Development of Post-Pareto Optimality Methods for Multiple Objective Optimization

In the past years, multiple objective optimization has been considered, as an important research area since in many real life problems there exists multiple criteria that need to be optimized simultaneously. The use of evolutionary algorithms or metaheuristic methods as solution methodologies lead to a large number of Pareto solutions rather than a single unique optimum. This Pareto-optimal set most of the time tends to be very large and the decision maker now faces the challenge of reducing its size to analyze a feasible number of solutions, thus deciding the best possible solution. In this work, two methods will be introduced for post-Pareto analysis in order to reduce the size of the Pareto-optimal set. The first method is a scalarization method using a Non-uniform weight generator with pseudo-ranking scheme. The second method, the Nash-Dominant Pareto set reduction algorithm, based on Game Theory and the Nash dominance concept. Furthermore, the two methods will be used to reduce the size of the Pareto-optimal set of very popular problems such as DTLZ1 Test Problem, Printed Wiring Board (PWB) Problem, and the Redundancy Allocation Problem (RAP)