A Parallel Memetic Algorithm to Solve the Vehicle Routing Problem with Time Windows

TL;DR

This paper introduces a parallel memetic algorithm designed to efficiently solve the vehicle routing problem with time windows, optimizing fleet size and total travel distance through cooperative parallel heuristics.

Contribution

It proposes a novel two-phase parallel approach combining heuristic and memetic algorithms for VRPTW, demonstrating high convergence and robustness.

Findings

High convergence capabilities of the algorithms

Robustness demonstrated on benchmark instances

Speedup analysis confirms efficiency

Abstract

This paper presents a parallel memetic algorithm for solving the vehicle routing problem with time windows (VRPTW). The VRPTW is a well-known NP-hard discrete optimization problem with two objectives. The main objective is to minimize the number of vehicles serving customers scattered on the map, and the second one is to minimize the total distance traveled by the vehicles. Here, the fleet size is minimized in the first phase of the proposed method using the parallel heuristic algorithm (PHA), and the traveled distance is minimized in the second phase by the parallel memetic algorithm (PMA). In both parallel algorithms, the parallel components co-operate periodically in order to exchange the best solutions found so far. An extensive experimental study performed on the Gehring and Homberger's benchmark proves the high convergence capabilities and robustness of both PHA and PMA. Also, we present the speedup analysis of the PMA.