An iterated local search algorithm for the team orienteering problem with variable profits

ABSTRACT

The orienteering problem (OP) is a routing problem that has numerous applications in various domains such as logistics and tourism. The objective is to determine a subset of vertices to visit for a vehicle so that the total collected score is maximized and a given time budget is not exceeded. The extensive application of the OP has led to many different variants, including the team orienteering problem (TOP) and the team orienteering problem with time windows. The TOP extends the OP by considering multiple vehicles. In this article, the team orienteering problem with variable profits (TOPVP) is studied. The main characteristic of the TOPVP is that the amount of score collected from a visited vertex depends on the duration of stay on that vertex. A mathematical programming model for the TOPVP is first presented and an algorithm based on iterated local search (ILS) that is able to solve modified benchmark instances is then proposed. It is concluded that ILS produces solutions which are comparable to those obtained by the commercial solver CPLEX for smaller instances. For the larger instances, ILS obtains good-quality solutions that have significantly better objective value than those found by CPLEX under reasonable computational times.

KEYWORDS:

• Orienteering problem
• variable profit
• mathematical programming model
• iterated local search

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Kien Ming Ng http://orcid.org/0000-0002-5372-0373

Graham Kendall http://orcid.org/0000-0003-2006-5103