Genetic Algorithm applied to the Capacitated Vehicle Routing Problem: an analysis of the influence of different encoding schemes on the population behavior

Genetic Algorithm (GA) is an optimization method that has been widely used in the solution of NP-Hard (Non-deterministic Polynomial-time) problems, among which is the Vehicle Routing Problem (VRP), widely known in the literature due to its applications in the logistics and supply sectors, and which is considered in this work. However, finding solution for any optimization problem using GA presupposes the adoption of a solution encoding scheme that, according to the literature, impacts its performance. However, there is a lack of works in the literature exploring this theme. In this work we carry out an analysis of the main encoding schemes (binary and integer) employed in the GA for the solution of the capacitated VRP (CVRP), in order to evaluate the influence of each of them on the behavior of the GA population and, consequently, on the algorithm performance. To this end, we developed a computational tool that allows visualizing the GA individuals (solutions) mapped to a two-dimensional space. Based on the experiments conducted, we observed that, in general, integer vectors provide better conditions for GA individuals to explore the solution space, leading to better results. The results found, besides corroborating some assumptions in the literature, may justify the preference for integer encoding schemes to solve CVRP in recent literature works. In addition, this study can contribute to the choice and/or proposition of heuristics that allow GA to search for better quality solutions for the VRP with less computational effort

SR-2: A Hybrid Algorithm for the Capacitated Vehicle Routing Problem

During the last decades a lot of work has been devoted to develop algorithms that can provide near-optimal solutions for the capacitated vehicle routing problem (CVRP). Most of these algorithms are designed to minimize an objective function, subject to a set of constraints, which typically represents aprioristic costs. This approach provides adequate theoretical solutions, but they do not always fit real-life needs since there are some important costs and some routing constraints or desirable properties that cannot be easily modeled. In this paper, we present a new approach which combines the use of Monte Carlo simulation and parallel and grid computing techniques to provide a set of alternative solutions to the CVRP. This allows the decision-maker to consider multiple solution characteristics other than just aprioristic costs. Therefore, our methodology offers more flexibility during the routing selection process, which may help to improve the quality of service offered to clients

A multi-criteria decision support system for a routing problem in waste collection

Autor proofThis work presents a decision support system for route planning of vehicles performing waste collection for recycling. We propose a prototype system that includes three modules: route optimization, waste generation prediction, and multiple-criteria decision analysis (MCDA). In this work we focus on the application of MCDA in route optimization. The structure and functioning of the DSS is also presented. We modelled the waste collection procedure as a routing problem, more specifically as a team orienteering problem with capacity constraints and time windows. To solve the route optimization problem we developed a cellular genetic algorithm. For the MCDA module, we employed three methods: SMART, ValueFn and Analytic Hierarchy Process (AHP). The decision support system was tested with real-world data from a waste management company that collects recyclables, and the capabilities of the system are discussed.FCT Fundação para a Ciência e Tecnologia, Project Scope: PEst-OE/EEI/UI0319/2

Solving Area Coverage Problem with UAVs: A Vehicle Routing with Time Windows Variation

In real life, providing security for a set of large areas by covering the area with Unmanned Aerial Vehicles (UAVs) is a difficult problem that consist of multiple objectives. These difficulties are even greater if the area coverage must continue throughout a specific time window. We address this by considering a Vehicle Routing Problem with Time Windows (VRPTW) variation in which capacity of agents is one and each customer (target area) must be supplied with more than one vehicles simultaneously without violating time windows. In this problem, our aim is to find a way to cover all areas with the necessary number of UAVs during the time windows, minimize the total distance traveled, and provide a fast solution by satisfying the additional constraint that each agent has limited fuel. We present a novel algorithm that relies on clustering the target areas according to their time windows, and then incrementally generating transportation problems with each cluster and the ready UAVs. Then we solve transportation problems with the simplex algorithm to generate the solution. The performance of the proposed algorithm and other implemented algorithms to compare the solution quality is evaluated on example scenarios with practical problem sizes