Solving Multiobjective Optimization Problems with Inequality Constraint Using An Augmented Lagrangian Function

We propose a method for solving multiobjective optimization problems under the constraints of inequality. In this method, the initial problem is transformed into a single-objective optimization without constraints using an augmented Lagrangian function and an ϵ-constraint approach. Indeed, the augmented Lagrangian function is used to convert a given problem with multiple objective functions into a single objective function. The ϵ-constraint approach allows for the transformation of constrained optimization problems into unconstrained optimization problems. To demonstrate the admissibility and Pareto optimality of the obtained solutions, we have provided two propositions with proofs. In addition, a comparison study is made with two other well-known and widely used methods, such as NSGA-II and BoostDMS, on convergence and distribution of obtained solutions using numerical results for fifty test problems taking in the literature. Based on all these theoretical and numerical results, we can say that the proposed method is the best way to solve multiobjective optimization problems.