DEVELOPMENT AND COMPARISON OF GENETIC ALGORITHMS FOR VEHICLE ROUTING PROBLEM WITH SIMULTANEOUS AND PICKUPS IN A SUPPLY CHAIN NETWORK

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 12, December 2018, pp , Article ID: IJMET_09_12_0499 Available online at aeme.com/ijmet/issues.asp?jtype=ijmet&vtype= =9&IType=12 ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed DEVELOPMENT AND COMPARISON OF GENETIC ALGORITHMS FOR VEHICLE ROUTING PROBLEM WITH SIMULTANEOUS DELIVERIES AND PICKUPS IN A SUPPLY CHAIN NETWORK Varun Kumar S. G. School of Management, Manipal Academy of Higher Education, Manipal, Karnataka, India R. Panneerselvam Department of Management Studies, School of Management, Pondicherry University, Pondicherry, India ABSTRACT The increased focus on environmental awareness and protection compelled many organizations across the world to adopt reverse logistics as their key functional business area. Vehicle routing problem with simultaneous deliveries and pickups (VRPSDP) is one of the major issues under reverse logistics and in this paper, an attempt is made to solve the same. Since this problem belongs to NP-hard class, an increase in number of customer nodes will increase the computational complexity of the problem. Due to the robustness of genetic algorithm in solving complex problem, Genetic Algorithms (GAs) with four different designs are proposed to solve VRPSDP. Experimental results are tested statistically using ANOVA with three factors, viz., Problem Size, Algorithm and Probability. Based on the significance using ANOVA with respect to the factor Algorithm, Duncan s multiple range test is carried out to draw inferences on proposed algorithms. Key words: Reverse Logistics, VRPSDP, Genetic Algorithms, Crossover,. Cite this Article: Varun Kumar S. G and R. Panneerselvam, Development and Comparison of Genetic Algorithms For Vehicle Routing Problem with Simultaneous Deliveries and Pickups In A Supply Chain Network, International Journal of Mechanical Engineering and Technology, 9(12), 2018, pp et/issues.asp?jtype=ijmet&vtype=9&itype e= editor@iaeme.com

2 Varun Kumar S. G and R. Panneerselvam 1. INTRODUCTION Supply chain and Logistics Management evolved as a key functional area in most of the organizations around the world and many entities are focusing on improvising the performance wherever possible. Legislative regulations and environmental protection acts made companies to change their way of operations for past few years, which lead to a creation of new field called Reverse Logistics. According to Reverse Logistics Association (RLA), "Reverse Logistics" refers to all activities associated with a product/service after the point of sale. The ultimate goal of the reverse logistics is to optimize or make more efficient aftermarket activity, thus saving money and environmental resources. The reverse logistics and its sub-processes could be well understood through Figure 1, where materials/products have to go through variety of processes. Figure 1.Reverse logistics processes Reverse logistics has different types of problems in it such as facility location problem, logistics network problem, vehicle routing problem and other general category of problems as given in Figure 2[21]. In this article one of the reverse logistics problems, Vehicle Routing Problem is considered. The vehicle routing problem has a set of variants and vehicle routing problem with simultaneous delivery and pickups is the one which synchronizes with the reverse logistics to a greater extent. In this paper, the Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP) is considered for study. A typical Vehicle Routing Problem (VRP) is concerned with delivering goods to a set of customers with known demands through vehicle routes that begin and finish at the depot with the minimum cost. The VRP has several sets of problems such as Capacitated VRP, VRP with backhauls, VRP time windows, VRPSDP, etc. The Vehicle Routing Problem with Simultaneous delivery and Pickups (VRPSDP) is a restricted VRP, where the objective of the problem is to satisfy both delivery demand and pickup demand simultaneously such that the total travel distance by a set of vehicles is minimized. The real world applications of VRPSDP include distribution of bottled drinks, chemicals, LPG cylinders, laundry services, etc. Figure 2. Types of reverse logistics problem editor@iaeme.com

