Theory and practice of population diversity in evolutionary computation

Divergence of character is a cornerstone of natural evolution. On the contrary, evolutionary optimization processes are plagued by an endemic lack of population diversity: all candidate solutions eventually crowd the very same areas in the search space. The problem is usually labeled with the oxymoron “premature convergence” and has very different consequences on the different applications, almost all deleterious. At the same time, case studies from theoretical runtime analyses irrefutably demonstrate the benefits of diversity. This tutorial will give an introduction into the area of “diversity promotion”: we will define the term “diversity” in the context of Evolutionary Computation, showing how practitioners tried, with mixed results, to promote it. Then, we will analyze the benefits brought by population diversity in specific contexts, namely global exploration and enhancing the power of crossover. To this end, we will survey recent results from rigorous runtime analysis on selected problems. The presented analyses rigorously quantify the performance of evolutionary algorithms in the light of population diversity, laying the foundation for a rigorous understanding of how search dynamics are affected by the presence or absence of diversity and the introduction of diversity mechanisms

When hillclimbers beat genetic algorithms in multimodal optimization

This paper investigates the performance of multistart next ascent hillclimbing and well-known evolutionary algorithms incorporating diversity preservation techniques on instances of the multimodal problem generator. This generator induces a class of problems in the bitstringdomain which is interesting to study from a theoretical perspective in the context of multimodal optimization, as it is a generalization of the classical OneMax and TwoMax functions for an arbitrary number of peaks. An average-case runtime analysis for multistart next ascent hill-climbing is presented for uniformly distributed equal-height instances of this class of problems. It is shown empirically that conventional niching and mating restriction techniques incorporated in an evolutionary algorithm are not sufficient to make them competitive with the hillclimbing strategy. We conjecture the reason for this behaviour is the lack of structure in the space of local optima on instances of this problem class, which makes an optimization algorithm unable to exploit information from one optimum to infer where another optimum might be. When no such structure exist, it seems that the best strategy for discovering all optima is a brute-force one. Overall, our study gives insights with respect to the adequacy of hillclimbers and evolutionary algorithms for multimodal optimization, depending on properties of the fitness landscape.info:eu-repo/semantics/publishedVersio