Metaheuristics for Continuous Optimization of High-Dimensional Problems: State of the Art and Perspectives

Abstract

The age of big data brings new opportunities in many relevant fields, as well as new research challenges. Among the latter, there is the need for more effective and efficient optimization techniques, able to address problems with hundreds, thousands, and even millions of continuous variables. Over the last decade, researchers have developed various improvements of existing metaheuristics for tacking high-dimensional optimization problems, such as hybridizations, local search and parameter adaptation. Another effective strategy is the cooperative coevolutionary approach, which performs a decomposition of the search space in order to obtain sub-problems of smaller size. Moreover, in some cases such powerful search algorithms have been used with high performance computing to address, within reasonable run times, very high-dimensional optimization problems. Nevertheless, despite the significant amount of research already carried out, there are still many open research issues and room for significant improvements. In order to provide a picture of the state of the art in the field of high-dimensional continuous optimization, this chapter describes the most successful algorithms presented in the recent literature, also outlining relevant trends and identifying possible future research directions.