| Optimization is an important area in scientific research.With the development of the society and techniques,engineering technology has bring many complexity opti-mization problems,such as the nonlinear control,neural network training,text cluster-ing,multi-parameter tuning,traffic route planning problems in the area of the com-munication system,automatic control,power system,mechanical engineering,civil engineering,bioengineering,chemical engineering.When solving these complexity problems,the traditional optimization algorithms such as the analytic methods or nu-merical analysis methods often performed not effective and the searching results can-not be satisfied within the limited searching times.In order to solve these problems,the intelligent randomized optimization algorithms have been proposed as the meta-heuristic method to solve these complex problems.The metaheuristic can be classified into two categories:the single-solution based metaheuristics and the population-based metaheuristics.Roughly speaking,the single-solution based metaheuristics are more exploitation oriented whereas the population based metaheuristics are more exploration oriented.Generally,the most studied population-based metaheuristics often related to swarm intelligence(SI)and evolutionary computation(EC).The swarm intelligence methods such the PSO algorithm and ACO algorithm often produce the computational intelligence by exploiting simple analogs of social interaction.The evolutionary com-putation methods such as the DE algorithm and GA algorithm are inspired by Darwin's evolutionary theory,where a population of individuals is modified by the genetic op-erators like the recombination and mutation.The algorithms based swarm intelligence overcome the limitations of the traditional algorithms in solving the problem and are not dependency upon the specific information of the searching problem.Moreover,the complexity of these swarm intelligence algorithms is often lower than the traditional problems.Particle Swarm Optimization(PSO)is a random SI algorithm that simulates the social behavior of bird groups.The algorithm has the advantages of simple structure,few control parameters and owns a strong global optimization ability.However,the systematism in theoretical studies and convergence analyses is still needed to investi-gate and it often trapped the particles into the local optimum when solving complex multimodal problems.The DE is an arguably one of the most powerful and versatile EC algorithm for the continuous parameter spaces.It adopts the crossover,mutation and greedy selection to generate the solutions in searching space.It is a new type of evolutionary optimization algorithm and has the advantages of simple structure,few parameters,stable search and can be easily implementated.However,the performance of DE has a strong dependency upon the control parameters.Besides,it may gradually stop generating successful solutions even the whole population has not converged to a fixed point,namely the phenomena of stagnation.In order to solve these typical prob-lems in PSO and DE,this dissertation has been made a deep investigated based on the principle and foundations of the both algorithms and designed more efficient optimiza-tion model to enhance the population diversity and avoid the premature convergence.The main content of this article can be summarized as follows:(1)The basic foundations and concepts of intelligent optimization are systemati-cally described in detail.The detailed content of these foundations includes the mathe-matical model of the optimization problems,the classification of optimization problems,the complexity of optimization problem,the classification of optimization algorithms,the complexity of the optimization algorithms and finally a review of the development of intelligent computation is provided.(2)Research on the PSO convergence analysis.The position and velocity conver-gence of the standard PSO algorithm is analyzed and the convergence conditions are deduced by the matrix analytic method.Moreover,the convergence conditions are veri-fied by experimental simulations.Then,the convergence conditions were used to further intestate the convergence of other two classical PSO algorithms,namely the weighted PSO algorithm and the constrained PSO algorithm.(3)Research on center-decenter PSO(CDPSO).A new particle swarm optimization algorithm based on center-discrete learning strategy is proposed(CDPSO algorithm).The algorithm designed two different learning strategies:the central learning strategy and the discrete learning strategy.The Centralized strategy is designed to enhance the deep searching ability in the search space by learning the experience from the elite information of the top rank individuals in current society.The decentralized strategy is designed to enhance the wide searching ability by learning much more information from the neighborhoods that randomly distributed among the population.In CDPSO,the particle conducted one strategy in each learning cycle and then replaced by another strategy in the next learning cycle.CDPSO take advantage of center learning strategy and the decentralized learning strategy to coevolve the swarm to global optimum.The experimental results demonstrated that the CDPSO algorithm showed a better balancing searching abilities than compared algorithms in unimodal and multimodal problems.(4)Research on vector coevolving PSO(VCPSO).VCPSO is completely different from the traditional PSO and its variants.It designed a novel vector partition technique to split the full dimension of a particle into several segments randomly and then opti-mized each segment by one of the learning operators independently.These operators co-evolved with each other and enhanced the population diversity with sub-dimension learning method.VCPSO extended the full dimension with only one learning strategy to the sub-dimension with discrete more learning strategies.The learning operator in the model can be flexibly expanded,and the idea of the random dimension division is the first time in the optimization field.Comprehensive experimental tests have showed that VCPSO has a strong competed ability in solving unimodal and multimodal problems.(5)Research on the convergence of DE algorithm.The convergence of DE algo-rithm has been analyzed by the stochastic compression operator of functional analysis theory.The analysis proofed that the basic DE algorithm conducted asymptotic conver-gence.In DE algorithm,the mutation operation and the cross operation can be merged as differential operator and the greedy selection operation can be regarded as a selec-tion operator.Therefore,the iterations in one generation can be regarded as a map from the difference operator and the selection to the searching space.Because of the greedy selection mechanism,the iterative sequence of the fitness of each individual presents a non-monotonic decreasing trend.Therefore,the iteration of DE can be regarded as a stochastic compression operator.DE algorithm has the asymptotic convergence accord-ing to the stochastic compression theorem.(6)Research on coevolving bare-bones differential evolution(CBDE).In order to avoid the premature convergence of DE algorithm,a new mutation strategy "DE-BB"strategy based on differential evolution algorithm and backbone particle swarm opti-mization algorithm is introduced to mix with other two classical DE mutant strategy.These strategies coevolved with each other and guided the population to the promis-ing area."DE-BB" strategy takes advantage of the bare bones swarm intelligence in exploitation and the strong exploration of various different DE algorithms.Besides,in order to detect the search stagnation phenomenon in DE algorithm,a supervisory mech-anism is introduced by monitoring the number of successful updated counts.Once an individual occurred the phenomena of stagnation,CBDE adaptively adjusts its learn-ing strategy or the corresponding parameters.Experimental results showed that CBDE performs better than most the state-of-the-art DE algorithms on a majority of test bench-mark functions. |
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