An accelerated method for solving constrained multi-objective optimization

Salehi Mokari, Niloofar; Basirzadeh, Hadi; Morovati, Vahid

doi:10.22124/jmm.2025.30721.2753

An accelerated method for solving constrained multi-objective optimization

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

² Department of Mathematics, University of Hormozgan, Bandarabbas, Iran

10.22124/jmm.2025.30721.2753

Abstract

A novel non-parametric algorithm is introduced for solving constrained multi-objective optimization problems. At each iteration, a convex sub-problem is solved to determine the search direction, while a non-monotone line search technique is used to determine the step size. An adaptive acceleration term, computed from changes in the search directions, is incorporated to scale the step and dynamically enhance convergence performance. The algorithm’s effectiveness relies on a diverse set of initial feasible solutions to accurately approximate the non-dominated boundary. Benchmark tests validate the approach, with Pareto fronts compared to those obtained using the Zoutendijk method. Numerical evaluations demonstrate superior performance in terms of convergence rate and solution quality. The algorithm is also applied to a real-world engineering design problem involving speed reduction, highlighting its computational efficiency and robustness in practical applications.

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