Braden Hancock, Brigham Young University
Engineering
In Evolutionary Multi-objective Optimization (EMO), the mechanism of epsilon-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. The main 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 interesting to the user. Many attempts have been made to resolve this issue, but each has resulted in either decreased computational efficiency or slower convergence. We therefore propose a new mechanism – Lamé-dominance – as a replacement for epsilon-dominance in EMO. The geometry of the Lamé curve naturally supports a greater concentration of solutions in directions of high tradeoff between objectives. This adaptable resolution of solutions in knee regions of the Pareto frontier will result in significant savings in time and money for complex optimization routines in large n-objective design scenarios.