3 Development and Comparison of Genetic Algorithms For Vehicle Routing Problem with Simultaneous Deliveries and Pickups In A Supply Chain Network 2. LITERATURE REVIEW In this section, a brief discussion is carried out on literature concerning VRPSDP for recent years in order to know the types of the solution methods used to solve VRPSDP. There are varieties of approaches for the defined problem which are presented here. Min (1989) is the first author to identify and solve VRPSDP by considering a practical problem faced by a public library with two vehicles, which serve 22 customers. The author addressed a real situation of a public library distribution system in Franklin County, Ohio and a three-phase sequential procedure was used as a solution method. Dethloff (2001) emphasized the need of VRPSDP in situations under reverse logistics, viz. re-usable packaging, recycled or remanufactured goods. The author proposed an algorithm with four different insertion criterions to solve the problem and obtained promising results. The summary of literature related to VRPSDP is mentioned in Table 1. Though sufficient works have been carried out, the experimental investigation for comparing the results of the algorithms with that of existing algorithms is not sound. One has to use ANOVA based on complete factorial experiment, which will help the researchers to split the effect of different factors, which have influence on the measure of performance. Then finally, testing the effect of the factor namely Algorithm, which includes the proposed algorithm and existing algorithms as its treatments or a set of proposed algorithms will give a realistic inference about the significance of the difference between the performances of the algorithms. Such comparison of algorithms should be followed in future researches by the investigators to strengthen their claim instead of using simple comparison of means of the performances of the algorithms. Table 1 Summary of Literature on VRPSDP Year Authors Problem Solution Method 1989 Min MVRPSDP Three phase sequential procedure 2001 Dethloff VRPSDP Construction Algorithm based on cheapest insertion 2005 Nagy and Salhi S&MD VRPPD Insertion based heuristics 2006 Montané and Galvão VRPSDP Tabu Search 2009 Ai and Kachitvichyanukul VRPSPD Particle swarm optimization 2009 Gajpal and Abad VRPSDP Ant colony system 2010 Çatay VRPSDP A new saving-based ant algorithm 2012 Tasan and Gen VRPSPD Genetic Algorithm 2012 Wang and Chen VRPSDPTW Genetic Algorithm 2013 Rieck and Zimmermann VRPSDP MILP 2014 Wassan and Nagy VRPDP ILP, Meta-heuristics 2014 Aguiar et al. VRPSDP Particle swarm optimization 2015 Cetin and Gencer VRPSPDHTW Mathematical model and heuristic algorithm 2015 Li et al. VRPSDP Meta-heuristic 2015 Johnson et al. VRPSDP Ant colony system 2016 Chen VRPSDP Adaptive hybrid GA 2016 Wang et al. VRPSDPTW Multi objective local search, Multi-objective memetic algorithm 2016 Sayyah et al. VRPSPD Effective ant colony optimization 2016 Berhan VRPSDP Clark-Wright saving algorithm Each and every meta-heuristic has a set of parameters/schemes, whose values/patterns will have influence on the measure of performance of an algorithm for a given problem. For example, in simulated annealing algorithm, the value of temperature is the most critical value, which should be decided based on detailed experimentation before finalizing the algorithm. Further, the kind of perturbation schemes used in this algorithm also affects the results. In genetic algorithm, one should use proper crossover method as well as mutation probability to editor@iaeme.com

4 Varun Kumar S. G and R. Panneerselvam have better solution accuracy. Similarly, each and every method has certain critical parameters/ patterns, which must be suitably selected for superior performance of the respective algorithm. There is lot of work on vehicle routing problem with simultaneous delivery and pickups (VRPSDP) in recent literature. This proves the fact that reverses logistics activities are in rising trend. Most of the authors have utilized algorithmic approach for this problem, which includes ACO, PSO, Tabu search and genetic algorithms. There is comparatively less work done in this area using genetic algorithms also in terms of varying operators of genetic algorithms. Therefore, in this study, it is proposed to utilize genetic algorithms as a solution approach for VRPSDP by varying crossover operators and mutation rates. 3. GENETIC ALGORITHMS The vehicle routing problem and its variants belong to a family of NP-hard problems. Hence, solving such problems will take enormous amount of computational time using exact methods. Due to this complex nature of the problem, solutions using heuristics will be helpful in order to address larger solution space in less computational time. Therefore, genetic algorithm is selected to solve this problem. Genetic Algorithm is one of the efficient meta-heuristics, which belongs to a family of heuristics which is capable of solving a large set of combinatorial problems. It is based on the process of natural selection and evolution. Due to its robustness in providing larger solution space, it is used widely as a powerful optimization method. Selection, Crossover and are the main components in implementing Genetic Algorithms STAGES OF GENETIC ALGORITHMS Genetic Algorithm implements the idea of natural selection and reproduction of evolution. The different stages of genetic algorithm are depicted in the Figure 3. Generate initial set of parents: The first step is to generate initial set of chromosomes called as parents. These individual chromosomes could be coded as binary or as integer values based on the type of problem. Since VRPSDP deals with different set of nodes, an integer representation is used in this study. Evaluation: Evaluation is the process of evaluating the fitness function of each chromosome. Here the fitness function is total distance travelled by a set of vehicles. Selection: It is the first step in the reproduction and there are different methods, viz. roulette selection, tournament selection, rank selection and elite selection to select the chromosomes. The rank selection method is chosen in this study as a selection method. Figure3.Stages of genetic algorithm editor@iaeme.com

