Multi-objective Evolutionary Algorithm Based on Decomposition with Adaptive Adjustment of Control Parameters to Solve the Bi-objective Internet Shopping Optimization Problem (MOEA/D-AACPBIShOP)

Abstract

The main contribution of this paper is the implementation of a multi-objective evolutionary algorithm based on decomposition with adaptive adjustment of control parameters applied to the bi-objective problem of Internet shopping (MOEA/D-AACPBIShOP). This problem considers minimizing the total cost of the shopping list and shipping time. The proposed MOEA/D-AACPBIShOP algorithm obtains an approximate Pareto set for nine types of real-world instances classified as small, medium, and large. The instances are obtained using the Web Scraping technique, extracting some information attributes of technological products from the Amazon site. This optimization problem is a very little studied variant of the Internet Shopping Problem (IShOP). The proposed algorithm is compared with two multi-objective algorithms: A Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the basic MOEA/D version. The results demonstrate that the three algorithms studied have a similar statistical performance with respect to the quality of the solutions they provide. To evaluate thse algorithms, the following metrics were used: Hypervolume, Generalized Dispersion, and Inverted Generational Distance. Additionally, the non-parametric Wilcoxon and Friedman tests are applied to validate the results obtained with a significance level of 5%.