Evolution-inspired local improvement algorithm solving orienteering problem

The orienteering problem (OP) is defined on a graph with scores assigned to the vertices and weights attached to the links. The objective of solutions to the OP is to find a route over a subset of vertices, limited in length, that maximizes the collective score of the vertices visited. In this paper we present a new, efficient method for solving the OP, called the evolution-inspired local improvement algorithm (EILIA). First, a multi-stage, hill climbing-based method is used to improve an initial random population of routes. During the evolutionary phase, both feasible and infeasible (routes that are too long) parts of the solution space are explored and exploited by the algorithm operators. Finally, infeasible routes are repaired by a repairing method. Computer testing of EILIA is conducted on popular data sets, as well as on a real transport network with 908 nodes proposed by the authors. The results are compared to an exact method (branch and cut) and to the best existing algorithms for OP. The results clearly show that EILIA outperforms existing heuristic methods in terms of the quality of its solutions. In many cases, EILIA produces the same results as the exact method.