5 Development and Comparison of Genetic Algorithms For Vehicle Routing Problem with Simultaneous Deliveries and Pickups In A Supply Chain Network Crossover: Once the selection of chromosomes is done, crossover operation is carried out in order to generate next generation offspring. There are various crossover operators used to generate offspring and in this study one-point crossover and sinusoidal motion crossover operators are used. : The purpose of using mutation operator is to avoid the convergence of solution to local optima and to achieve global optima. In this study, four different mutation probabilities are used in order to improve the fitness function values of the next generation offspring. Termination: It is the maximum number of generations to be carried out to achieve optimal fitness value of a specific problem. Elitism: It helps to select the best fitness value from every generation and listed in an array in either ascending or descending order based on the nature of the problem. Two crossover operators in the genetic algorithms used in this study are One Point Crossover and Sinusoidal Motion Crossover (Developed by authors) [23]. 4. DEVELOPMENT OF FOUR VARIANTS FOR GENETIC ALGORITHMS TO SOLVE VRPSDP Vehicle routing problem with simultaneous deliveries and pickups belongs to a class of NPhard type and therefore, a sophisticated solution method is desired to obtain results in reasonable computational time. To solve complex problem such as VRPSDP, there are few algorithms available and genetic algorithms are most appropriate in terms of providing robust solution in realistic time. Therefore, an attempt has made in this chapter to develop four variants of genetic algorithm in order to find solution for VRPSDP. The solution space to search for the best solution can be redefined by varying the parameters and, selection and crossover method of the genetic algorithm, which are termed as variants of genetic algorithms. There are several parameters in the genetic algorithm such as selection method, crossover operator, and mutation operator. Here, an effort has been made to create new variants by changing selection methods and crossover operators which are then tested at several mutation probabilities. Combination of two selection methods with the two crossover operators are used to develop four variants of genetic algorithms, which are as listed below. Rank selection method in continuous manner (M 1 ) Rank selection method with cascading effect (M 2 ) One-point Crossover (O 1 ) Sinusoidal motion crossover, which is developed in this research (C 1 ) A rank selection method lists the parent chromosomes according to their fitness value, which in turn provides best chromosomes that are to be selected at any given point of time. Rank selection method in continuous manner (M 1 ) and Rank selection method with cascading effect (M 2 ) are the two different selection order used for crossover operation. One-point crossover is the simplest and most commonly used crossover operator and sinusoidal motion crossover is the main contribution to this research. The combinations of these two selection methods with two crossover operators provide four variants of genetic algorithms as listed below. M 1 O 1 This variant of GA uses rank selection of chromosomes in continuous manner and utilizes one-point crossover method to generate offspring. M 1 C 1 - This variant of GA uses rank selection of chromosomes in continuous manner and utilizes sinusoidal motion crossover to create offspring editor@iaeme.com

