Metaheuristic algorithm for solving the multi-objective vehicle routing problem with time window and drones

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

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.

In this paper, we consider a variant of vehicle routing problem with multiple trip and time windows. In this alternative problem, we think about the scheduling of trucks to a number of customers in the presence of fixed fleet and time windows constraints. This type of problem can be described as determining a number of vehicle trips minimising total travelled distance complying with the time windows and the multiple use of vehicles. We call this problem a multiple trips fixed fleet vehicle routing problems with time windows (MTFFVRPTW). To solve this variant, a new hybrid evolutionary algorithm for transport optimisation problems, called estimation of distribution algorithm with local search is used. The proposed algorithm integrates a double structure of distribution technique, which is used to introduce the variables dependency. To evaluate our approach we provide a number of experimentation to a modified Solomon's instances for the case of multiple trips. The results show that the hybrid proposed algorithm offer a good quality solution in the term of objective functions, also in the running time.

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.

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.

‘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.

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.

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.

The presence of multiple, often conflicting, objectives is a naturally occurring scenario in real-world decision making. Such problems are characterized by the existence of a set of efficient solutions instead of a single optimum. Evolutionary algorithms (EAs), which employ a population based search mechanism over a bounded decision/solution space, have emerged as popular tools for concurrently obtaining a good approximation to the entire efficient set, instead of finding a single solution at a time. While EAs hardly impose any restrictions on the form of the objective functions to be optimized, their design is generally based on the requirement that the feasible solution space of the problem be fixed. However, a situation contrary to the aforementioned is seen to occur during a bi-level formulation of the vehicle routing problem. Moreover, the problem is general enough to conceivably arise in many real-world situations. In light of this fact, the present paper alleviates the stated requirement by incorporating a bi-level perspective into a multi-objective EA. Thereafter, a preliminary study is carried out on the multi-objective variant of the NP-hard vehicle routing problem with time window constraints (VRPTW), in order to demonstrate the efficacy of the proposed approach.KeywordsBi-level ProgrammingMulti-Objective OptimizationEvolutionary AlgorithmVehicle Routing Problem with Time Windows

An Australian company is faced with the logistics problem of distributing small quantities of fibre boards to hundreds of customers every day. The resulting Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints has to be solved within a single hour, hence the use of a heuristic instead of an exact method. In previous work, the loading was performed after optimising the routes, which in some cases generated infeasible solutions in need of a repair mechanism. In this work, the feasibility of the loading constraints is maintained during the route optimisation. Iterated Local Search has proved very effective at solving vehicle routing problems. Its success is mainly due to its biased sampling of locl optima. However, its performance heavily depends on the perturbation procedure. We trialled different perturbation procedures where the first one perturbs the given solution by moving deliveries that incur the highest cost on the objective function, whilst the second one moves deliveries that have been shifted less frequently by the local search in previous iterations. Our industry partner provided six sets of daily orders which have varied characteristics in terms of the number of customers, customer distribution, number of fibre boards and fibre boards’ sizes. Our investigations show that an instance becomes more constrained when the customer order contains many different board sizes, which makes it harder to find feasible solutions. The results show that the proposed perturbation procedures significantly enhances the performance of iterated local search specifically on such constrained problems.

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.

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

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.

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).