Multi-Objective Vehicle Routing Problem with Time Windows and Fuel Consumption Minimizing

‘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.

Last-mile delivery service providers and drivers often choose routes deviating from the shortest distance, influenced by personal preferences and various business-level factors. This study introduces an innovative data-driven optimization approach for learning preferences of decision-makers (DMs) in multi-objective vehicle routing problems. Utilizing real-world historical data from a last-mile delivery logistics platform, we develop a machine-learning framework to learn DMs’ preferences in designing delivery routes. To design our approach we focus on a multi-objective capacitated vehicle routing problem with time windows and develop an integrated framework that combines supervised learning models, sampling techniques, and optimization methods to determine preference weights for objective functions based on selected features. We conduct extensive numerical experiments to test the proposed data-driven optimization approach. Our findings suggest that analyzing historical planned and actual routes reveals DMs’ preferences, such as prioritizing workload balance and minimizing fleet usage over travel distance alone. Furthermore, this study offers insights into key factors shaping last-mile delivery logistics, including workload distribution and deviations from pre-planned routes, enabling more informed and human-centered decision-making in logistics optimization. • Learning decision-makers’ preferences in multi-objective vehicle routing optimization. • Combines machine learning with ALNS for scalable, efficient routing solutions. • Validated using 800+ real-world scenarios from a commercial logistics platform. • Demonstrates improved workload balance and fleet utilization.

The Vehicle Routing Problem with Time Windows involves finding the lowest-cost set of routes to deliver goods to customers, which have service time windows, using a homogeneous fleet of vehicles with limited capacity. In this paper, we propose and analyze the performance of an improved multi-objective evolutionary algorithm, that simultaneously minimizes the number of routes, the total travel distance, and the delivery time. Empirical results indicate that the simultaneous minimization of all three objectives leads the algorithm to find similar or better results than any combination of only two objectives. These results, although not the best in all respects, are better in some aspects than all previously published approaches, and fully multi-objective comparisons show clear improvement over the popular NSGA-II algorithm.KeywordsTime WindowMutation OperatorTravel DistanceDelivery TimeVehicle Route ProblemThese 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.

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Optimization of maintenance services of a company working in the gas metering sector is investigated. In particular, daily tasks of operators are optimized by exploiting the paradigm of vehicle routing problems with a set of predefined time windows that overlap one with the others and four competing objectives to take into account. First, an exact integer formulation is presented that can be solved only for a reduced number of customer sites to visit. Then, a heuristic approach is proposed to find approximate solutions with huge savings on the computational effort, also for high‐dimensional instances. Numerical results on both real and synthetic scenarios showcase the effectiveness of the approach.

In some special rescue scenarios, the needed goods should be transported by drones because of the landform. Therefore, in this study, we investigate a multi-objective vehicle routing problem with time window and drone transportation constraints. The vehicles are used to transport the goods and drones to customer locations, while the drones are used to transport goods vertically and timely to the customer. Three types of objectives are considered simultaneously, including minimization of the total energy consumption of the trucks, total energy consumption of the drones, and the total number of trucks. An improved artificial bee colony algorithm is designed to solve the problem. In the proposed algorithm, each solution is represented by a two-dimensional vector, and the initialization method based on the Push-Forward Insertion Heuristic is embedded. To enhance the exploitation abilities, an improved employed heuristic is developed to perform detailed local search. Meanwhile, a novel scout bee strategy is presented to improve the global search abilities of the proposed algorithm. Several instances extended from the Solomon instances are used to test the performance of the proposed improved artificial bee colony algorithm. Experimental comparisons with the other efficient algorithms in the literature verify the competitive performance of the proposed algorithm.

Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: first the global pairwise relationships are analysed using the Kendall correlation method; then the ranges of the values found on the given Pareto front are estimated and assessed; next these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally local relationships are identified using scatter-plots. Experiments are presented for three different combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem and multiobjective vehicle routing problem with time windows. Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives.

This paper applies Particle Swarm Optimization algorithm (PSO) in a Multi-objective Vehicle Routing Problem with Time Window (MVRPTW). Firstly, through the problem analysis, establish a versatile mathematical model. Secondly, introduce an effective particle code to successfully implement the algorithm. Finally, examples prove that PSO can be obtained the optimal solution quickly and efficiently of MVPRTW.

