A multi-objective genetic algorithm for robust design optimization

Abstract

Real-world multi-objective engineering design optimization problems often have parameters with uncontrollable variations. The aim of solving such problems is to obtain solutions that in terms of objectives and feasibility are as good as possible and at the same time are least sensitive to the parameter variations. Such solutions are said to be robust optimum solutions. In order to investigate the trade-off between the performance and robustness of optimum solutions, we present a new Robust Multi-Objective Genetic Algorithm (RMOGA) that optimizes two objectives: a fitness value and a robustness index. The fitness value serves as a measure of performance of design solutions with respect to multiple objectives and feasibility of the original optimization problem. The robustness index, which is based on a non-gradient based parameter sensitivity estimation approach, is a measure that quantitatively evaluates the robustness of design solutions. RMOGA does not require a presumed probability distribution of uncontrollable parameters and also does not utilize the gradient information of these parameters. Three distance metrics are used to obtain the robustness index and robust solutions. To illustrate its application, RMOGA is applied to two well-studied engineering design problems from the literature.

A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

“…In such situations, DMs prefer solutions that are robust against small changes in decision variables [156][157][158]. There have been some discussions on robust multi-objective optimization [159][160][161][162][163][164], but little research has studied the robustness in decision making, except for measuring attractiveness by a categorical based evaluation technique (MAC-BETH) [165]. The analysis of the mapping relationship from decision variables to objectives [166] helps searching robust solutions in the preference-based methods.…”

Exact Analysis for Next Release Problem

“…The applications and studies of robust optimisation can be widely found in other non software engineering research literature [39], [40] but are seldom found in the requirements engineering research. In requirements engineering, to the best of our knowledge, there are only three studies applying robust optimisation on requirements optimisation area.…”

Multiobjective robustness for portfolio optimization in volatile environments

“…Other definitions of robustness include: consistency of results between different runs [26], and reliability of results in uncertain environments, where the fitness function optimum is time varying [8]. Jin and Mian [14,18] improve the robustness of a single objective optimization problem by treating it as a multiobjective problem where robustness is an extra objective.…”