Abstract
Vehicle Routing Problems (VRP) comprise many variants obtained by adding to the original problem constraints representing diverse system characteristics. Different variants are widely studied in the literature; however, the impact that these constraints have on the structure of the search space associated with the problem is unknown, and so is their influence on the performance of search algorithms used to solve it. This article explores how assignation constraints (such as a limited vehicle capacity) impact VRP by disturbing the network structure defined by the solution space and the local operators in use. This research focuses on Fitness Landscape Analysis for the multiple Traveling Salesman Problem (m-TSP) and Capacitated VRP (CVRP). We propose a new Fitness Landscape Analysis measure that provides valuable information to characterize the fitness landscape’s structure under specific scenarios and obtain several relationships between the fitness landscape’s structure and the algorithmic performance.
Highlights
The Capacitated Vehicle Routing Problem (CVRP) is a classical combinatorial optimization problem that has attracted much attention given its many applications and the difficulty of obtaining good solutions. (Even Traveling Salesman Problem (TSP), the simplest variant of Vehicle Routing Problems (VRP), is NP-complete—for more detailed complexity considerations the reader is referred to [1])
We focus on multiple Traveling Salesman Problem (m-TSP) and CVRP, which corresponds to a transition from an unconstrained base problem to problems restricted at various levels of vehicle capacity
We explore (1) the potential of using standard Fitness Landscape Analysis (FLA) measures and the one that we propose to differentiate between fitness landscapes obtained by using different representations and local operators and (2) the possibility to use information, statistical and feasibility FLA measures to predict the difficulty of searching the fitness landscape of a VRP instance with Simulated Annealing
Summary
The Capacitated Vehicle Routing Problem (CVRP) (the reader is referred to the monograph by Toth and Vigo [1] for an introduction to Vehicle Routing Problems) is a classical combinatorial optimization problem that has attracted much attention given its many applications and the difficulty of obtaining good solutions. (Even TSP, the simplest variant of VRP, is NP-complete—for more detailed complexity considerations the reader is referred to [1]). CVRP models the following situation: Given a central depot, a set of customers with known demands, and a set of vehicles of equal capacity, we need to choose a set of economic routes that allows delivering the amount of product requested by the customers without exceeding the vehicle capacity, where each customer is visited exactly once This situation is quite distant from real-life distribution systems, but provides a context for different formulations and variants which has led to the development of a wide range of algorithms that yield good solutions. Vidal et al [2] provides a detailed review of the evolution of VRP solution methods for variants that include many additional characteristics and decisions, called attributes In this context, hybrid algorithms have exhibited the best performance for VRP, both from the solution quality and the computational time points of view.
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