Multiobjective Evolutionary Algorithm With Controllable Focus on the Knees of the Pareto Front

The optimal solutions of a multiobjective optimization problem correspond to a nondominated front that is characterized by a tradeoff between objectives. A knee region in this Pareto-optimal front, which is visually a convex bulge in the front, is important to decision makers in practical contexts, as it often constitutes the optimum in tradeoff, i.e., substitution of a given Pareto-optimal solution with another solution on the knee region yields the largest improvement per unit degradation. This paper presents a selection scheme that enables a multiobjective evolutionary algorithm (MOEA) to obtain a nondominated set with controllable concentration around existing knee regions of the Pareto front. The preference-based focus is achieved by optimizing a set of linear weighted sums of the original objectives, and control of the extent of the focus is attained by careful selection of the weight set based on a user-specified parameter. The fitness scheme could be easily adopted in any Pareto-based MOEA with little additional computational cost. Simulations on various two- and three-objective test problems demonstrate the ability of the proposed method to guide the population toward existing knee regions on the Pareto front. Comparison with general-purpose Pareto based MOEA demonstrates that convergence on the Pareto front is not compromised by imposing the preference-based bias. The performance of the method in terms of an additional performance metric introduced to measure the accuracy of resulting convergence on the desired regions validates the efficacy of the method.