6 Varun Kumar S. G and R. Panneerselvam M 2 O 1 - This variant of GA uses rank selection of chromosomes in cascading manner and utilizes one-point crossover to generate offspring. M 2 C 1 - This variant of GA uses rank selection of chromosomes in cascading manner and utilizes sinusoidal motion crossover to create offspring. 5. RESEARCH METHODS In the general vehicle routing problem, the complexity of the problem increases with an increase in the number of nodes and hence it belongs to NP-hard category. Since, the VRPSDP is a conditioned VRP with more constraints; it also falls under NP-hard category. As discussed in the earlier section, a more sophisticated method is needed to solve such problem. Algorithmic Research method has been used in this study to solve the VRPSDP due to the nature and complexity of the problem. There are many algorithms available to solve problems under NP hard category. Genetic Algorithm is a prominent and widely used algorithm for such category and hence it is considered to solve the VRPSDP problem. A complete factorial experiment with three factors, viz. Problem Size, Algorithm and probability, is carried out to examine the results of the problems solved using the genetic algorithms 6. COMPARISON OF GENETIC ALGORITHM METHODS Results obtained using four variants are compared with each other to verify whether there is any significance difference among these methods. For this purpose, three factorial ANOVA design is utilized and tested using SPSS software. Factorial design has three factors viz., GA Methods, Problem Instance Sizes and the Probabilities, where each factor has four levels. GA method has M 1 O 1,M 1 C 1,M 2 O 1 and M 2 C 1 as four levels, Problem instance sizes has four levels, viz. 10, 25, 50 and 100 as nodes and Probability has 0.0, 0.1, 0.2 and 0.3 as four levels. The number of replications used here is 3. The results of the factorial design used here with all these settings are shown in Table 4. The proposed genetic algorithms of this research have certain assumptions and limitations which are as listed below. a) The locations of the customer nodes are very well known with accuracy. b) Delivery demand and pickup demand quantities across all the nodes are well known in advance. c) Planning of routes and scheduling of vehicles are done prior to departure. d) The product/goods transported are homogeneous in nature. e) There is only one depot with certain number of vehicles. f) The capacity of each vehicle in the depot is assumed as 80% of its full capacity based on a sensitivity analysis in the range from 60% of full capacity to 90% of full capacity in steps of 5% of full capacity. The null hypotheses of the experiment are listed below. There are no significant differences among the treatments of the factor, Algorithm in terms of average distance travelled. There are no significant differences among the treatments of the factor, Problem Size in terms of average distance travelled. There are no significant differences among the treatment combinations of the factor, Algorithm and the factor, Problem Size in terms of average distance travelled editor@iaeme.com

7 Development and Comparison of Genetic Algorithms For Vehicle Routing Problem with Simultaneous Deliveries and Pickups In A Supply Chain Network There are no significant differences among the treatments of the factor, Probability in terms of average distance travelled. There are no significant differences among the treatment combinations of the factors, Algorithm and Probability in terms of average distance travelled. There are no significant differences among the treatment combinations of the factors, Problem Size and Probability in terms of average distance travelled. There are no significant differences among the treatment combinations of the factors, Algorithm, Problem Size and Probability in terms of average distance travelled. Level of significance used is 5% DESIGN OF COMPLETE FACTORIAL EXPERIMENT AND DATA COLLECTION THROUGH EXECUTION OF GENETIC ALGORITHMS In this section, the comparison of four variants of genetic algorithms, viz. M 1 O 1, M 1 C 1, M 2 O 1 and M 2 C 1 using a complete factorial experiment with three factors, viz. Algorithm (A), Problem Size(B) and Probability (C) has been carried out. The factor, Algorithm has four levels, which are M 1 O 1, M 1 C 1, M 2 O 1 and M 2 C 1. The factor Problem Size has four levels, which are 10, 25, 50 and 100. The factor, Probability has four levels, which are 0, 0.1, 0.2 and 0.3. The number of replications under each experimental combination of the three factors is 3. Therefore, for this experiment, the total number of observations is192. The ANOVA model of this complete factorial experiment is given below. Y ijkl = µ + A i + B j + AB ij + C k + AC ik + BC jk + ABC ijk + e ijkl where, µ is the overall mean Y ijkl is the l th replication in terms of total distance travelled under the i th level of factor A, j th level of factor B and the k th level of factor C. AB ij B AC ik BC jk A i B j is the effect on the total distance travelled of the i th level of the factor A is the effect on the total distance travelled of the j th level of the factor B is the effect on the total distance travelled of i th level of the factor A and the j th level of factor C k is the effect on the total distance travelled of k th level of the factor C is the effect on the total distance travelled of i th level of the factor A and k th level of factor C is the effect on the total distance travelled of j th level of the factor B and k th level of factor C ABC ijk is the effect on the total distance travelled of i th level of the factor A, j th level of factor B and k th level of factor C e ijkl is the error associated with the total distance travelled with respect to l th replication under i th level of factor A, j th level of factor B and k th level of factor C editor@iaeme.com

