An efficient evolutionary algorithm for the orienteering problem

Abstract

This paper deals with the Orienteering Problem, which is a routing problem. In the Orienteering Problem, each node has a profit assigned and the goal is to find the route that maximizes the total collected profit subject to a limitation on the total route distance. To solve this problem, we propose an evolutionary algorithm, whose key characteristic is to maintain unfeasible solutions during the search. Furthermore, it includes a novel solution codification for the Orienteering Problem, a novel heuristic for node inclusion in the route, an adaptation of the Edge Recombination crossover developed for the Travelling Salesperson Problem, specific operators to recover the feasibility of solutions when required, and the use of the Lin-Kernighan heuristic to improve the route lengths. We compare our algorithm with three state-of-the-art algorithms for the problem on 344 benchmark instances, with up to 7397 nodes. The results show a competitive behavior of our approach in instances of low-medium dimensionality, and outstanding results in the large dimensionality instances reaching new best known solutions with lower computational time than the state-of-the-art algorithms.