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A Multi-Objective Genetic Algorithm with Controllable Convergence on Knee Regions

A knee region on the Pareto-optimal front of a multi-objective optimization problem consists of solutions with the maximum marginal rates of return, i.e. solutions for which an improvement on one objective is accompanied by a severe degradation in another. The trade-off characteristic renders such solutions of particular interest in practical applications. This paper presents a multi-objective evolutionary algorithm focused on the knee regions. The algorithm facilitates better decision making in contexts where high marginal rates of return are desirable by providing the decision makers with a high concentration of solutions on the knee regions of the Pareto-front approximation. The proposed approach computes a transformation of the original objectives based on weighted-sum functions. The transformed functions identify niches which correspond to knee regions in the objective space. The extent and density of coverage of the knee regions are controllable by the niche strength and pool size parameters. Although based on weighted-sums, the algorithm is capable of finding solutions in the non-convex regions of the Pareto-front. The application of the algorithm on test problems with multiple knee regions and skew on the Pareto-optimal front produces promising results.