Hybrid PACO with enhanced pheromone initialization for solving the vehicle routing problem with time windows

The Vehicle Routing Problem with Time Windows (VRPTW) is a well-known combinatorial optimization problem found in many practical logistics planning operations. While exact methods designed for solving the VRPTW aim at minimizing the total distance traveled by the vehicles, heuristic methods usually employ a hierarchical objective approach in which the primary objective is to reduce the number of vehicles needed to serve the customers while the secondary objective is to minimize the total distance. In this paper, we apply a holistic approach that optimizes both objectives simultaneously. We consider several state-of-the-art Ant Colony Optimization (ACO) techniques from the literature, including the Min-Max Ant System, Ant Colony System, and Population-based Ant Colony Optimization (PACO). Our experimental investigation shows that PACO outperforms the others. Subsequently, we introduce a new pheromone matrix initialization approach for PACO (PI-PACO) that uses information extracted from the problem instance at hand and enforces pheromone assignments to edges that form feasible building blocks of tours. Our computational tests show that PI-PACO performs better than PACO. To further enhance its performance, we hybridize it with a local search method. The resulting algorithm is efficient in producing high quality solutions and outperforms similar hybrid ACO techniques.