A unified matheuristic for solving multi-constrained traveling salesman problems with profits

In this paper, we address a rich Traveling Salesman Problem with Profits encountered in several real-life cases. We propose a unified solution approach based on variable neighborhood search. Our approach combines several removal and insertion routing neighborhoods and efficient constraint checking procedures. The loading problem related to the use of a multi-compartment vehicle is addressed carefully. Two loading neighborhoods based on the solution of mathematical programs are proposed to intensify the search. They interact with the routing neighborhoods as it is commonly done in matheuristics. The performance of the proposed matheuristic is assessed on various instances proposed for the Orienteering Problem and the Orienteering Problem with Time Window including up to 288 customers. The computational results show that the proposed matheuristic is very competitive compared with the state-of-the-art methods. To better evaluate its performance, we generate a new testbed including instances with various attributes. Extensive computational experiments on the new testbed confirm the efficiency of the matheuristic. A sensitivity analysis highlights which components of the matheuristic contribute most to the solution quality.