Multiobjective memetic algorithm based on adaptive local search chains for vehicle routing problem with time windows

Multi-tasking optimization (MTO) has attracted increasing attention in the domain of evolutionary computation. Different from single-tasking optimization, MTO can solve multiple optimization tasks simultaneously to improve the performance of solving each optimization task by inter-task knowledge transfer. Multifactorial evolutionary algorithm (MFEA) is one of the most widely used MTO algorithm based on assortative mating and vertical cultural transmission. This work extends MFEA by integrating bone route and large neighborhood local search to solve multi-objective vehicle routing problem with time window (VRPTW). The VRPTW is modeled as two related tasks, i.e., one is a multi-objective version of VRPTW (the main task), and the other is a single-objective version of VRPTW (the auxiliary task). The resultant new algorithm namely multi-objective multi-factorial memetic algorithm (MOMFMA) solve the two tasks simultaneously where the information between the tasks is exchanged in the evolutionary process. In addition to the implicit information transfer of MFEA, the bone route is introduced to enable explicit information transfer between tasks. Particularly, bone routes are constructed as semi-finished product solutions and used in large neighborhood local search. The bone route and the large neighborhood local search work together to speed up the convergence of the algorithm. MOMFMA is tested on Solomon’s 56 datasets and the experimental results demonstrate that the efficiency of MOMFMA.

The vehicle routing problem with Time windows (VRPTW) issue has attracted significant attention in the operations research community in recent years. The primary objective of VRPTW is defined as the minimization of the number of routes or vehicles. Minimization of the total travel cost is secondary objective. In this paper, VRPTW is examined and a hybrid ant colony system coupled with randomized algorithm (RA) and Pareto local search (PLS) algorithm (RPACS-VRPTW), is proposed. The RPACS-VRPTW can efficiently reduce costs of the constructive procedure of the solution in the ant colony system (ACS). Computational results for partial benchmark problems show that the approach proposed outperforms some other previously known heuristic methods.

‘Route balance’ is the difference between the longest and the shortest among all the route lengths. The route balance is frequently considered in a vehicle routing problem (VRP) for balancing the distance travelled among delivery vehicles. This is a common practice since in VRPs there are no time elements. However, in recent years, some research works have considered route balance in a vehicle routing problem with time windows (VRPTW). As there are more time elements in VRPTW, this paper refutes that route balance is sufficient for VRPTW by simultaneously optimising makespan and workload imbalance using ‘total time balance’ instead of route balance. On the other hand, ‘total time balance’ is the difference between the longest total time taken and the shortest total time taken among delivery vehicles. As such, makespan is the longest total time taken among vehicles. Total time taken for a vehicle is the sum of vehicle run time, waiting time and service time. In order to demonstrate the importance of using total time balance instead of route balance on VRPTW, three different multi-objective VRPTW models, namely, (1) only with general VRPTW objectives (i.e. ‘total distance travelled’ by all vehicles and ‘total number of vehicles’ used), (2) general VRPTW objectives with route balance and (3) general VRPTW objectives with total time balance are developed and solved by fitness aggregated genetic algorithm (FAGA) for 36 Solomon’s benchmark instances. By comparison of the makespan produced by the FAGA between the three cases, the importance of using total time balance instead of route balance on multi-objective VRPTW is demonstrated. Also, the makespan produced by the FAGA for the third case, i.e. general VRPTW objectives with total time balance is compared with the makespan produced by fitness aggregated differential evolution (FADE). By comparing makespan with statistical testing between FAGA and FADE, the outperformance of FAGA over FADE is verified. To check the practicality of the total time balance on multi-objective VRPTW, an instance with real time windows is also solved for the three cases by the FAGA and its makespan are compared and reported.

