3. For a further analysis, Friedman rank test was performed (see results in Fig.2). The CSO TLBO achieved the best rank in comparison to the other optimization algorithms.

B. COMPARISON OF PARETO DOMINANCE BASED CSO TLBO WITH CULTURAL PSO AND ITS VARIANTS
The performance of Pareto dominance based CSO TLBO algorithm was compared with that of cultural PSO and its variants on two objective ZDT [57] and three objective DTLZ [56] benchmark problems. The algorithms were statistically compared by computing the hypervolume for 30 independent trials. The results of PSO and its variants were   directly taken from [58]. For a fair comparison, the population size (PN) and generation (gen) of CSO TLBO were kept the same as in [58]. Each benchmark problem was attacked by CSO TLBO with the value of PN and number of function evaluation as 100 and 30,000, respectively. The optimization results were compared on the normalized hypervolume (Table 5). CSO TLBO performed better than cultural PSO and cultural QPSO on ZDT1, ZDT2, ZDT3, ZDT6, and DTLZ1. The ranks of the different algorithms obtained by Friedman test aregiven in Fig.3, in which the CSO TLBO obtained the best rank. VOLUME 8, 2020

C. COMPARISON OF PARETO DOMINANCE BASED CSO TLBO WITH CSO AND TLBO
The performance of Pareto dominance based CSO TLBO was compared with that of CSO as well as TLBO on two objective ZDT [55] and three objective DTLZ [56] benchmark problems. The algorithms were statistically compared by computing the hypervolume for 30 independent trials. Each benchmark problem was examined by CSO TLBO with the values of PN and gen as 200 and 750, respectively. The test problems were compared based on the normalized hypevolume (Table 6). From Table 5, it is observed that the proposed algorithm performed better than the standalone CSO and TLBO algorithm on all the benchmark functions. The ranks of the different algorithms obtained by Friedman test are given in Fig.5, in which the CSO TLBO yielded the best rank among all the methods involved.

VIII. PERFORMANCE OF PARETO DOMINANCE BASED CSO TLBO ON CEC 2009 BENCHMARK FUNCTIONS
The proposed Pareto dominance based CSO TLBO algorithm was further tested on CEC 2009 benchmark functions. The algorithm-specific parameters of CSO TLBO were tuned as in Table 3. Moreover, the performance of the proposed algorithm in attacking the benchmark problems was compared with that of NSGA II and MOEA/D. The aforesaid algorithms were statistically compared on the basis of the hypervolume. The performances of NSGA II and MOEA/D on CEC 2009 benchmark functions were taken from [49]. The general control parameters of CSO TLBO were set the same as [61]. Table 7 reports the performance comparison of the proposed algorithm with NSGA II and MOEA/D on CEC 2009 benchmark functions. It is observed that our method performed better than NSGA II and MOEA/D on all the benchmark functions except F8 and F9. In addition, the Friedman ranks of the three algorithms are shown in Fig. 5. It is observed that the Pareto dominance based CSO TLBO yielded the best rank.

IX. PERFORMANCE OF PARETO DOMINANCE BASED CSO TLBO ON CHARGING STATION PLACEMENT PROBLEM A. TEST SYSTEM AND INPUT PARAMETERS
The EV charging station placement problem was validated on the test network formed by superimposition of IEEE 33 bus distribution network and 25 node road network as shown FIGURE 6. Test network [38]. in Fig.6. The line, branch, and outage data of IEEE 33 bus test network were taken from [2]. The road network data was from [9]. The EVs were assumed to follow the two following routes:Route 1-  Table 8 presents the superimposed nodes with respect to distribution as well as road network and the points of charging demand. The points of charging demand were computed   based on the consideration that the driving range of EV was 150 km [52], [53], and it followed either Route 1 or Route 2. The values of the input parameters were selected as in Table 9. In the simulations, it was assumed that each fast charging station had 10 servers or charger units, and each slow charging station had 20 servers or charger units.. The algorithm-specific parameters of CSO TLBO were tuned as in Table 3.

B. OPTIMAL ALLOCATION OF CHARGING STATIONS
The optimization problem explained in Section 2 was explored using CSO TLBO. Table 10 Figure 7 elaborates the Pareto front obtained by CSO TLBO. Table 11 represents the values of the three objective functions for the four planning schemes mentioned in Table 10. In Plan 1, the optimized values of cost, VOLUME 8, 2020  VRP index, and accessibility index were 1.5389 × 10 7 $, 12.5010, and 0.0006, respectively. In Plan 2, the optimized values of cost, VRP index, and accessibility index were 1.4783 × 10 7 $, 14.0792, and 0.0013, respectively. The values of cost and accessibility index of plan 2 were better than that of Plan 1. However, the value of VRP index of Plan 1 was better than that of Plan 2. In Plan 3, the optimized values of cost, VRP index, and accessibility index were 2.1316 × 10 7 $, 13.7128, and 0.0014, respectively. The value of cost for Plan 3 was worse than that of Plan 1 and Plan 2. However, the value of accessibility index of Plan 3 was better than that of Plan 1and Plan 2. In Plan 4, the optimized values of cost, VRP index, and accessibility index were 2.1316 × 10 7 $, 13.7128, and 0.0014, respectively. The cost associated with Plan 4 was better than Plan 3 but much worse than Plan 1 and Plan 2. The value of VRP index for Plan 4 was better than Plan 2 and Plan 3 but worse than Plan 1. The value of accessibility index for Plan 4 was equal to Plan 2 and better than Plan 1 but worse than Plan 3. Figure8 illustrates the voltage profile of the buses for all the four plans in Table 10. The voltage profile of the buses after placement of charging stations (charging stations were placed at the locations obtained by pareto optimal solutions listed in Table 10 by using CSO TLBO) degraded as shown in Fig. 8. From Fig.8, it is clear that the voltage profile of Plan 1 is better than the other three plans.

