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

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.

Hyperbolic Augmented Lagrangian algorithm for multiobjective optimization problems

“…In this case, the concept of Pareto optimality is used, demonstrating an optimal solution to a multiobjective problem. In recent years, multiobjective optimization concepts have proven valuable for solving a wide variety of problems in various domains, including physics, economics, transportation, social choice, and many others [27,38,39].…”