Multimodal Optimization

Multimodal optimization is currently getting established as a research direction that collects approaches from various domains of evolutionary computation that strive for delivering multiple very good solutions at once. We start with discussing why this is actually useful and therefore provide some real-world examples. From that on, we set up several scenarios and list currently employed and potentially available performance measures. This part also calls for user interaction: currently, it is very open what the actual targets of multimodal optimization shall be and how the algorithms shall be compared experimentally. In-tutorial discussion of this topic will be encouraged. As there has been little work on theory (not runtime complexity; rather the limits of different mechanisms) in the area, we present a high-level modelling approach that provides some insight in how niching can actually improve optimization methods if it fulfils certain conditions. While the algorithmic ideas for multimodal optimization (as niching) originally stem from biology and have been introduced into evolutionary algorithms from the 70s on, we only now see the consolidation of the field. The vast number of available approaches is getting sorted into collections and taxonomies start to emerge. We present our version of a taxonomy, also taking older but surpisingly modern global optimization approaches into account. We highlight some single mechanisms as clustering, multiobjectivization and archives that can be used as additions to existing algorithms or building blocks of new ones. We also discuss recent relevant competitions and their results, point to available software and outline the possible future developments in this area.