8 Varun Kumar S. G and R. Panneerselvam Table 4 Experimental Results of Variants of Genetic Algorithm Problem Size 0 probability Replication Algorithm M 1 O 1 M 1 C 1 M 2 O 1 M 2 C 1 Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Rcdp Table 4 Experimental Results of Variants of Genetic Algorithm (Continued) 50 Problem Size probability Replication Algorithm M 1 O 1 M 1 C 1 M 2 O 1 M 2 C 2 RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp editor@iaeme.com

9 Development and Comparison of Genetic Algorithms For Vehicle Routing Problem with Simultaneous Deliveries and Pickups In A Supply Chain Network Problem Size probability Replication Algorithm M 1 O 1 M 1 C 1 M 2 O 1 M 2 C 2 RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp RCdp IDENTIFICATION OF BEST ALGORITHM The identification of the best genetic algorithm from among the four proposed algorithms involves the following two stages. Checking whether there are significant differences among the four proposed algorithms using ANOVA. If there are significant differences among the four proposed genetic algorithms, then identification of the best genetic algorithm from among the four proposed genetic algorithms using Duncan s Multiple Range Test ANOVA to Check Significant Differences among Proposed Genetic Algorithms In this section, whether there are significant differences among the proposed four genetic algorithms, viz. M 1 O 1, M 1 C 1, M 2 O 1 and M 2 C 1 is checked using ANOVA. The application ANOVA for the results in terms of total distance travelled as shown in the Table 4 gives the results as shown in Table 5. Table 5 Results of ANOVA Degrees of Mean Sum of Source Sum of Squares F Ratio P Value Inference Freedom Squares Algorithm Significant Problem Size Significant Algorithm * Problem Size Insignificant Probability Insignificant Algorithm * Insignificant Probability Problem Size* Insignificant Probability Algorithm * Problem Size * Insignificant Probability Error Total editor@iaeme.com

10 Varun Kumar S. G and R. Panneerselvam It is evident from the results of the Table 5 that the four methods developed in this research, have significant differences among themselves in terms of the total distance travelled by all the vehicles. This means that their average results in terms of distance travelled by all the vehicles differ with each other. Similarly, there are significant differences among the problem sizes in terms of the total distance travelled by all the vehicles. This inference supports the fact that the problems sizes selected in this research are not biased. In the case of applying mutation probability, the results show that there are no significant differences among the mutation probability in terms of total distance travelled by all vehicles. There are no significant differences among the treatments of each of the interaction terms, viz. Algorithm, Problem Size, Algorithm * Problem Size, Probability, Algorithm * Probability, Problem Size * Probability, and Algorithm * Problem Size and Probability. Since, there are significant differences among the genetic algorithms, the next stage of the comparison is to perform Duncan s Multiple Range Test to find the best genetic algorithm Application of Duncan s Multiple Range Test (DMRT) to Find the Best GENETIC ALGORITHM From the results obtained by ANOVA, it is evident that proposed four variants of Genetic Algorithms differ significantly with each other. Using Duncan s Multiple Range Test, which is a post hoc test, the best algorithm in terms of obtaining minimum total distance is found as explained below. Step 1: Based on the data given in the Table 4, the descending order of the treatment (GA Method) means in terms of total distance travelled by all vehicles is shown in Table 6. Mean of algorithm M 1 O 1 Table 6 Descending Order of Treatment means of Algorithms Mean of algorithm M 2 O 1 Mean of algorithm M 1 C 1 Mean of algorithm M 2 C Step 2: For each treatment mean, the standard error is computed using the following formula. SE Y.j = From the ANOVA table shown in the Table 5, the values of mean sum of squares (MSS Error) and the number of observations under each treatment (n) of algorithm are given below. MSS Error = and n = 48. So, SE Y.j =. = Step 3: From the Duncan s table for multiple ranges with degrees of freedom of 128 and significance level (α) of 0.05, three significant ranges are shown in Table 7 Table 7 Multiple Ranges from Duncan s Table j Significant Range editor@iaeme.com

