Multi-objective Evolutionary Algorithm Based on Decomposition to Solve the Bi-objective Internet Shopping Optimization Problem (MOEA/D-BIShOP)

The main contribution of this paper is to develop a new solution method applied to the bi-objective Internet shopping problem. The first objective of this problem considers minimizing the total cost of the shopping list, and the second objective is minimizing the shopping list delivery time. This solution consists of a Multi-objective Evolutionary Algorithm Based on Decomposition to Solve the Biobjective Internet Shopping Optimization Problem (MOEA/D-BIShOP). The proposed MOEA/D-BIShOP algorithm obtains an approximate Pareto optimal set for nine types of real-world instances classified according to their size into small, medium, and large. These instances have been obtained through web scraping, which consists of extracting information from some technology products on the Amazon site. The Biobjective Internet shopping optimization problem is different from the Internet shopping optimization problem because it considers the purchase cost and the delivery conditions of each product. This algorithm is compared to the state-of-the-art work by applying two heuristics to each objective respectively and obtaining an approximate Pareto Front (APF), transforming the second objective function into a constraint within an integer linear programming algorithm. The results demonstrate that the proposed algorithm (MOEA/D-BIShOP) has equal statistical performance compared to the only work from the state-of-the-art. Three metrics were used: Hypervolume, Generalized Dispersion, and Inverted Generational Distance. The non-parametric Wilcoxon and Friedman test is applied to validate the results obtained with a significance level of 5%.