A Large Population Size Can Be Unhelpful in Evolutionary Algorithms

The utilization of populations is one of the most important features of evolutionary algorithms (EAs). There have been many studies analyzing the impact of different population sizes on the performance of EAs. However, most of such studies are based computational experiments, except for a few cases. The common wisdom so far appears to be that a large population would increase the population diversity and thus help an EA. Indeed, increasing the population size has been a commonly used strategy in tuning an EA when it did not perform as well as expected for a given problem. He and Yao (2002) showed theoretically that for some problem instance classes, a population can help to reduce the runtime of an EA from exponential to polynomial time. This paper analyzes the role of population further in EAs and shows rigorously that large populations may not always be useful. Conditions, under which large populations can be harmful, are discussed in this paper. Although the theoretical analysis was carried out on one multi-modal problem using a specific type of EAs, it has much wider implications. The analysis has revealed certain problem characteristics, which can be either the problem considered here or other problems, that lead to the disadvantages of large population sizes. The analytical approach developed in this paper can also be applied to analyzing EAs on other problems.Comment: 25 pages, 1 figur

Populações baseadas em multisets para algoritmos evolutivos

Os algoritmos evolutivos simulam a evolução natural de uma população de indivíduos aplicando iterativamente operadores genéticos, recombinação, mutação e seleção dos mais aptos. O processo evolutivo pode ser visto como um processo de otimização. Nesse caso, os indivíduos representam soluções do problema e as variáveis do problema são codificados no equivalente aos genes. Estes algoritmos podem ser facilmente implementados e existem variantes especializadas para resolver várias classes de problemas. Uma das maiores dificuldades apresentadas por estes algoritmos é a convergência prematura da população para soluções sub-ótimas antes do espaço de procura ser devidamente explorado. Várias estratégias foram desenvolvidas para reduzir este risco e, neste trabalho, estudamos a possibilidade de substituir a representação da população. Tradicionalmente as populações são representadas como coleções de indivíduos e nesta tese propomos a sua substituição por um multiconjunto (multiset). Esta nova forma de representação das populações, que denominamos multipopulações, permite manipular um conjunto de genomas e os seus clones, multi-indivíduos, de uma forma muito eficiente. Adaptamos o processo evolutivo para otimizar multipopulações, estudamos o seu comportamento em vários tipos de algoritmos e problemas e desenvolvemos operadores genéticos especializados para trabalhar com a nova representação. Em resultado disso obtemos uma forma inovadora de manter uma elevada diversidade genética na população. As experiências realizadas permitiram-nos compreender melhor a dinâmica que a nova representação introduz no processo evolutivo e mostrar a sua eficácia.Evolutionary algorithms simulate the natural evolution of a population of individuals by iteratively applying genetic operators, recombination, mutation and selection of the fittest. The evolutionary process can be viewed as an optimization process. In this case, individuals represent problem solutions and the problem variables are encoded in that equivalent to the gene. These algorithms can be easily implemented and there are specialized variants to solve different classes of problems. One of the biggest difficulties presented by these algorithms is the premature convergence of the population to suboptimal solutions before the search space is properly explored. Several strategies were developed to reduce this risk and, in this thesis, we studied the possibility of replacing the representation of the population. Traditionally populations are represented as collections of individuals and in this thesis we propose its replacement by a multiset. This new form of population representation, which we call multipopulations, allows manipulating a set of genomes and their clones, multi-individuals, in a very efficient way. We adapt the evolutionary process to optimize multipopulations, study their behavior on various types of algorithms and problems, and develop specialized genetic operators to work with the new representation. As a result, we get an innovative way to maintain a high genetic diversity in the population. The experiments allowed us to better understand the dynamics that the new representation introduces in the evolutionary process and show its effectiveness

Computational complexity of evolutionary algorithms, hybridizations, and swarm intelligence

Bio-inspired randomized search heuristics such as evolutionary algorithms, hybridizations with local search, and swarm intelligence are very popular among practitioners as they can be applied in case the problem is not well understood or when there is not enough knowledge, time, or expertise to design problem-specific algorithms. Evolutionary algorithms simulate the natural evolution of species by iteratively applying evolutionary operators such as mutation, recombination, and selection to a set of solutions for a given problem. A recent trend is to hybridize evolutionary algorithms with local search to refine newly constructed solutions by hill climbing. Swarm intelligence comprises ant colony optimization as well as particle swarm optimization. These modern search paradigms rely on the collective intelligence of many single agents to find good solutions for the problem at hand. Many empirical studies demonstrate the usefulness of these heuristics for a large variety of problems, but a thorough understanding is still far away. We regard these algorithms from the perspective of theoretical computer science and analyze the random time these heuristics need to optimize pseudo-Boolean problems. This is done in a mathematically rigorous sense, using tools known from the analysis of randomized algorithms, and it leads to asymptotic bounds on their computational complexity. This approach has been followed successfully for evolutionary algorithms, but the theory of hybrid algorithms and swarm intelligence is still in its very infancy. Our results shed light on the asymptotic performance of these heuristics, increase our understanding of their dynamic behavior, and contribute to a rigorous theoretical foundation of randomized search heuristics

Theoretical Analysis of Diversity Mechanisms for Global Exploration

Maintaining diversity is important for the performance of evolutionary algorithms. Diversity mechanisms can enhance global exploration of the search space and enable crossover to find dissimilar individuals for recombination. We focus on the global exploration capabilities of mutation-based algorithms. Using a simple bimodal test function and rigorous runtime analyses, we compare well-known diversity mechanisms like deterministic crowding, fitness sharing, and others with a plain algorithm without diversification. We show that diversification is necessary for global exploration, but not all mechanisms succeed in finding both optima efficiently