A Novel Class of Test Problems for Performance Evaluation of Niching Methods

Abstract

This paper proposes a novel procedure for generating parametric scalable functions with diverse properties to strengthen numerical evaluation of niching methods. It combines three simple basic functions to form a composite multimodal function, in which the function parameter controls the number of global minima. The resultant composite function may show a variety of challenges in global optimization such as high condition, correlation, and presence of many undesirable local minima, as well as those peculiar to multimodal optimization, such as nonuniformly distributed global minima with dissimilar basin sizes. Moreover, the proposed procedure results in computationally inexpensive composite functions, when compared to those generated by available methods. This allows for benchmarking long-term success of niching methods on problems with many global minima. Six parametric benchmark functions are proposed in which the function parameter controls the number of global minima. Detailed analysis on distribution, basin shapes and sizes of the global minima is provided. One of the proposed test problems involve constraints, a matter which did not receive much attention in the past. These test functions are employed to compare some of the most successful niching methods in the literature. The numerical results disclose a drastic disparity between the performance of different niching methods on the composite functions and the existing test problems, demonstrating that the proposed composite functions simulate distinct challenges. Our findings highlight importance of the core search algorithm and challenge suitability of many niching strategies in more complicated landscapes and higher dimensions.