A genetic algorithm for the simultaneous delivery and pickup problems with time window

‘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.

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.

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.

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.

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).

The vehicle routing problem with time windows (VRPTW) is an extension of the well-known vehicle routing problem (VRP). It involves a fleet of homogeneous vehicles, originating and terminating at a central depot, with limited capacity and maximum travel time to service a set of customers with known demands and service-time windows. The objective is to find a set of feasible routes that minimizes the total costs using some measures of solution quality. This paper focuses on the study of a hybrid of two search heuristics, Tabu Search (TS) and Genetic Algorithm (GA) on VRPTW. TS is a local search technique that has been successfully applied to many NP-complete problems. On the other hand, GA which is capable of searching multiple search areas in a search space is good in diversification. In this paper, we create a hybrid that combines the strengths of the two search heuristics. Experimental results indicate that such a hybrid outperforms the individual heuristics alone.

A Vehicle Routing Problem with Flexible Time Windows

The mobile production vehicle routing problem: Using 3D printing in last mile distribution

The Vehicle Routing Problem with Time Windows (VRPTW) is a critical combinatorial optimization problem in modern logistics, where finding optimal routes is essential for minimizing operational costs and enhancing service reliability. While Genetic Algorithms (GAs) are a powerful tool for solving VRPTW, their effectiveness is often undermined by premature convergence, a phenomenon in which the algorithm stagnates at suboptimal solutions, thus failing to achieve maximum efficiency. This study directly addresses this challenge by systematically evaluating how different reproduction schemes impact GA performance. The primary objective is to identify operator combinations that mitigate premature convergence to achieve superior solution quality, measured by total travel time, while also analyzing the trade-off with computational cost. We investigate combinations of conventional operators, such as Tournament Selection (TS) and Order Crossover (OX), against more advanced schemes, including Split Rank Selection (SRS) and Multi-Parent Order Crossover (MPOX), as well as different mutation methods, namely Scramble Mutation (SM) and Inversion Mutation (IM). Results demonstrate that advanced schemes, particularly the combination of SRS, MPOX, and IM, yield the most robust convergence and the lowest average total travel time of 48,422.8 minutes. However, this superior performance requires the longest computation time at 30.9 h. In contrast, conventional operator combinations are significantly faster, with execution times as low as 8.7 h, but they produce lower-quality solutions and exhibit unstable convergence. This study highlights the crucial role of the reproduction scheme in balancing the trade-off between solution quality and computational efficiency, confirming that a synergistic combination of advanced operators is essential for solving complex VRPTW instances effectively.

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.

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, 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.

Cellular Genetic Algorithms (cGAs) are a subclass of Genetic Algorithms (GAs) in which the population diversity and exploration are enhanced thanks to the existence of small overlapped neighborhoods. Such kind of structured algorithms is well suited for complex problems. In this paper, a cGA for solving the vehicle routing problem with time windows (VRPTW) is proposed. The benchmark of Solomon is selected for testing the proposed cGAs, and compares them with some other heuristics in the literature. The results demonstrate that the proposed cGA has a good potential for solving this kind of problems.KeywordsGenetic AlgorithmTime WindowVehicle Route ProblemVehicle RouteVehicle Route Problem With Time WindowThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.