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This paper presents a technique for addressing multiobjective optimization issues subject to inequality constraints. This technique converts the original problem into a single-objective optimization without constraints by employing an augmented Lagrangian function and an ϵ-constraint method. Specifically, the augmented Lagrangian function transforms problems with multiple objectives into a single objective function, while the ϵ-constraint method changes constrained optimization problems into unconstrained ones. We provide two propositions complete with proofs to verify the admissibility and Pareto optimality of the solutions derived. Furthermore, we conduct a comparative analysis with two established methods, NSGA-II and BoostDMS, focusing on the convergence and distribution of solutions across fifty test problems sourced from existing literature. The collective theoretical and empirical evidence suggests that our proposed method is superior for solving multiobjective optimization problems. [ABSTRACT FROM AUTHOR]

In this article, we propose an adaptation of the Hyperbolic Augmented Lagrangian algorithm to solve multiobjective optimization problems. After conducting a literature review, we provide a definition of the Hyperbolic Augmented Lagrange method. Under clearly defined assumptions, we demonstrate that any limit point of a sequence generated by the proposed approach is feasible and constitutes a Pareto-optimal solution. To assess the effectiveness of the proposed algorithm, we incorporate two variants of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, thereby offering two approaches for solving well-known tests problems from the literature. We employ metrics to evaluate the performance of these two approaches. [ABSTRACT FROM AUTHOR]

This paper proposes an algorithm for solving multiobjective optimization problems using the attack technique of the Grey Wolf. It is a metaheuristic method called a Multiobjective Optimizer based on Grey Wolf Attack Technique (MOGWAT). In fact, it is inspired by the modified Hybrid Grey Wolf Optimizer and Genetic Algorithm (HmGWOGA), which is a single objective optimization algorithm specially designed for positive objective functions. The MOGWAT method combines the multiple objective functions of the initial problem into a single objective function, and then penalizes constraint functions to get an unconstrained single-objective optimization. The use of an effective single-objective optimizer allows reaching the optimal solutions. These solutions are also the Pareto optimal solutions of the initial problem according to some parameters. Through some theorems, we have established the theoretical foundation and performance of our method. Furthermore, in order to highlight the numerical performance of the method, we have tackled three groups of problems: 16 test problems from the Zitzler-Deb-Thiele benchmarks, 2 instances from the CEC 2009 benchmarks, and 2 real-world problems from literature. Our numerical results have been compared to the ones obtained with the NSGA-II method. This comparison was made using some computed performance parameters. The outcomes of the comparison have enabled us to prove the effectiveness and efficiency of our new approach in terms of speed and convergence. [ABSTRACT FROM AUTHOR]