L-dominance: An approximate-domination mechanism for adaptive resolution of Pareto frontiers

In Evolutionary Multi-objective Optimization (EMO), the mechanism of 𝜖-dominance has received significant attention because of its ability to guarantee convergence near the Pareto frontier and maintain diversity among solutions at a reasonable computational cost. A noticeable weakness of this mechanism is its inability to vary the resolution it provides of the Pareto frontier based on the frontier’s tradeoff properties. We therefore propose a new mechanism—L-dominance, based on the Lamé curve—as an alternative to 𝜖-dominance in EMO. The geometry of the Lamé curve naturally supports a greater concentration of Pareto solutions in regions of significant tradeoff between objectives. This variable resolution of solutions allows an algorithm using L-dominance to generate fewer solutions to describe the Pareto frontier as a whole while maintaining a desired concentration of solutions where the frontier requires greater detail. The L-dominance mechanism is analyzed theoretically and by simulation on five test problems, and is shown to result in increasingly significant computational gains as the dimensionality of problems increases.