Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms

Appolinaire Tougma, K. Some
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Abstract

This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison.
多目标优化算法的增量拉格朗日不精确指数惩罚函数
本文使用基于非精确指数惩罚函数的增强拉格朗日法来解决受约束的多目标优化问题。本研究提出了两种算法。第一种算法使用梯度投影法,第二种算法使用最陡下降法。通过这些算法,我们能够生成一组近似初始问题帕累托最优解的非支配点。我们还针对生成的帕累托静止点集合的两种不同标准,提出了一些理论收敛性证明。此外,我们还比较了我们的方法和 NSGA-II 以及文献中一些测试问题的增强拉格朗日锥法。对所得解的数值分析表明,我们的方法在用于比较的测试问题上具有竞争力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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