11 Development and Comparison of Genetic Algorithms For Vehicle Routing Problem with Simultaneous Deliveries and Pickups In A Supply Chain Network Step 4: By multiplying the significant ranges shown in the Table 7 with the standard error obtained in Step 2 Least Significant Ranges (LSR) are obtained and they are summarized in Table 8. Table 8 Least Significant Ranges Range j Least Significant Range * = * = * = Step 5: The treatment means are placed in descending order on the horizontal line shown in Figure 5. In the Figure 5, the Least Significant Range and the corresponding Actual Range for each pair of algorithms are shown on a horizontal line connection those pair of algorithms. In the Figure 5, it is clear that the algorithm M 2 C 1 is superior to all algorithms, because the actual range is greater than the respective LSR value for each of the pair of algorithms, viz. M 2 C 1 with M 1 C 1, M 2 C 1 with M 1 O 1 and M 2 C 1 with M 2 O 1. Hence, the algorithm M 2 C 1 proved to be superior to all other algorithms. Further, the algorithm M 1 C 1 is proved to be superior to the algorithms M 1 O 1 and M 2 O 1, because the actual range (AR) is more than the corresponding least significant range (LSR) for each of these pairs of algorithms (M 1 C 1 and M 1 O 1, and M 1 C 1 and M 2 O 1 ). Figure 5.Differences between treatment means and LSR values The algorithms, viz. M 2 O 1 and M1O 1 are not significantly different in terms of their performance, because the actual range (AR) is less than the corresponding least significant range (LSR) for this pair of algorithms. Since the algorithm M 2 C 1 is superior to all other algorithms proposed in this research, it is identified as the best algorithm among all the algorithms. 7. CONCLUSION In this article, VRPSDP has been addressed which is a sub-problem under Reverse Logistics using Genetic Algorithms as solution method. Due to the restrictions imposed on the problem settings, four variants of Genetic Algorithms have been developed by varying selection methods and crossover operators namely M 1 O 1, M 1 C 1, M 2 O 1 and M 2 C 1. These methods are tested on various problem instances with sizes 10, 25, 50 and 100 respectively. The four editor@iaeme.com

12 Varun Kumar S. G and R. Panneerselvam algorithms source codes are developed and run on C# on.net platform. The results obtained are tested for statistical significance using a complete factorial experiment with three factors, viz. Problem Size, and Method and probability. Since, there are significant differences among the methods, Duncan multiple range test has been carried out to find the best method (GA algorithm). From the Duncan multiple range test, the method M 2 C 1 is proved to be the best method, which This variant of GA uses rank selection of chromosomes in cascading manner and utilizes sinusoidal motion crossover to create offspring. There is plenty of scope for further research in the area of VRPSDP as there is lot of uncertainty and complexity linked with the increase in the number of customer nodes. The main objective of this research was to minimize total distance travelled for a fleet of vehicles. Further, several objectives can be achieved, such as optimum utilization of vehicle capacity, minimization of various transportation costs associated and minimizing travelling time for a fleet of vehicles, etc. REFERENCES [1] Aguiar, B. C. X. C., Siqueira, P. H., Aguiar, G. F. and Souza, L. V. Particle Swarm Optimization for Vehicle Routing Problem with Fleet Heterogeneous and Simultaneous Collection and Delivery. Applied Mathematical Sciences, 8(77), 2014, pp [2] Ai, J. and Kachitvichyanukul, K. A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Computers & Operations Research, 36, 2009, pp [3] Anand, E. and Panneerselvam, R. Development of efficient genetic algorithm for open shop scheduling problem to minimise makespan. International Journal of Advanced Operations Management, 10(3), 2018, pp [4] Berhan, E. Stochastic Vehicle Routing Problems with Real Simultaneous Pickup and Delivery Services.Journal of Optimization in Industrial Engineering, 19, 2016, pp [5] Çatay, B. A new saving-based ant algorithm for the vehicle routing problem with simultaneous pickup and delivery.expert Systems with Application, 37,2010, pp [6] Cetin, S. and Gencer, C. A Heuristic Algorithm for Vehicle Routing Problems with Simultaneous Pick-Up and Delivery and Hard Time Windows. Open Journal of Social Sciences, 3, 2015, pp [7] Chen, Z. A routing Optimization Adaptive Hybrid Genetic Algorithm Research. Journal of Software Engineering, 10, 2016, pp [8] Dethloff, J. Vehicle routing and reverse logistics: the vehicle routing problem with simultaneous delivery and pick-up.or Spektrum, 23, 2001,pp [9] Gajpal, Y. and Abad, P. An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup. Computers & Operations Research, 36, 2009,pp [10] Johnson, F., Vega, J., Cabrera, G. and Cabrera, E. Ant Colony System for a Problem in Reverse Logistic. Studies in Informatics and Control, 24(2), 2015, pp [11] Li, J., Pardalos, P. M., Sun, H., Pei, J. and Zhang, Y. Iterated local search embedded adaptive neighbourhood selection approach for the multi-depot vehicle routing problem with simultaneous deliveries and pickups.expert Systems with Applications, 42,2015, pp [12] Min, H. The multiple vehicle routing problem with simultaneous delivery and pickup points. Transportation Research A, 23, 1989,pp editor@iaeme.com

