An Optimal Algorithm for the Orienteering Tour 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.

A branch and cut approach to the cardinality constrained circuit problem

“…The objective is to find a route R starting and ending at v 0 that maximizes the total collected reward ( v∈V(R) p v ) subject to the constraint that the total travel cost ( e∈R t e ) is less than Q. Heuristics for solving the OP are given by Golden et al [17] and Ramesh et al [34]; and polyhedral approaches for OP are given by Fischetti et al [14] and Leifer and Rosenwein [26].…”

A Bi-Modal Routing Problem with Cyclical and One-Way Trips: Formulation and Heuristic Solution

“…The Orienteering Problem also contains rewards at each node; the objective is to maximise the total reward collected subject to a time constraint. See, for example, Golden et al [13] and Ramesh et al [14].…”

Operational Planning for Multiple Heterogeneous Unmanned Aerial Vehicles in Three Dimensions

“…Ramesh, Yoon, and Karwan developed an exact method using a branchand-bound algorithm that utilizes the Lagrangian relaxation and problem reformulation to obtain an integer solution [35].…”