Vehicle routing problem with time windows (VRPTW) is an important logistics problem, which appears to be multiobjective in real world. Recently, a general multiobjective VRPTW (MOVRPTW) with five objectives has been defined, and a set of MOVRPTW problem instances based on data from real world have been proposed. These instances indicate more truly multiobjective nature and represent more realistic and challenging MOVRPTW cases. In this paper, a local search-based multiobjective optimization algorithm is proposed for the real-world MOVRPTW instances. Considering the problem structure of MOVRPTW, we design different local search methods for different objectives. These simple but effective local search methods cooperate to optimize different objectives simultaneously. More problem-specific knowledge can be extracted by using objectivewise local search components, and thus, high-quality solutions are expected to be generated. The proposed algorithm is tested on 45 realistic and challenging MOVRPTW benchmark instances from real world. Experimental results show that the proposed algorithm can obtain better solutions than the previous evolutionary algorithm-based multiobjective algorithm on new MOVRPTW cases. Additional results on 56 Solomon instances show the stability of the proposed algorithm across data sets.

We propose an evolutionary algorithm (EA) for the vehicle routing problem with time windows (VRPTW). In particular, a crossover operator suitable for solving the VRPTW are presented. The proposed crossover is designed by extending edge assembly crossover (EAX) which was originally designed for the traveling salesman problem (TSP). Moreover, we propose an efficient modification procedure to eliminate violations of the capacity constraints and the time window constraints because intermediate solutions generated by EAX violate these constraints. The EA is composed of EAX, the modification procedure and a very simple local search. The EA is applied to the well-known Gering and Homberger benchmarks for the VRPTW. The EA finds new best-known solutions in 119 of the 180 instances (200 - 600 customer benchmarks).

Vehicle Routing Problem with Time Windows (VRPTW) is a constrained NP-hard problem that designs the least cost routes from one depot to a set of geographically scattered points. Most of traditional techniques are difficult to solve this kind of problem. In this paper, we explored the validity of another swarm-intelligence-based model-Bacterial Foraging Optimization (BFO) for VRPTW solving. Original BFO, BFO with linear decreasing chemotaxis step (BFO-LDC) and BFO with non-linear decreasing chemotaxis step (BFO-NDC) are used to obtain the best solutions of a given VRPTW problem, respectively. The experimental results demonstrated that the proposed BFO algorithms have the potential to solve Vehicle Routing Problem with Time Windows (VRPTW) with rapid convergence rate and the good result accuracy.

In the field of operations research, the vehicle routing problem with time windows (VRPTW) has been widely studied because it is extensively used in practical applications. Real-life situations discussed in the relevant research include time windows and vehicle capabilities. Among the constraints in a VRPTW, the practical consideration of the fairness of drivers’ performance bonuses has seldom been discussed in the literature. However, the shortest routes and balanced performance bonuses for all sales drivers are usually in conflict. To balance the bonuses awarded to all drivers, an auction bidding approach was developed to address this practical consideration. The fairness of performance bonuses was considered in the proposed mathematical model. The nearest urgent candidate heuristic used in the auction bidding approach determined the auction price of the sales drivers. The proposed algorithm both achieved a performance bonus balance and planned the shortest route for each driver. To evaluate the performance of the auction bidding approach, several test instances were generated based on VRPTW benchmark data instances. This study also involved sensitivity and scenario analyses to assess the effect of the algorithm’s parameters on the solutions. The results show that the proposed approach efficiently obtained the optimal routes and satisfied the practical concerns in the VRPTW.

Hybridization of tabu search with feasible and infeasible local searches for periodic home health care logistics

The Vehicle Routing Problem with Time Windows (VRPTW) consists of a homogenous set of vehicles and a set of customer located in a city. In VRPTW all the vehicles starts from the depot visit the customer and end at the depot. Each customer is visited exactly by one vehicle within the specified time window. The objective is to minimize the number of vehicles and total distance travelled simultaneously. This represents the multiobjective Vehicle Routing Problem with Time Windows. The proposed work consists of Hybrid Genetic Search with Diversity Control using the Genetic Algorithm for solving the VRPTW. The Pareto approach is used for finding the set of optimal solutions for achieving the multiobjective. The crossover operator is used for exchanging the best routes, which have shortest distance. Two mutation operators such as relocation mutation operator and split mutation operator were used in this application. In this, it accounts penalty for an infeasible solutions with respect to time-window and duration constrains. The computations are performed using the instances which are obtained from the VRPLIB.

