| Optimization problems are ubiquitous in many areas of the real world. Swarmintelligence optimization (SIO) algorithms are the techniques of computation that resolveoptimization problems by simulating intelligent behavior in biotic population. However,how to effectively simulate intelligent behavior in biotic population to better improveperformances of SIO algorithms remain to be further explored. As biotic population is acomplicated and self-organizing network in which each individual is denoted as a node anddynamic interactions among them are represented as edges, it will more really simulate theinteractions among individuals to further reflect the corresponding intelligence of bioticpopulation if SIO algorithms can simulate self-organizing evolutionary process of bioticpopulation and study individual behavior through network. The objective of this study is toconstruct various self-organizing topologies which include invariable or dynamic numbersof nodes as well as directional or non-directional edges in order to improve performance ofSIO algorithms by using complex network models to simulate self-organizing structure ofbiotic population and then investigate topological characteristics and the relationshipsbetween evolutions of topological characteristics measures and performances of SIOalgorithms, etc.The mechanism of interaction among particles is a key factor influencing theperformance of Particle Swarm Optimization (PSO) algorithm. In order to overcome thepremature convergence, an Extended Particle Swarm Optimization (EPSO) algorithm isproposed. Interaction mechanism among particles is redefined based on the attraction andrepulsion force in Artificial Physics. Based on a rule that particle fitness values arecompared to define attraction and repulsion force among particles, each particle randomlymoves along the direction of total forces produced by all particles to look for the globaloptimum. Moreover, convergent condition and global convergence of EPSO algorithmwere analyzed in theory. Results of simulation showed that EPSO had better performance.Firstly, static topologies of EPSO algorithm were investigated to constructself-organizing topologies improving performances of EPSO. In this part, someconclusions such as a key influence of degree of nodes and degree distribution onperformance of EPSO, etc. were drawn in theory and simulation experiment including therelations among information spreading, measure of topological characteristics and performances of EPSO, impact of topological characteristics and parameters of EPSO onits performances as well as optimal topology of EPSO.Secondly, a self-organizing topology driven by particles’ fitness (SOTDF) underinvariable size was constructed by simulating individuals that are willing to interact withbetter but not worse in animal groups based on the above conclusions from statictopologies of EPSO. Analyses of relationships between topology and performances ofEPSO in theory and simulation experiments show that the capability of node attractingconnections has great influences on topological characteristics and performances of EPSO.Compared with related algorithms, EPSO based on SOTDF (EPSO-SOTDF) has betterperformance. Meanwhile, EPSO-SOTDF algorithm has been applied to resolve the controlproblem of chaotic system. Simulation results suggested that EPSO-SOTDF has manyadvantages. In order to further improve performances of EPSO, a self-organizing topologydriven by particles’ fitness under invariable size was constructed based on an idea ofsurvival of the fittest, which involved the equivalent number of deletion-compensation ofnodes (DC model). The relationships among evolving parameters of topology, measures oftopological characteristics and information spreading were obtained from analyses oftopological characteristics in theory and simulation experiments. Also, from analyses ofthe relationships between evolution of measures of topological characteristics andperformances of EPSO in simulation experiment, it demonstrated that informationspreading speed with increasing speed meets the needs of search of EPSO in differentstages. Comparison of performance of EPSO based on DC model (EPSO-DC) withEPSO-SOTDF shows that DC model can balance effectively exploration capability ofEPSO between the global and the local as a result of EPSO-DC outperformingEPSO-SOTDF.Thirdly, inspired by real growing network and research results about dynamicpopulation size of PSO as well as considered limited population size in EPSO, aself-organizing topology driven by particles’ fitness and its degree was constructed, whichis a modified model of fitness model in complex networks (abbreviate: MF model). Withinthe maximum of population size MF model is growing network, while above the maximumof population size MF model evolves according to mechanism of deletion-compensation ofnodes. Meanwhile, updated equation of velocity of EPSO related to topology wasconstructed (MEPSO) in order to significantly improve convergent capability of EPSO andthen convergent condition and global convergence of MEPSO algorithm were analyzed.An asynchronous mechanism combining MF model evolving with MEPSO running is proposed. The relationships between evolving parameters of topology and measures oftopological characteristics were obtained from analyses of topological characteristics intheory and simulation experiments. In the meantime, simulation experiment analyzed theimpact of evolving parameters and measures of topological characteristics on performancesof MEPSO, which showed that MFMEPSO is more competitive when compared withrelative algorithm.Finally, due to shortage of non-directional self-organizing topologies, a directedself-organizing topology driven by particles’ fitness is constructed under invariable sizethrough simulation of individuals that are willing to interact with better but not worse inanimal groups. Simulation experiment obtained directed topological characteristics, whichsuggested that EPSO based on such directed topology has better performance. |
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