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In the present paper, we study the behaviour of a hybrid Iterative Local Search heuristic (ILS). A Large Neighborhood Search heuristic (LNS) and a Variable Neighborhood Descent with Random neighborhood ordering (RVND) are used in the local search phase of the proposed ILS. The approach is evaluated on a well-known variant of the Vehicle Routing Problem (VRP) called Capacitated Profitable Tour Problem (CPTP). In this variant, the vehicles are no longer required to visit all the customers. However, a specific profit is obtained each time a customer is visited. The goal of the CPTP is to design routes with maximum difference between collected profits and routing costs, which satisfy the capacity constraint of the vehicles. The experimental study consists in comparing different combinations of ILS, LNS and RVND. The computational results show that the hybridization of the three heuristics leads to better solutions. Furthermore, comparisons with a Variable Neighborhood Search and two Tabu Searches from the literature indicates that our hybrid approach is competitive.

Behaviour of a Hybrid ILS Heuristic on the Capacitated Profitable Tour Problem