A comprehensive study of vehicle routing problem with time windows using an improved multi-objective evolutionary algorithms

‘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.

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.

In this paper, an optimization algorithm based on lagrangian relaxation is proposed to solve the vehicle routing problem with time windows (VRPTW). The VRPTW is the generalization of the Vehicle Routing Problem, with a service time interval constraint available with every customer node. Here, an approach is used which relaxes the constraint set that justify that each customer should be serviced. The problem consists of introducing optimal lagrangian multipliers and then the subgradient method is used to find the appropriate multipliers. Here the problem focuses on, compared to the problems in the literature, not only the minimization of the transportation cost but also the used number of vehicles. The method has been implemented and tested on a series of well known benchmark test problems. The algorithm results to be very competitive and the results are better than the optimal solution.

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.

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).

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.

Blood Supply Chain (BSC) concerns with flow of blood products from blood collection by donors to transfusion of blood components to patients. BSC comprises of collection, testing, processing, storage, distribution and transfusion activities, which are normally responsibility of Blood Centre and hospitals. In Malaysia, National Blood Centre (PDN) is responsible to organize blood donation, collection and processing. Current procedure practised by PDN is to have vehicles sending staffs and equipment while one vehicle is assigned to collect donated blood from donation sites and transport the blood to PDN within six hours. As consequence, vehicles shortages are encountered and resources optimization unachieved especially when many blood donation sites involved per day. This paper presents the results of a preliminary study which aims at proposing blood collection optimal routes for blood collecting vehicles that adhere to all pre-determined time windows for blood collection at blood donation sites. A Mixed Integer Goal Programming (MIGP) model based on Vehicle Routing Problem with Time Windows (VRPTW) has been formulated. The MIGP model pursues four goals, namely, to minimize total distance travelled, to minimize total travel time, to minimize total waiting time of vehicles and to minimize number of vehicles (routes). The model was solved using preemptive goal programming approach and existing heuristics for the VRPTW. Based on the results, it can be concluded that the donated blood can be collected and transported using reduced number of vehicles as proposed by the MIGP model’s optimal compared to the total number of vehicles used by current practice, Thus, the proposed VRPTW based MIGP model has promising significant impact for donated blood transportation in terms of resources optimization and costs savings. The model and approach could be easily extended to solve larger problem involving large number of donation sites with variants of time windows for the sites.

This paper presents a comparison of two approaches for solving the vehicle routing problem with time windows (VRPTW). Scheduling of vehicles for pickup and delivery is a common problem in logistics and may be expressed as VRPTW, for which both exact and approximate techniques are available. It is therefore interesting to compare such techniques to evaluate their performance and Figure what is the best option based on the instance features and size. In this work, we compared Mixed Integer Linear Programming (MILP) with Set-Based Particle Swarm optimization (S-PSO). Both algorithms are tested on the full 56 instances of the Solomon dataset. The results show that the two algorithms perform similarly for lower number of customers while there are significant differences for the cases with higher number of customers. For higher number of customers MILP consistently performs as good as or better than S-PSO for the clustered data, both with short and long scheduling horizons, while the S-PSO outperforms MILP in most cases with random and mixed random clustered data with long scheduling horizons. Furthermore when the algorithms perform the same with regards to the main objective (number of vehicles), MILP generally achieves a better result in the second objective (distance traveled).

The Clustered Vehicle Routing Problem with Time Window (CVRPTW) is an extension of the traditional Vehicle Routing Problem (VRP), which aims to find a high efficiency and feasible solution. In actual situation, the distribution of customer is not dispersed, but centralized in several regions. CVRPTW has greater research implications. Compared with Vehicle Routing Problem with Time Window (VRPTW), CVRPTW often has many constraints. The process of finding the optimal solution is more complicated, and the consumption of time resources is relatively large. Therefore, this paper proposes a multiobjective evolutionary algorithm with fast convergence strategy (MOEA-FCS) to solve CVRPTW. The fast convergence strategy divides the population into subpopulations, each of subpopulation evolves in different directions. Experimental results show that MOEA-FCS converges much faster than NSGA-II and SPEA2, the distribution of solutions is better than NSGA-II and SPEA2.

This paper investigates a well-known complex combinatorial problem known as the vehicle routing problem with time windows (VRPTW). Unlike the standard vehicle routing problem, each customer in the VRPTW is served within a given time constraint. This paper solves the VRPTW using an improved artificial bee colony (IABC) algorithm. The performance of this algorithm is improved by a local optimization based on a crossover operation and a scanning strategy. Finally, the effectiveness of the IABC is evaluated on some well-known benchmarks. The results demonstrate the power of IABC algorithm in solving the VRPTW.

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

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.

In this paper, the vehicle routing problem with time windows (VRPTW) was considered, and a mixed integer programming mathematic model of VRPTW was proposed in detail. Meantime, an improved ant colony algorithm (IACA) was proposed to overcome the shortcomings of premature convergence and slow convergence of conventional ant colony algorithm (ACA). The experiment results showed that the IACA can solve VRPTW effectively.

Solving Multi-objective Vehicle Routing Problem with Time Windows by FAGA

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.