Strategies Of Solving Complex Optimization Problems Based On QPSO Algorithm

Many practical problems in engineering,science,management,etc.can be reduced to complex optimization problems,and thus it is crucial to effectively solve such problems.Complex optimization problems are usually high-dimensional,multi-objective,dynamic,uncertain,and multi-constrained.The swarm intelligence algorithm including Particle Swarm Optimization(PSO)algorithm is a class of common algorithms for solving complex optimization problems.However as the dimensionality,objectives,constraints increase,the performance and efficiency of the algorithm decrease correspondingly.Therefore,designing new algorithmic strategies to deal with the performance and efficiency bottlenecks of algorithms for solving complex optimization problems is a hot research topic in the field of swarm intelligence algorithms.This dissertation aims at solving high-dimensional and multi-constrained complex problems,especially high-dimensional optimization problems(i.e.large-scale optimization problems).In order to solve large-scale optimization problems using Quantum-behaved Swarm Optimization(QPSO),the following new strategies and methods are proposed in the dissertation.(1)A new method of resource allocation is proposed.Because the dimension of large-scale optimization problems is considerably high,the first step of many Cooperative Co-evolution(CC)algorithms is to decompose large-scale optimization algorithms into multiple sub-problems,and then use the swarm intelligence algorithm to optimize sub-problems independently.Transforming the large-scale optimization problems into solving low-dimensional optimization problems can reduce the difficulty in problem solving.However,most of the existing methods focus on the decomposition strategy and the improvement of swarm intelligence algorithms,but they have not considered using computing resources rationally.Therefore,this dissertation proposes a new adaptive resource allocation method combined with QPSO to solve large-scale optimization problems.The method firstly distributes a reasonable number of fitness evolutions to each sub-problem,and then allocates computing resources according to their contribution.Meanwhile,in order to be able to employ the diversity control strategy in the proposed algorithm,we propose a phased diversity control method.Moreover,based on the two diversity measurements,namely the distance-to-average point diversity and entropy diversity,the asymptotic behavior of the diversities in QPSO is investigated and the correlations of the diversities with the best fitness of the swarm are analyzed.It is found that the distance-to-average point diversity plays more important role in the search process of the QPSO algorithm,which provide the theoretical basis for our proposed diversity control method.(2)A surrogate assisted quantum-behaved particle swarm optimization(SA-QPSO)algorithm is proposed to solve large-scale optimization problems.The idea of surrogate model assisted swarm intelligence algorithms(SAEAs)is to use the approximate fitness value obtained by surrogate model to replace the real fitness value,thereby reducing the computational resources and speeding up the search speed of the algorithm.In the traditional SAEAs,the training time grows exponentially as the number of samples in the training set increases.In addition,the random selection method shows that poor samples are used to train the substitution model,which misleads the search direction.Therefore,SA-QPSO reduces the training time by selecting a certain number of samples to train the surrogate model,and also discards the poorest sample every fixed number of iterations by using the Manhattan distance-based measurement.The experimental results show that the proposed algorithm can find a more satisfactory solution with the same number of iterations than the state-of art algorithms.(3)A new framework named multi-layer competition framework is proposed to enhance the search ability of the QPSO algorithm.The framework can be used for general population-based random search algorithms including particle swarm optimization algorithms.The multi-competition framework contains two strategies.The first one is the competition strategy,which is inspired by social competition.The benign social competition can lead the group develops in the right direction.At the same time,multi-layer competition concept can let particle from lower layer fly to the upper layer,while the upper-layer particles may also be moved from the upper-layer to the lower-layer through competition.Too many layers may decrease the convergence speed sharply,so that the framework is generally suggested to set to be three layers.The second strategy is a two-stage waiting strategy.Large-scale optimization problems often have many local optima.If the algorithm converges quickly,the algorithm will fall into local optima easily.In order to improve the global search ability of the algorithm with the multi-layer competition strategy considered,the particle in the current layer is guided by the mean of personal best positions of the particles in the adjacent upper layer.This strategy enables the algorithm to pull away particles from the local optima with higher probability.Subsequently,two algorithms based on multi-layer competition framework are proposed,namely HCPSO and HCQPSO.By analysis of the experiments results,we find that the hierarchical competition framework can effectively improve the global search ability of the algorithm,which is desirable for solving of large-scale optimization problems.(4)Furthermore,in this dissertation also applies the QPSO algorithm to several real complex problems.Firstly,the algorithm is used to deal with the classification of hyperspectral faces.In this problem,due to the information redundancy,the recognition rate of the classification algorithm on hyperspectral faces dataset is not high enough.Therefore,two band selection methods are proposed,namely the cluster based band selection and the QPSO-based band selection method.From experimental results,we find that the QPSO-based band selection method can not only obtain a comparable recognition rate,but also is shown to be more reasonable.Secondly,an adaptive probability distribution QPSO algorithm for complex engineering design optimization problems is proposed.By using adaptive Gaussian distribution to balance the global search and local search abilities of the algorithm at different stages.Compared with genetic algorithms or other gradient-based swarm intelligence algorithms,few parameters are needed to adjust for different problems but the algorithm can be guaranteed to find a better feasible solution.Two multi-constrained engineering optimization problems are used to test the proposed algorithm,and the experimental results show that the proposed method has better performance than the existing state-of-art algorithms.The research in this dissertation provides a theoretical guidance for the use of swarm intelligence optimization algorithms to solve large-scale complex optimization problems,and have certain theoretical and academic value.In addition,several proposed methods successfully and effectively solve the practical complex optimization problems,which imply that the research in this dissertation is of value in engineering applications.