Prof. Olaf Frommann, Hochschule Bremen, Institut für Aerospace Technologie

Title:
About the Dilemma of Contradictory Goals in Multi-Objective Optimization

Abstract:

Multi-Objective Optimization often leads to the problem of dealing with competing and contradictory goals, that need to be satisfied. The question is, how much each single one of them is fulfilled in relation to the others. The inderdependencies can be visualized by the so-called Pareto Front, which shows the limit, where one goal can only be improved if the quality of another is degraded. Nevertheless, one needs to decide which combination of qualities is satisfactory. Usually, this is accomplished by the application of a weighted sum for the criteria within the objective function. Despite the fact that the choice of the weighting factors is rather arbitrary, it will only work on convex Pareto Fronts. It will be shown that, if there are concave sections, this approach cannot describe every possible combination of goals. As a solution to this limitation an alternative way to set up the objective function will be proposed. An additional advantage is the inherent simplicity in assessing single criteria and their interdependencies.