Benchmark Functions for CEC’2013 Special Session and Competition on Niching Methods for Multimodal Function Optimization

Population-based meta-heuristic algorithms such as Evolutionary Algorithms (EAs) in their original forms are usually designed for locating a single global solution. These algorithms typically converge to a single solution because of the global selection scheme used. Nevertheless, many realworld problems are “multimodal” by nature, i.e., multiple satisfactory solutions exist. It may be desirable to locate many such satisfactory solutions so that a decision maker can choose one that is most proper in his/her problem domain. Numerous techniques have been developed in the past for locating multiple optima (global or local). These techniques are commonly referred to as “niching” methods. A niching method can be incorporated into a standard EA to promote and maintain formation of multiple stable subpopulations within a single population, with an aim to locate multiple globally optimal or suboptimal solutions. Many niching methods have been developed in the past, including crowding [1], fitness sharing [2], deterministic crowding [3], derating [4], restricted tournament selection [5], parallelization [6], stretching and deflation [7], clustering [8], clearing [9], and speciation [10], etc. Although these niching methods have been around for many years, further advances in this area have been hindered by several obstacles: most studies focus on low dimensional multimodal problems (2 or 3 dimensions), therefore it is difficult to assess these methods’ scalability to both high modality and dimensionality; some niching methods introduces new parameters which are difficult to set, making these methods difficult to use; different benchmark test functions or different variants of the same functions are used, hence comparing the performance of different niching methods is difficult. We believe it is now time to adopt a unifying framework for evaluating niching methods, so that further advances in this area can be made with ease. In this technical report, we put together 20 benchmark test functions (including several identical functions with different dimension sizes), with different characteristics, for evaluating niching algorithms. The first 10 benchmark functions are simple, well known and