Numerical algorithms for generating an almost even approximation of the Pareto front in nonlinear multi-objective optimization problems

A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important fea...

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Vydáno v:Applied soft computing Ročník 165; s. 112001
Hlavní autoři: Dolatnezhadsomarin, Azam, Khorram, Esmaile, Yousefikhoshbakht, Majid
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.11.2024
Témata:
Hyperplane
Multi-objective optimization problem
Pareto front
Pareto optimal solution
Pascoletti-Serafini scalarization approach
Pareto optimal solution
Pareto front
Pascoletti-Serafini scalarization approach
Multi-objective optimization problem
Hyperplane
ISSN:1568-4946
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Shrnutí:A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important features of this approximation is a uniform distribution of points on the full Pareto front in order to present a wide variety of solutions to the decision maker who chooses a final solution. While a few algorithms consider this property, two algorithms based on the Pascoletti-Serafini (PS) scalarization approach are proposed. In addition, six well-known test problems with convex and non-convex Pareto fronts are considered to show the effectiveness of the proposed algorithms. Their results are compared with some algorithms including Normal Constraint (NC), Benson type, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), S-Metric Selection Evolutionary Multiobjective Algorithm (SMS-EMOA), Differential Evolution (DE) with Binomial Crossover and MOEA/D-DE. The computational results on CPU time and reasonable distribution of points obtained on the Pareto front show that the presented algorithms perform better than other algorithms on these criteria. In addition, although the proposed algorithms compete closely with some algorithms in terms of CPU time, they have more non-dominated solutions and more appropriate distribution than they do in most problems. [Display omitted] •Two modified Pascoletti-Serafini scalarization approach are proposed.•Six well-known test problems with convex and non-convex Pareto fronts are applied to show effectiveness of the algorithms.•The presented algorithms have acceptable performance with regarding to the other algorithms.
ISSN:1568-4946
DOI:10.1016/j.asoc.2024.112001