Discrete Particles Swarm Optimization Algorithm for Uniform

发布时间：2023-02-17 10:29

　　实验是人们认识和改造世界的重要手段,今天的生活中无处不存在试验。统计试验可以抽象的理解为安排一系列通过不同的输入获得不同输出的检验活动。,通过分析这种变化之间的关系建立统计模型。而试验设计则是试着用最节约的试验次数(输入)获得尽可能的信息。一个试验的所有可能输入的输入组合可能非常多,全部都进行试验通常不现实;很多时候也没有必要对所有的试验组合进行试验,我们只需要对部分组合进行试验。对于这个部分如何选择的问题的不同回答导出了许多不同的试验理念和方法。空间填充试验是一种尽量使试验点均匀散布于目标实验区域的试验设计方法。如:超级拉丁方设计、最小最大、最大最小距离设计、均匀设计。偏差是评价一个设计在目标区域内的均匀性的最为广泛和流行的准则。一个具有最小偏差值的设计被称为该偏差准则下的最优设计。显然给定偏差准则后,如何在海量的备选设计中寻找偏差最小的最优设计,随着试验问题越来越复杂,这一优化问题也变的越来越具有挑战性。很多专家学者对这一优化问题提出了许多具有深刻洞察力的方法。本文引入近几年在随机优化领域被广泛使用的离散粒子群算法,对这一算法的不同参数设置进行了改进和优化,使该算法能适应最优空间填...

【文章页数】：100 页

【学位级别】：博士

【文章目录】：
ACKNOWLEDGEMENT
Abstract
摘要
List of Abbreviations
CHAPTER ONE:INTRODUCTION
    1.1 Background Information
    1.2 Statement of the problem
    1.3 Objectives
        1.3.1 General objective
        1.3.2 Specific objectives
    1.4 Research Questions
    1.5 Justification of the study
CHAPTER TWO: LITERATURE REVIEW
    2.0 Introduction
    2.1 Design of Experiment
        2.1.1 Basic terms used in Experimental Designs
        2.1.2 Basic Principles of Experimental Designs
        2.1.3 Factorial Designs
    2.2 Uniform Design
        2.2.1 Uniform design as a space filling design
        2.2.2 Uniformity criterion: the discrepancy
            2.2.2.1 The Star Discrepancy
            2.2.2.2 The Local Discrepancy
            2.2.2.3 The Centered L₂ discrepancy
            2.2.2.4 The wrap-around L₂ discrepancy
            2.2.2.5 The Mixture Discrepancy
            2.2.2.6 Symmetric discrepancy
    2.3 Construction of Uniform Design
    2.4 Optimization
        2.4.1 Classification of Optimization Problems
            2.4.1.1 Constrained Optimization
            2.4.1.2 Unconstrained Optimization
            2.4.1.3 Dynamic Optimization
            2.4.1.4 Least Square Optimization
        2.4.2 Optimization Techniques
            2.4.2.1 Local Optimization
            2.4.2. 2 Global Optimization
        2.4.3 Optimization Algorithms
            2.4.3.1 Local search algorithm
            2.4.3.2 Simulating annealing
            2.4.3.3 Genetic algorithm
            2.4.3.4 Stochastic evolutionary algorithms
            2.4.3.5 Threshold accepting
        2.4.4 To Generate Symmetrical And Asymmetrical Uniform Designs From U(n;n^s)
        2.4.5 Uniform Designs with large n
    2.5 Particle Swarm Optimization
        2.5.1 The particle swarm algorithm
            2.5.1.1 Global best PSO
            2.5.1.2 Local best PSO
    2.6 Discrete particle swarm optimization
CHAPTER THREE:METHODOLOGY
    3.1 Discrete particle swarm optimization for the designs matrices
        DPSO FLOW CHART
        3.1.1 Initialization
        3.1.2 The function value
        3.1.3 The learning process
        3.1.4 Accepting strategy
        3.1.5 Update process
CHAPTER FOUR: NUMERICAL RESULTS
    4.0 Introduction
    4.1 The number of designs in the design space
    4.2 Parameters used in the swarm
        4.2.1 The number of initial particles in the swarm
        4.2.2 The number of iterations
        4.2.3 probR
        4.2.4 The constants p and g
    4.3 Comparison with TA
        4.3.1 under WD
        4.3.2 under CD
        4.3.3 under SD
    4.4 Asymmetric and symmetric designs
    4.5 for large n
    4.6 Special cases (orthogonality)
        4.6.1 use of orthogonal array for multilevel designs
        4.6.2 orthogonal and nearly orthogonal Latin hypercube designs for high levelled designs
CHAPTER FIVE:CONCLUSION AND DISCUSSION
Future work
APPENDIX
References



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