A Computational Study of Genetic Crossover Operators for Multi-Objective Vehicle Routing Problem with Soft Time Windows

The article describes an investigation of the effectiveness of genetic algorithms for multi-objective combinatorial optimization (MOCO) by presenting an application for the vehicle routing problem with soft time windows. The work is motivated by the question, if and how the problem structure influences the effectiveness of different configurations of the genetic algorithm. Computational results are presented for different classes of vehicle routing problems, varying in their coverage with time windows, time window size, distribution and number of customers. The results are compared with a simple, but effective local search approach for multi-objective combinatorial optimization problems

A multi-objective model for a multi-period distribution management problem

The problems arising in commercial distribution are complex and involve several players and decision levels. One important decision is related with the design of the routes to distribute the products, in an efficient and inexpensive way. This article deals with a complex vehicle routing problem that can be seen as a new extension of the basic vehicle routing problem. The proposed model is a multi-objective combinatorial optimization problem that considers three objectives and multiple periods, which models in a closer way the real distribution problems. The first objective is cost minimization, the second is balancing work levels and the third is a marketing objective. An application of the model on a small example, with 5 clients and 3 days, is presented. The results of the model show the complexity of solving multi-objective combinatorial optimization problems and the contradiction between the several distribution management objective.Distribution problem, multi-objective models

Multi-Objective UAV Mission Planning Using Evolutionary Computation

This investigation purports to develop a new model for multiple autonomous aircraft mission routing. Previous research both related and unrelated to this endeavor have used classic combinatoric problems as models for Unmanned Aerial Vehicle (UAV) routing and mission planning. This document presents the concept of the Swarm Routing Problem (SRP) as a new combinatorics problem for use in modeling UAV swarm routing, developed as a variant of the Vehicle Routing Problem with Time Windows (VRPTW). The SRP removes the single vehicle per target restraint and changes the customer satisfaction requirement to one of vehicle on location volume. The impact of these alterations changes the vehicle definitions within the problem model from discrete units to cooperative members within a swarm. This represents a more realistic model for multi-agent routing as a real world mission plan would require the use of all airborne assets across multiple targets, without constraining a single vehicle to a single target. Solutions to the SRP problem model result in route assignments per vehicle that successfully track to all targets, on time, within distance constraints. A complexity analysis and multi-objective formulation of the VRPTW indicates the necessity of a stochastic solution approach leading to the development of a multi-objective evolutionary algorithm. This algorithm design is implemented using C++ and an evolutionary algorithm library called Open Beagle. Benchmark problems applied to the VRPTW show the usefulness of this solution approach. A full problem definition of the SRP as well as a multi-objective formulation parallels that of the VRPTW method. Benchmark problems for the VRPTW are modified in order to create SRP benchmarks. These solutions show the SRP solution is comparable or better than the same VRPTW solutions, while also representing a more realistic UAV swarm routing solution

Genetic Algorithms with Neural Cost Predictor for Solving Hierarchical Vehicle Routing Problems

When vehicle routing decisions are intertwined with higher-level decisions, the resulting optimization problems pose significant challenges for computation. Examples are the multi-depot vehicle routing problem (MDVRP), where customers are assigned to depots before delivery, and the capacitated location routing problem (CLRP), where the locations of depots should be determined first. A simple and straightforward approach for such hierarchical problems would be to separate the higher-level decisions from the complicated vehicle routing decisions. For each higher-level decision candidate, we may evaluate the underlying vehicle routing problems to assess the candidate. As this approach requires solving vehicle routing problems multiple times, it has been regarded as impractical in most cases. We propose a novel deep-learning-based approach called Genetic Algorithm with Neural Cost Predictor (GANCP) to tackle the challenge and simplify algorithm developments. For each higher-level decision candidate, we predict the objective function values of the underlying vehicle routing problems using a pre-trained graph neural network without actually solving the routing problems. In particular, our proposed neural network learns the objective values of the HGS-CVRP open-source package that solves capacitated vehicle routing problems. Our numerical experiments show that this simplified approach is effective and efficient in generating high-quality solutions for both MDVRP and CLRP and has the potential to expedite algorithm developments for complicated hierarchical problems. We provide computational results evaluated in the standard benchmark instances used in the literature

Data driven safe vehicle routing analytics: a differential evolution algorithm to reduce CO2 emissions and hazardous risks

Contemporary vehicle routing requires ubiquitous computing and massive data in order to deal with the three aspects of transportation such as operations, planning and safety. Out of the three aspects, safety is the most vital and this study refers safety as the reduction of CO2 emissions and hazardous risks. Hence, this paper presents a data driven multi-objective differential evolution (MODE) algorithm to solve the safe capacitated vehicle routing problems (CVRP) by minimizing the greenhouse gas emissions and hazardous risk. The proposed data driven MODE is tested using benchmark instances associated with real time data which have predefined load for each of the vehicle travelling on a specific route and the total capacity summed up from the customers cannot exceed the stated load. Pareto fronts are generated as the solution to this multi-objective problem. Computational results proved the viability of the data driven MODE algorithm to solve the multi-objective safe CVRP with a certain trade-off to achieve an efficient solution. Overall the study suggests 5% increment in cost function is essential to reduce the risk factors. The major contributions of this paper are to develop a multi-objective model for a safe vehicle routing and propose a multi-objective differential evolution (MODE) algorithm that can handle structured and unstructured data to solve the safe capacitated vehicle routing problem

Optimal multi-objective discrete decision making using a multidirectional modified Physarum solver

This paper will address a bio-inspired algorithm able to incrementally grow decision graphs in multiple directions for discrete multi-objective optimization. The algorithm takes inspiration from the slime mould Physarum Polycephalum, an amoeboid organism that in its plasmodium state extends and optimizes a net of veins looking for food. The algorithm is here used to solve multi-objective Traveling Salesman and Vehicle Routing Problems selected as representative examples of multi-objective discrete decision making problems. Simulations on selected test case showed that building decision sequences in two directions and adding a matching ability (multidirectional approach) is an advantageous choice if compared with the choice of building decision sequences in only one direction (unidirectional approach). The ability to evaluate decisions from multiple directions enhances the performance of the solver in the construction and selection of optimal decision sequences