Two modified Pascoletti–Serafini methods for solving multiobjective optimization problems and multiplicative programming problems

• Published in: Soft computing (Berlin, Germany) Germany), 2023-11, Vol.27 (21), p.15675-15697
• Main Authors: Dolatnezhadsomarin, Azam, Khorram, Esmaile, Yousefikhoshbakht, Majid
• Format: Article
• Language: English
• Subjects: Algorithms; Approximation; Artificial Intelligence; Computational Intelligence; Continuity (mathematics); Control; Convex analysis; Engineering; Linear programming; Mathematical Logic and Foundations; Mechatronics; Methods; Multiple objective analysis; Optimization; Pareto optimization; Pareto optimum; Programming; Robotics
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-023-08809-2

In this paper, a modified Pascoletti–Serafini scalarization approach, called MOP_MPS, is proposed to generate approximations of a Pareto front of bounded multi-objective optimization problems (MOPs). The objective is obtaining some points with an almost even distribution overall Pareto front. This algorithm is applied to six test problems with convex, non-convex, connected, and dis-connected Pareto fronts, and its results are compared with results of some famous algorithms. The results emphasize that MOP_MPS is effective and competitive in comparing with the other considered algorithms. In addition, it is shown that an optimal solution of a multiplicative programming problem is a properly Pareto optimal solution of an MOP. By considering this relation between MOPs and multiplicative programming problems (MPPs), another algorithm based on MOP_MPS, called MPP_MPS, is suggested for approximately solving non-linear MPPs in which functions multiplied are continuous and bounded from below. The computational results on seven problems of convex MPPs demonstrate that the algorithm is much better than a cut and bound algorithm presented by Shao and Ehrgott in terms of CPU time.