A Genetic Algorithm in Combination with a Solution Archive for Solving the Generalized Vehicle Routing Problem with Stochastic Demands

Abstract

This work presents a steady-state genetic algorithm enhanced by a complete trie-based solution archive for solving the generalized vehicle routing problem with stochastic demands using a preventive restocking strategy. As the necessary dynamic programming algorithm for the solution evaluation is very time consuming, considered candidate solutions are stored in the solution archive. It acts as complete memory of the search history, avoids reevaluations of duplicate solution candidates, and is able to efficiently transform them into guaranteed new ones. This increases the diversity of the population and reduces the risk of premature convergence. Similar to a branch-and-bound algorithm, the tree structure of the solution archive is further exploited to compute lower bounds on the nodes to cut off parts of the solution space that evidently do not contain good solutions. Since in each iteration a not yet considered solution candidate is generated and completeness can be efficiently checked, the overall method is in principle an exact enumeration algorithm, which leads to guaranteed optimal solutions for smaller instances. Computational results of this algorithm show the superiority over the so far state-of-the-art metaheuristic and also prove its effectiveness on the nongeneralized version of this problem.