Editorial to the special issue on "Theoretical Foundations of Evolutionary Computation"

E VOLUTIONARY computation methods, such as evolutionary algorithms or swarm intelligence algorithms, have been successfully applied to a wide range of difficult problems. These include classical NP-hard combinatorial optimization problems and a variety of hard real-world optimization problems. Real-world problems, in particular, are difficult to solve using traditional search methods because often they are nonlinear, highly constrained, multiobjective, and can include a number of uncertainties. Many different evolutionary computation methods for dealing with complex problems have been proposed over the years. The theoretical analysis of evolutionary computation has made immense progress during the last 10 years [1]–[3]. Such analysis provides useful insights into the working principles of evolutionary computation techniques. This insight not only leads to a better understanding of the type of problems suitable for a given type of algorithm, but it also provides design guidelines for developing new more powerful methods in practice. Previous theoretical studies have shown the runtime behavior of bio-inspired computation methods including evolutionary algorithms, ant colony optimization, and particle swarm optimization. These studies explain, in a strict mathematical way, how these algorithms behave on different problem classes. Fitness landscape analysis has provided new insights that enable construction of better mutation and recombination search operators for important problems such as satisfiabilty (SAT) [4] and the travelling salesman problem (TSP) [5]. In the continuous domain, powerful algorithms such as covariance matrix adaptation evolution strategy (CMA-ES) [6] have been designed based on earlier theoretical investigations. Investigations into hypervolume indicators have lead to new high performing algorithms for multiobjective problems [7]. Although this is just a small example of the theoretical results obtained during the last 10 years, it clearly shows the importance of theoretical work in the area of evolutionary computation and the impact it can have on the design of high performance algorithms. This special issue highlights recent advances in the theory of evolutionary computation. We selected four papers (out of 22 submissions) to illustrate different aspects of theoretical work being conducted in the evolutionary computation field. Each paper describes both strict mathematical investigations and experimental studies. solving larger problems by suitably assembling solutions to smaller sub-problems. In classic algorithmics, this concept is found in dynamic programming and divide-and-conquer approaches. In evolutionary computation it is found in the use of crossover, the building block hypothesis and all methods that alter the components of the evolutionary algorithm, based on previously learned information on the problem structure. In …