Structural analysis of Pareto-optimal solution sets for multi-objective optimization: An application to outer window design problems using Multiple Objective Genetic Algorithms

Abstract

In single-objective optimization problems, with only one optimal design objective, the absolute optimal solution to maximize/minimize the objective function can be determined. However, in most real design problems, the optimization problems are multi-objective, where two or more independent design objectives must be optimized simultaneously, and no single absolute optimal solution necessarily exists. In these cases, it is helpful for designers to recognize the range of alternative solutions that exist in Pareto-optimal sets and choose an acceptable solution from among them. In this paper, the authors carried out multi-objective optimization using Multiple Objective Genetic Algorithms through a real case study involved in indoor environmental design – the design of outer windows. Then the authors analyzed structure of Pareto-optimal solution sets. Here we present the analysis process as well as the case study details, and show how the method proposed here is effective at finding an acceptable solution for multi-objective optimization problems.