A variable space search heuristic for the Capacitated Team Orienteering Problem

The Capacitated Team Orienteering Problem (CTOP) is a variant of the well-known Team Orienteering Problem where additional capacity limitation constraints are considered for each vehicle. Solving CTOP consists of organizing a set of routes that maximize the total profit collected from the served customers while taking into consideration the capacity and travel time limitation for each vehicle. In this paper, we propose a variable space search heuristic to solve CTOP. Our algorithm alternates between two search spaces: the giant tour and routes search spaces. We develop a hybrid heuristic as a framework for our algorithm composed of a combination between Greedy Randomized Adaptive Search Procedure and Evolutionary Local Search. Several local search techniques were developed in each search space to improve the quality of the solutions and the giant tours. A dedicated optimal split procedure and a concatenation technique are performed to ensure the link between the search spaces. This approach shows its high performance on the benchmark of CTOP, and proves its competitiveness in comparison to the other heuristic methods available in the literature as it yields to strict improvements with small computational time.