Abstract
AbstractThe performance of Differential Evolution (DE) for multiobjective optimization problems (MOPs) can be greatly enhanced by hybridizing with other techniques. In this paper, a new hybrid DE incorporating preference based local search is proposed. In every generation, a set of nondominated solutions is generated by DE operation. Usually these solutions distribute unevenly along the obtained nondominated set. To get solutions in the sparse region of the nondominated set, a mini population and preference based local search algorithm is specifically designed, and is used to exploit the sparse region by optimizing an achievement scalarizing function (ASF) with the dynamically adjusted reference point. As a result, multiple solutions in the sparse region can be obtained. Moreover, to retain uniformly spread nondominated solutions, an improved e-dominance strategy, which would not delete the extreme points found during the evolution, is proposed to update the external archive set. Finally, numerical result...
Highlights
Many real world problems involve optimization of two or more objectives
achievement scalarizing function (ASF) in interactive methods is a good choice for two reasons: one is it has the minimal solution among Pareto optimal solutions of the original problem, the other is ASF can lead the local search towards the preference region of the reference point
In this hybrid algorithm, the local search is performed on ASF established by the randomly selected reference point with probability, where the reference point may be in dense region, and the local search makes no contribution for adding solutions in sparse region
Summary
Many real world problems involve optimization of two or more objectives. Very often, the objectives contradict each other, and improvement of one objective may lead to deterioration of another. Thiele et al proposed a preference-based evolutionary approach, called PBEA16, which incorporates preference information into an indicator-based evolutionary algorithm IBEA18 and aims to produce a good, probably small set of approximate efficient solutions related to the reference point. ASF in interactive methods is a good choice for two reasons: one is it has the minimal solution among Pareto optimal solutions of the original problem, the other is ASF can lead the local search towards the preference region of the reference point. In Ref. 23, a hybrid approach was proposed by incorporating ASF based local search to NSGA-II In this hybrid algorithm, the local search is performed on ASF established by the randomly selected reference point with probability, where the reference point may be in dense region, and the local search makes no contribution for adding solutions in sparse region.
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