C. FINAL DECISION MAKING
The four simulated plans obtained by CSO TLBO are shown in Table 10. The characteristics of those four plans are discussed in the previous sub-section. However, it is difficult to select the best plan among these four plans because of conflicting objective functions. In practice, some criteria cannot be measured by crisp values, due to the ambiguity arising from human qualitative judgement [61]. For the quantification of such cases, fuzzy reasoning can be used. In the present work, a fuzzy evaluation system was applied for the final decision making [55]. The cost, VRP index, and accessibility indices were chosen as the three aspects for final decision making. In the fuzzy decision making, low cost, low VRP index and high accessibility were preferred features and hence received a higher evaluation. Table 12 gives the scale of the three objective functions based on the aforementioned fuzzy criteria. The scores of each plan obtained by the fuzzy evaluation system are provided in Table 13. The radar charts of all the four plans are shown in Fig. 9. Table 14 reports the area occupied by the radar charts of the four plans shown in Fig. 9. The area occupied by the radar chart is computed by Heron's formula. The four plans had their respective   advantages and disadvantages. The area occupied by Plan 1 is the biggest as compared to the other three plans indicating that Plan 1 is the most advantageous plan.

D. COMPARISON OF THE PERFORMANCE OF CSO TLBO WITH OTHER STATE OF ART ALGORITHMS
For examining the proposed Pareto dominance based CSO TLBO algorithm, its performance was further compared with that of NSGA II algorithm. In order to compare the quality of the solutions of multi-objective CSO TLBO and NSGA II, a statistical analysis was made for 50 independent trials. These two algorithms were statistically compared by computing hypervolume, diversity index, and number of Pareto solutions of the results obtained by the aforesaid algorithms for 50 independent trials. Table 15 gives the results of statistical comparison of CSO TLBO with NSGA II algorithm, which clearly shows that the hypervolume of CSO TLBO was more than that of NSGA II. Thus, the spread and closeness VOLUME 8, 2020  of the Pareto front obtained by CSO TLBO were better than that of NSGA II. The diversity index is regarded as a measure of diversity existing between the non-dominated solutions obtained by the algorithms [54]. A large value of the diversity index indicates the algorithm yields Pareto optimal solutions that are diverse in nature. The best and the worst diversity index of CSO TLBO were more than that of NSGA II (Table 15). Thus, we can conclude that the solutions obtained by CSO TLBO are more diverse in nature. Furthermore, the convergence graph of CSO TLBO, CSO, TLBO, and NSGA II is shown in Fig. 10.
The number of Pareto solutions is another metric used to compare the performances of multi-objective evolutionary algorithms. The algorithm that yields more number of Pareto solutions is more preferable, as it gives the decision maker more alternatives [52]. The number of Pareto solutions obtained by CSO TLBO and NSGA II were the same (Table 15). Therefore, the both algorithms give the decision maker the equal number of alternative planning schemes. The time complexity analysis of the proposed algorithm was also performed. The time complexity or computational time of the proposed algorithm was also compared. Table 16 reports the average run time of CSO TLBO and NSGA II in handling the charging station placement problem. The average run time of CSO TLBO was more than NSGA II. In CSO TLBO, both CSO and TLBO were executed in some generations. As a consequence, the average run time of CSO TLBO was more than that of NSGA II.

X. CONCLUSION
The construction of charging station is indeed very important to promote EVs. The placement of charging stations must consider cost, distribution network characteristics, and accessibility of the charging stations simultaneously. In our paper, the charging station placement problem was represented in a multi-objective framework with cost, VRP index, and accessibility index as the objective functions. The scientific contribution of this work lies in not only proposing a multi-objective framework to solve the charging station placement problem but also developing a Pareto dominance based multi-objective CSO TLBO for the charging station placement problem and fuzzy selection of Pareto optimal solutions. Thus, we have explored an integrated planning scheme for charging stations by using multi-objective optimization, fuzzy decision making, and radar charting. The hybrid algorithm is found to be superior in handling the charging station placement problem as well as standard benchmark problems. Our future work aims at the performance comparison of this new algorithm in dealing with other optimal placement problems. Cost of electricity m

Abbreviations
Maximum number of locations in which charging station will be placed q Total number of charging demand points w 1 Weight assigned to V w 2 Weight assigned to R w 21 Weight assigned to SAIFI w 22 Weight assigned to SAIDI w 23 Weight assigned to CAIDI w 3 Weight XIAO-ZHI GAO received the D.Sc. (Tech.) degree from the Helsinki University of Technology (Aalto University), Finland, in 1999. In January 2004, he was a Docent (Adjunct Professor) with the Helsinki University of Technology. He is currently a Professor with the University of Eastern Finland, Finland. He has published more than 400 technical articles on refereed journals and international conferences. His current Google Scholar H-Index is 31. His research interests include nature-inspired computing methods with their applications in optimization, data mining, machine learning, control, signal processing, and industrial electronics.