(R1886) Effect of Aggregation Function in MOMA-Plus Method For Obtaining Pareto Optimal Solutions

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

Dirichlet’s problem on a cracked trapezium

This paper deals with solving Poisson’s equation with conditions on Dirichlet’s limits in an isosceles trapezium with two cracks. The large singular finite elements method used gives satisfactory results in all the domain of study. Numerical values obtained are very accurate for the constraint function and its first derivatives except at the ends of cracks where major changes were registered.Keywords: Large elements, finite elements, singularities, crack