Abstract
Recently, by taking advantage of evolutionary multiobjective optimization techniques in diversity preservation, the means of multiobjectivization has attracted increasing interest in the studies of multimodal optimization (MMO). While most existing work of multiobjectivization aims to find all optimal solutions simultaneously, in this paper, we propose to approximate multimodal fitness landscapes via multiobjectivization, thus providing an estimation of potential optimal areas. To begin with, an MMO problem is transformed into a multiobjective optimization problem (MOP) by adding an adaptive diversity indicator as the second optimization objective, and an approximate fitness landscape is obtained via optimization of the transformed MOP using a multiobjective evolutionary algorithm. Then, on the basis of the approximate fitness landscape, an adaptive peak detection method is proposed to find peaks where optimal solutions may exist. Finally, local search is performed inside the detected peaks on the approximate fitness landscape. To assess the performance of the proposed algorithm, extensive experiments are conducted on 20 multimodal test functions, in comparison with three state-of-the-art algorithms for MMO. Experimental results demonstrate that the proposed algorithm not only shows promising performance in benchmark comparisons, but also has good potential in assisting preference-based decision-making in MMO.
Highlights
M ULTIMODAL optimization (MMO), which refers to single-objective optimization involving multiple optimal solutions, has attracted increasing interest recently [1]–[3]
It should be noted that, since the local search is merely performed inside a decision space region specified by a given peak, we suggest that the search space should be constrained to a small hyperbox around the seed solution, where each dimension is set as 5% of feasible range as defined by (2)
Since the performance of EMO-multimodal optimization (MMO) is largely dependent on the proposed MOFLA method and the peak detection method, we present some empirical results to further demonstrate the advantages of both methods, especially when applied to preference-based decision-making
Summary
M ULTIMODAL optimization (MMO), which refers to single-objective optimization involving multiple optimal (or near-optimal) solutions, has attracted increasing interest recently [1]–[3]. Since most EAs have been originally designed for conventional single-objective optimization which involves only one optimal solution, they are not directly applicable to MMO due to their poor capability of population diversity preservation [14]. To address such an issue, researchers have proposed a variety of solution approaches that can be roughly categorized into the following three groups. Given two candidate solutions x1 and x2, solution x1 is said to dominate the other solution x2 iff
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