A clustering procedure for reducing the number of representative solutions in the Pareto Front of multiobjective optimization problems

In many multiobjective optimization problems, the Pareto Fronts and Sets contain a large number of solutions and this makes it difficult for the decision maker to identify the preferred ones. A possible way to alleviate this difficulty is to present to the decision maker a subset of a small number of solutions representatives of the Pareto Front characteristics. In this paper, a two-steps procedure is presented, aimed at identifying a limited number of representative solutions to be presented to the decision maker. Pareto Front solutions are first clustered into "families", which are then synthetically represented by a "head-of-the-family" solution. Level Diagrams are then used to represent, analyse and interpret the Pareto Front reduced to its head-of-the-family solutions. The procedure is applied to a reliability allocation case study of literature, in decision-making contexts both without or with explicit preferences by the decision maker on the objectives to be optimized.