Generating Pareto Optimal Solutions for Multi-Objective Optimization Problems Using Goal Programming (Contemporary Mathematics, 2024)
Goal programming (GP) is a well-known multi-criteria decision-making tool that is supported by a network of practitioners and researchers who aim to develop its mathematical foundation to cover a wide range of applications. The popularity of GP models stems from their structure, which is based on a satisfying philosophy. This philosophy takes into consideration the preferences of the decision-maker concerning the model parameters. Therefore, the GP model provides the decision-maker with one satisfactory solution that reflects the trade-off between competing objectives. Nevertheless, there is no guarantee regarding the efficiency of this solution. Consequently, this study is designed to improve the quality of decision-making processes by addressing the efficiency issue with the solutions of GP models. The main contribution of this paper is to improve the mathematical framework of the GP model so that it can generate a set of Pareto optimal solutions rather than just one solution. This allows stakeholders to have a complete picture of the feasible space of solutions and select the solution that represents the best compromise according to their preferences. As a result, the proposed methodology is called generational GP. In addition, the study enhances the quality of GP solutions by integrating the notion of the hypervolume subset selection problem with the suggested technique. This, in turn, overcomes the efficiency problem of GP solutions. The performance of the proposed method has been validated through an application to the flow shop scheduling problem. However, our modeling approach is useful for decision-makers in different fields of study. Finally, the merits of the generational GP method are highlighted, with a strong emphasis on potential areas for future research.
Keywords: multi-objective optimization problems; Pareto optimal solutions; generational GP; hypervolume subset selection problem; green permutation flowshop scheduling problem