The vehicle routing problem with time windows (VRPTW) has previously been investigated as a multi-objective problem. In this paper estimated carbon emissions is added as an objective alongside the number of vehicles required and distance travelled. We term this new problem formulation (E)VRPTW. In order to estimate emissions we require detailed information regarding the nature of the route to be taken. As previous benchmark VRPTW problem instances do not supply such information we generate new problem instances based upon street network data from Open Street Map. Results suggest that by adding emissions as the third objective, in many cases the search may be directed to areas that allow improvement in the distance and vehicles objectives. As emissions and distance are inherently related, we do not search for pareto fronts. Rather we attempt to find solutions that either minimise distance or minimise vehicles used. Adding the third emissions objective is shown to enable a multi-objective EA to find improved solutions in terms of minimal vehicles or minimal distance when compared to the same multi-objective EA using only two objectives.

Capacitated vehicle routing problem with time window (CVRPTW) is a critical issue in forwarding business. In this problem, normal cargoes (excluding freeze and hazardous goods) are normally consolidated before shipping to customer sites. Two objectives of delivery lead-time and total shipping cost are considered subject to vehicle capacity and time windows constraints. The fuzzy-compromise programming approach is utilised to handle the multi-objective model. Then, a so-called adaptive inertia weight particle swarm optimisation (AIWPSO) algorithm is applied to handle the cases of large number of delivered customers. In this work, a real case of a leading forwarding company in Vietnam is investigated to validate the proposed solution.

Besides its economic purpose, the vehicle routing problem has also garnered attention due to its social and environmental objectives in recent years.In terms of ensuring sustainability, it is beneficial to consider these three objectives together.CO 2 emissions, which is one of the causes of global warming, which we have felt more prominently in the past few years, has also affected the policies of logistics companies.Organizing working hours and ensuring fairness among employees are also one of our motivations in this study.Financial objectives has always taken into account.Simulated annealing algorithm and adaptive large neighborhood search algorithm are developed for the solution of the multi-objective mix integer mathematical model, in which financial, environmental, and social objective functions, which include alternative ways with different properties between nodes and different speed options.Small problems can be solved with exact solution method in literature, but to solve medium and larger samples heuristic algorithms are needed.When comparing algorithms, Simulated Annealing also gives better results than Adaptive Large Neighborhood Search in a shorter time.

This paper was targeted at minimizing the expectation of traveling distance maximizing the expectation of customers' degree satisfaction, a multi-objective vehicle routing problem with stochastic demand (VRPSD) model based on soft time window was proposed. In order to solve the problem, a hybrid PSO algorithm based on Pareto optimization method was designed in this paper. The paper made the standard PSO algorithm discrete by re-defining operators and employing swap recon, utilized challenge tournament method to construct Pareto optimal solution set, applied an external archive to keep the diversity of solutions. Ultimately, a standard example is used to verify the validity of the algorithm.

This study proposes a genetic algorithm to solve the biobjective vehicle routing problem with time windows simultaneously considering total distance and distance balance of active vehicle fleet. A new complex chromosome is used to present the active vehicle route. Through tournament selection, one-point crossover, and migrating mutation operator, the solution of the problem is solved. In experiment on Solomon's benchmark problems, considering the total distance and distance balance, the results are improved in all classes of problems. According to the experimental results, the suggested approach is sufficient and the average GA performance is good.

Article history: Received December 10, 2013 Received in revised format 16 March 2014 Accepted April 29 2014 Available online May 14 2014 A crucial issue in humanitarian relief operations is vehicle routing because there are many difficulties in roads that people face when a disaster is occurred. In such circumstances, selecting more reliable routes could help rescue team act more efficacious. Therefore, we propose a mathematical model that maximizes the reliability of selected routes in disaster relief routing process using a multiple attribute decision making (MADM) technique. Furthermore, the proposed model minimizes the total cost that imposed to system. For this reason, the model is a multi-objective vehicle routing problem (VRP). The problem considered here is NP-hard and its objective is to find near optimal solutions, rather than optimal ones, using the nondominated sorting genetic algorithm. © 2014 Growing Science Ltd. All rights reserved.

Vehicle routing is considered the basic issue in distribution management. In real-world problems, customer demand for some commodities increases on special situations. On the one hand, one of the factors that are very important for customers is the timely delivery of the demanded commodities. In this research, customers had several different kinds of demands. Therefore, a new routing model was introduced in the form of integer linear programming by combining the concepts of time windows and multiple demands and by considering the two contradictory goals of minimizing travel cost and maximizing demand coverage. Moreover, two approaches were designed for the problem-solving model based on the NSGA-II algorithm with diversification of the mutation operator structure. The two criteria of spread and coverage of non-dominated solutions were used to compare algorithms. Study of some typical created problems indicated the validity of the model and the computational efficiency of the proposed algorithm. The proposed algorithm could increase the criterion of solution spread by about 10%, and increased the number of obtained solutions on the Pareto border compared to other algorithms, which indicated its high efficiency.