When solving multi-objective optimization problems (MOPs) with big data, traditional multi-objective evolutionary algorithms (MOEAs) meet challenges because they demand high computational costs that cannot satisfy the demands of online data processing involving optimization. The gradient heuristic optimization methods show great potential in solving large scale numerical optimization problems with acceptable computational costs. However, some intrinsic limitations make them unsuitable for searching for the Pareto fronts. It is believed that the combination of these two types of methods can deal with big MOPs with less computational cost. The main contribution of this paper is that a multi-objective memetic algorithm based on decomposition for big optimization problems (MOMA/D-BigOpt) is proposed and a gradient-based local search operator is embedded in MOMA/D-BigOpt. In the experiments, MOMA/D-BigOpt is tested on the multi-objective big optimization problems with thousands of variables. We also combine the local search operator with other widely used MOEAs to verify its effectiveness. The experimental results show that the proposed algorithm outperforms MOEAs without the gradient heuristic local search operator.

A parallel algorithm of simulated annealing to solve the vehicle routing problem with time windows (VRPTW) is considered. The VRPTW is an NP-hard bicriterion optimization problem in which both the number of vehicles and the total distance traveled by vehicles are minimized. The objective is to establish to what extent the computation time required to solve the VRPTW can be decreased by a number of co-operating parallel processes with no loss of quality of solutions. The quality of a solution is meant as its proximity to the optimum (or best known) solution. Furthermore, some factors are proposed which allow to rank the VRPTW benchmarking tests according to their difficulties

A vehicle routing problem with time windows (VRPTW) has been studied widely in the literature. Most effective methods to find a solution are still heuristics, which are constructed from the inventor’s ideas of how a good solution should be obtained, and their efficiency is quantified only by empirical data. However, these ideas may or may not yield a near-optimal solution. It would be better if we can identify some characteristics of a solution to VRPTW to help guide the heuristic in the right direction. Arnold and Sörensen had proposed a statistical learning model to determine a characteristic of a near-optimal solution for a vehicle routing problem (VRP). They used that knowledge to create a guided heuristic for a local search and the results were impressive. Therefore, we wish to extend this work to VRPTW by defining new solution metrics that involve time windows constraints and using a statistical tool to obtain characteristic(s) of a good solution to VRPTW. By applying a machine learning model, we examined 14,000 VRPTW instances to identify the key characteristics that differentiate high-quality solutions. Our experiment revealed that the average width per route is the most distinguishing characteristic, which also holds true for the standard VRP according to Arnold and Sorensen's findings. Moreover, the runner-up characteristics are the average compactness per route, measured by width, and the average total travel time and service time per route. These insights contribute to a deeper understanding of the VRPTW solution structures and offer a meaningful direction for the development of more effective heuristics.

An evolutionary programming algorithm for continuous global optimization

In this study, Vehicle Routing Problem with Time Windows (VRPTW) with known customer demands, a single depot and identical vehicles, is considered. Minimizing the total distance and the total waiting time of the vehicles are determined as objective functions for VRPTW which is capable to serve the customers in a prespecified time interval. A hybridized version of genetic algorithm which is a metaheuristic solution technique with constructive heuristic methods is proposed to produce effective solutions for VRPTW. By using sweep algorithm in initial population generation phase of genetic algorithm, it is planned to begin the search with high quality solution sets and in this way, get more feasible solutions faster. A benchmark problem in the literature is solved and obtained results are compared with the results of genetic algorithm with the nearest neighbor algorithm based algorithm. It is observed that the proposed genetic algorithm beginning with sweep based initial population generation algorithm reaches more effective solutions.

In this paper, we discuss the vehicle routing problem with time windows (VRPTW) where stochastic travel times are assumed. In a first step, a variable neighborhood search (VNS) approach is proposed for the VRPTW where deterministic data is assumed. This approach is extended in a second step by adding a sampling approach to deal with the stochastic travel times. Problem instances are proposed that are based on the well-known Solomon instances from the literature. The resulting routes are executed in a stochastic environment to assess the performance of the proposed heuristic. Computational experiments demonstrate that it is reasonable to incorporate stochastic knowledge into VRPTW algorithms.