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The research of population structure in evolutionary algorithms

王 藝叡 富山大学

2020.03.24

概要

Complex networks have been attracting much attention and developed rapidly over the past two decades. In nature and society, numerous networks have been described widely, such as Internet, E-mail, interpersonal relationship, collaboration, citation and so on. Investigations in various networks demonstrate these networks have some identical characteristics of topologies including small world, scale free, community structure and hierarchical framework. The discovery of these characteristics can make people better understand inherent regulation of abstract networks. Therefore, the complex network is regarded as an effective tool to depict and interpret the elusive phenomenon generated by real world. The aim involves two aspects where one is to cognize and analyze the essence of complicated system in terms of multiple viewpoints and the other is to enhance the application of research objective.

Evolutionary algorithms (EAs) such as genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO) are effective methods to resolve various problems. As population-based algorithms, EAs continually evolve their populations to derive better results on optimization problems. Their population structures can influence interaction among individuals such that their performances are also determined. Adjusting population structures can become a kind of methods to improve performance of EAs. Studies have proved that population structures can remarkably help the evolution of individuals so as to reinforce the properties of EAs.

In this thesis, three kinds of EAs including differential evolution (DE), brain storm optimization (BSO) and gravitational search algorithm (GSA) are researched from the viewpoint of population structure. For them, my work mainly focuses on the following aspects: (1) Construction and implementation of complex networks; (2) Relationship between population structures and transmitting information; (3) Interaction among individuals in different population structures; (4) New proposals to modify population topologies for improving performance of EAs. The specific contents are given as follows.

(1) For DE, a population interaction network (PIN) is proposed to investigate the relationship constituted by populations. The cumulative distribution function (CDF) of degree in PIN is analyzed by five fitting models on twelve benchmark functions. The goodness of fit is used to measure fitting results. Experimental results demonstrate that CDF meets cumulative Poisson distribution. Besides, the number of nodes in PIN and the rate parameter λ in the fitted Poisson distribution are further studied using different control parameters of DE, which exhibits the effect and characteristic of the population interaction.

(2) For BSO, to theoretically analyze its performance from the viewpoint of population evolution, the PIN is used to construct the relationship among individuals. Four experiments in different dimensions, parameters, combinatorial parameter settings and related algorithms are implemented, respectively. Experimental results indicate the frequency of average degree of BSO meets a power law distribution on functions with low dimension, which shows the best performance of algorithm among three kinds of dimensions. The parameters of BSO are investigated to find the influence of population interaction with the power law distribution on the performance of algorithm, and respective parameter can change the relationship among individuals. In addition, mutual effect among parameters is analyzed to find the best combinatorial result to significantly enhance the performance of BSO. Contrast among BSO, DE and PSO demonstrates a power law distribution is more effective for boosting the population interaction to enhance the performance of BSO.

(3) For GSA, a hierarchical GSA with an effective gravitational constant (HGSA) is proposed to address premature convergence and low search ability. Three contrastive experiments are carried out to analyze the performances between HGSA and other GSAs, heuristic algorithms and PSOs on function optimization. Experimental results demonstrate the effective property of HGSA due to its hierarchical structure and gravitational constant. A component-wise experiment is also established to further verify the superiority of HGSA. Additionally, HGSA is applied to several real-world optimization problems so as to verify its good practicability and performance. Finally, time complexity analysis is discussed to conclude that HGSA has the same computational efficiency in comparison with other GSAs.

The thesis is organized as follows. Chapter 1 introduces background and related work of EAs as well as contributions of this thesis. Chapter 2 presents the research of population structure on DE. Chapter 3 describes several characteristics of population structure on BSO. Chapter 4 gives an improved GSA based on a modified population structure. Chapter 5 summarizes some general conclusions and points out several future work.

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