A Novel Particle Swarm Optimization Algorithm to Solve the Internet Shopping Optimization Problem with Shipping Costs

Abstract

In this paper, we approach the Internet Shopping Optimization Problem with Shipping Costs (IShOP), an NP-hard-relevant problem in the current e-commerce environment. To our knowledge, several solution metaheuristic algorithms have been reported in the literature. In this paper, we propose a novel Particle Swarm Optimization algorithm (PSO) to solve the problem. PSO incorporates a neighborhood diversification technique (NDT), a local search (LS) technique, and an adaptive parameter tuning (APT) method. The proposed algorithm (NDTLSAA-PSO) includes two techniques at the end of each iteration to avoid premature convergence in the search process, balancing exploration and exploitation in selecting candidate solutions. A comparison of the performance of the proposed algorithm has been made against the performance of the best state-of-the-art memetic algorithm solution of the IShOP. A total of 90 instances classified into three groups of small, medium, and large sizes were resolved. The Wilcoxon and Holm non-parametric tests were applied to validate the significance of the differences observed between these two algorithms. The results show that the proposed NDTLSAA-PSO algorithm is superior to the memetic algorithm. In addition, the proposed algorithm obtains the best results in all the in-stances evaluated in terms of quality.