Enhancement on the modified artificial bee colony algorithm to optimize the vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW) is a non-deterministictime hard (NP-hard) with combinatorial optimization problem (COP). The Artificial Bee Colony (ABC) is a popular swarm intelligence algorithm for COP. In this study, existing Modified ABC (MABC) algorithm is revised to solve the VRPTW. While MABC has been reported to be successful, it does have some drawbacks, including a lack of neighbourhood structure selection during the intensification process, a lack of knowledge in population initialization, and occasional stops proceeding the global optimum. This study proposes an enhanced Modified ABC (E-MABC) algorithm which includes (i) N-MABC that overcomes the shortage of neighborhood selection by exchanging the neighborhood structure between two different routes in the solution; (ii) MABC-ACS that solves the issues of knowledge absence in MABC population initialization by incorporating ant colony system heuristics, and (iii) PMABC which addresses the occasional stops proceeding to the global optimum by introducing perturbation that accepts an abandoned solution and jumps out of a local optimum. The proposed algorithm was evaluated using benchmark datasets comprising 56 VRPTW instances and 56 Pickup and Delivery Problems with Time Windows (PDPTW). The performance has been measured using the travelled distance (TD) and the number of deployed vehicles (NV). The results showed that the proposed E-MABC has lower TD and NV than the benchmarked MABC and other algorithms. The E-MABC algorithm is better than the MABC by 96.62%, MOLNS by 87.5%, GAPSO by 53.57%, MODLEM by 76.78%, and RRGA by 42.85% in terms of TD. Additionally, the E-MABC algorithm is better than the MABC by 42.85%, MOLNS by 17.85%, GA-PSO and RRGA by 28.57%, and MODLEN by 46.42% in terms of NV. This indicates that the proposed E-MABC algorithm is promising and effective for the VRPTW and PDPTW, and thus can compete in other routing problems and COPs.