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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]

We propose a new metaheuristic, HmGWOGA-MO, for solving multiobjective optimization problems operating with a population of solutions. The method is a hybridization of the HmGWOGA method, which is a single objective optimization method, and the ϵ-constraint approach, which is an aggregation technique. The ϵ-constraint technique is one of the best ways to transform a problem with many objective functions into a single objective problem because it works even if the problem has any kind of Pareto optimal front. Previously, the HmGWOGA method was designed to optimize a positive single-objective function without constraints. The obtained solutions are good. That is why, in this current work, we combined have it with the ϵ-constraint approach for the resolution of multiobjective optimization problems. Our new method proceeds by transforming a given multiobjective optimization problem with constraints into an unconstrained optimization of a single objective function. With the HmGWOGA method, five different test problems with varying Pareto fronts have been successfully solved, and the results are compared with those of NSGA-II regarding convergence towards the Pareto front and the distribution of solutions on the Pareto front. This numerical study indicates that HmGWOGA-MO is the best choice for solving a multiobjective optimization problem when convergence is the most important performance parameter. [ABSTRACT FROM AUTHOR]

In this work, we have proposed some variants of MOMA-Plus method that we have numerically tested for the resolution of nonlinear multiobjective optimization problems. This MOMA-Plus method and variants differ from each other by the choice of aggregation functions in order to reduce the number of objective functions. The theoretical results allowing us to use these aggregation functions to transform multiobjective optimization problems into single objective optimization problems are proved by two theorems. This study has highlighted the advantages of each aggregation function according to the type of Pareto front of the optimization problem. Six benchmarks test problems have been solved in this work by each of these methods and a comparative study was carried out through the performance indicators which are the differentiation with Pareto front, the convergence to the Pareto front and distributivity on the Pareto front. This allowed us to classify these methods on these benchmarks by using the Graphical Analysis for Interactive Assistance (GAIA) method. [ABSTRACT FROM AUTHOR]

This work is devoted to evaluate the performances of the MOMA-Plus method in solving multiobjective optimization problems. This assessment is doing on the complexity of its algorithm, the convergence and the diversity of solutions in relation to the Pareto front. All these parameters were evaluated on non-linear multiobjective test problems and obtained solutions are compared with those provided by the NSGA-II method. This comparative study made it possible to highlight the performances of MOMA-Plus method for solving non-linear multiobjective problems. [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]