Multi Criteria Decision Making: a tool to take decisions in Multi Objective Optimization
Mattia Ciprian, Nader Fateh, Valentino Pediroda, Carlo Poloni · AIAA Infotech@Aerospace 2007 Conference and Exhibit · 2007
Many real-world engineering design involve simultaneous optimization of multiple objectives, with remarkable differences with the single-objective optimization. The goal of the single-objective optimization is finding the best solution, which corresponds to the maximum value of one objective function. On the contrary, in the multi-objective case, the goal is to find the best compromise solutions between the different conflicting criterions. For these reasons, new optimization approaches are needed. The Pareto approach (inside the Game Theory methodology) has been demonstrated as an efficient way to solve problems with multicriterion choice; by following this approach one could achieve not only a solution, but a set with the best compromise designs among different objectives. Since only one design among all the alternatives could be put on production, an efficient way to select the more appropriate alternative is needed. In the final Pareto set all the solutions are non dominated but only one is the best compromise according to the project manager requirements. In order to solve the choosing problem, a useful numeric tool comes to the aid: Multi Criteria Decision Making (MCDM). MCDM is both an approach and a set of techniques, with the goal of providing an overall ordering of designs, starting from the most preferred to the least preferred one. In this paper different MCDM techniques are adopted, in order to understand the capability and the differences between the different algorithms. The database is the optimal Pareto set of an aeronautic example, the multi objective design of a transonic airfoil with uncertainties.