Representation of solution for multiobjective optimization: RSMO for generating a Su sant Pareto front

Summary form only given. Multi-objective optimization problems are very common in the process of engineering design optimization. They are ones of the hardest optimization problems, which arise in many real-word applications. There exist a plethora of methods for solving these problems. Most of them use iterative process to generate a set of points approximating the Pareto set in a single simulation run (Evolutionary Multi-objective Optimization methods) or by transforming the multi-objective problems to a series of single optimization problems (weighting sum method, e constraint, Normal Boundary Intersection method, Normal constraint method,...). In practice, we seek to obtain enough points to cover the Pareto front with a sufficient number of solutions. The quality of the obtained results is judged by its ability to generate an evenly distributed curve. Therefore a convenient strategy is to be adopted to avoid high costs. In this paper, a novel approach to generate a sufficient Pareto points to represent the optimal solutions along the Pareto frontier(RSMO) is proposed. This approach can be regarded as a representation formula of the solution of the multi-objective optimization. The multi-objective problem is transformed to a minimization of integral which involves diffierent functions to be optimized. The method deals with both convex and non-convex problems. However, in this paper, we restrict our study to convex problems. To demonstrate the efficiency and the accuracy of the new method, four typical convex multi-objective test functions were chosen from the global optimization literature. RSMO is compared to some very used multi-objective optimization methods inengineering optimization. For this comparison were used the followings algorithms : Normalized Normal Constraint (NNC), Normal Boundary Intersection (NBI)