A multiobjective optimization approach via systematical modification of the desirability function shapes

In this study, a method for solution of the multi-objective optimization problems via the desirability function aided particle swarm optimization has been proposed. The desirability function has been applied for normalization of each objective and then aggregation to a single objective. The geometric mean of the desirability values regarding each objective has been calculated as a part of the method. On the other hand, using a single-objective optimization algorithm yields a single solution rather than a complete solution set. Hence, the idea of changing the shapes of the desirability functions is implemented in order to achieve a complete solution set; in fact, this constitutes the main theme of this study. Therefore, the multi-objective problem has been degraded to a single-objective one, and it has been solved numerous times for each alternative desirability function shape. As a result, a set of biased solutions has been obtained in a very practical manner.