L-Dominance: A New Mechanism Combining ǫ -Dominance and Pareto Knee Exploitation in Evolutionary Multi-objective Optimization Braden J. Hancock * , Tim B. Nysetvold † , and Christopher A. Mattson ‡ Brigham Young University, Provo,UT, 84602, USA In Evolutionary Multi-objective Optimization (EMO), the mechanism of ǫ -dominance has received a lot of attention because of its ability to guarantee convergence near the Pareto frontier and maintain diversity among solutions at a reasonable computational cost. A significant weakness of this mechanism is its inability to also identify and exploit knee regions of the Pareto frontier, which are frequently the regions of the frontier that are most interestingto the user. We therefore propose a new mechanism—L-dominance, based on the Lam´ e curve—as an alternative to ǫ -dominance in EMO. The geometry of the Lam´ e curve naturally supports a greater concentration of solutions in directions of high tradeoff between objectives than a corresponding ǫ -box of the same area. This adaptable resolution of solutions in knee regions of the Pareto frontier will result in significant gains in computational efficiency for complex optimization routines in large n-objective design scenarios. I. Introduction Nearly all design problems include multiple objectives. Often, these objectives are in conflict with each other. In recent years, one of the most popular approaches for performing numerical optimization in such scenarios has been Evolutionary Multi-objective Optimization (EMO). In EMO methods, multiple potential solutions evolve simultaneously toward the Pareto frontier—the region of the design space that represents all non-dominated solutions. An introduction to EMO methods and principles can be found in (Deb 2008). 5 The goals of these methods are typically to * Research Assistant, Department of Mechanical Engineering, and AIAA Student Member † Research Assistant, Department of Mechanical Engineering, and AIAA Student Member ‡ Associate Professor, Department of Mechanical Engineering, and AIAA Member (mattson@byu.edu) 1 of 11 Downloaded by BRIGHAM YOUNG UNIVERSITY on April 27, 2015 | http://arc.aiaa.org | DOI: 10.2514/6.2015-0381 53rd AIAA Aerospace Sciences Meeting 5-9 January 2015, Kissimmee, Florida AIAA 2015-0381 Copyright © 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. AIAA SciTech