13 Development and Comparison of Genetic Algorithms For Vehicle Routing Problem with Simultaneous Deliveries and Pickups In A Supply Chain Network [13] Montané, F. A. T. and Galvão, R. D. A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service.computers & Operations Research, 33,2006, pp [14] Nagy, G. and Salhi, S. Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries. European Journal of Operational Research, 162, 2005, pp [15] Panneerselvam, R. Design and Analysis of Algorithms., 2nd Edition, PHI Learning, 2016, New Delhi. [16] Panneerselvam, R. Operations Research, PHI Learning, 2006, New Delhi. [17] Panneerselvam, R. Production and Operations Management, 3rd Edition, PHI Learning, 2012, New Delhi. [18] Panneerselvam, R. Research Methodology, 2nd Edition, PHI Learning, 2012, New Delhi. [19] Rieck, J. and Zimmermann, J. Exact Solutions to the Symmetric and Asymmetric Vehicle Routing Problem with Simultaneous Delivery and Pick-Up. Business Research, 6(1), 2013, pp [20] Sayyah, M., Larki, H. and Yousefikhoshbakht, M. Solving the Vehicle Routing Problem with Simultaneous Pickup and Delivery by an Effective Ant Colony Optimization. Journal of Industrial Engineering and Management Studies, 3(1), 2016, pp [21] Tasan, A. S. and Gen, M. A genetic Algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries. Computers & Industrial Engineering, 62, 2012, pp [22] Varun Kumar, S. G. and Panneerselvam, R. Literature Review of Reverse Logistics Problem. Industrial Engineering Journal, VII (10), 2014, pp [23] Varun Kumar, S. G. and Panneerselvam, R. A Study of Crossover Operators for Genetic Algorithms to Solve VRP and its Variants and New Sinusoidal Motion Crossover Operator.International Journal of Computational Intelligence Research, 13(7), 2017, pp [24] Wang, C., Zhao, F., Mu, D. and Sutherland, J.W. Simulated annealing for a vehicle routing problem with simultaneous pickup-delivery and time windows. In: Prabhu, V., Taisch, M., Kiritsis, D. (eds.) APMS. IAICT, 415,2013, pp [25] Wang, H. F. and Chen, Y. Y. A genetic algorithm for the simultaneous delivery and pickup problems with time window.computers & Industrial Engineering, 62, 2012, pp [26] Wang, J., Zhou, Y., Wang, Y., Zhang, J., Chen, C. L. P. and Zheng, Z. Multiobjective Vehicle Routing Problems with Simultaneous Delivery and Pickup and Time Windows: Formulation, Instances, and Algorithms.IEEE Transactions On Cybernetics, 46(3),2016, pp [27] Wassan, N.A. and Nagy, G. Vehicle Routing Problem with Deliveries and Pickups: Modelling Issues and Meta-Heuristics Solution Approaches. International Journal of Transportation, 2(1), 2014, pp editor@iaeme.com