多模態(tài)多目標(biāo)優(yōu)化問題在學(xué)術(shù)研究和工業(yè)應(yīng)用中廣泛存在,比如航天發(fā)射任務(wù)設(shè)計、汽車發(fā)動機設(shè)計等等。近年來,多模態(tài)多目標(biāo)優(yōu)化受到越來越多的關(guān)注,許多學(xué)者對此進行了研究。在多模態(tài)多目標(biāo)優(yōu)化問題中,優(yōu)化目標(biāo)是找到所有具有相同目標(biāo)向量但在決策空間中分布不同的帕累托最優(yōu)解。本論文研究了幾種具有代表性的多目標(biāo)演化優(yōu)化算法在多模態(tài)多目標(biāo)優(yōu)化問題上的表現(xiàn)。實驗結(jié)果表明,隨著算法的執(zhí)行,由于沒有解的多樣性的保護機制,決策空間中解的多樣性會變得越來越差。為了解決該問題,本論文提出了兩種決策空間中解的多樣性的維護機制。本論文的主要工作包括:（1）提出了一種子種群搜索方法來求解多模態(tài)多目標(biāo)優(yōu)化問題。首先,將一個種群分為幾個子種群;之后,在優(yōu)化過程中,每個子種群對應(yīng)一個帕累托最優(yōu)解集。配對、雜交、變異、環(huán)境選擇等優(yōu)化過程在每個子種群中獨立進行。為了使子種群互相遠(yuǎn)離,使用了兩個指標(biāo)來使得解在決策空間中形成小環(huán)境。第一個指標(biāo)是解與其所處的子種群的中心之間的距離。第二個指標(biāo)是解與另一個最近的子種群的中心之間的距離。將這種方法應(yīng)用到SPEA2和IBEA兩種具有代表性的多目標(biāo)演化優(yōu)化算法上。實驗結(jié)果表明對于大多數(shù)多模態(tài)多目標(biāo)... 

【文章頁數(shù)】：88 頁

【學(xué)位級別】：碩士

【文章目錄】：
摘要
ABSTRACT
Chapter 1 Introduction
    1.1 Background
    1.2 Related Work
        1.2.1 Real-world MMOPs
        1.2.2 Algorithms Proposed Before 2016
        1.2.3 Algorithms Proposed After 2016
    1.3 Main Contributions
    1.4 Thesis Organization
Chapter 2 Preliminaries
    2.1 Multi-objective Optimization Problem
    2.2 Multi-modal Multi-objective Optimization Problem
    2.3 Basic Definitions
    2.4 Representative Evolutionary Multi-objective Optimization Algorithms
        2.4.1 Dominance-based EMOA: SPEA2
        2.4.2 Indicator-based EMOA: IBEA
        2.4.3 Decomposition-based EMOA: MOEA/D
    2.5 Evaluation Methods
        2.5.1 IGD and IGDX
        2.5.2 Visual Examination
    2.6 Test Problems
        2.6.1 Scalable Polygon Test Problem
        2.6.2 SYM-PART 1 Test Problem
        2.6.3 SS-UF1 Test Problem
        2.6.4 Omni Test Problem
        2.6.5 TWO-ON-ONE Test Problem
    2.7 Summary
Chapter 3 Subpopulation Searching
    3.1 The Proposed Method
        3.1.1 The Basic Idea of Subpopulation Searching
        3.1.2 Implementation of Subpopulation Searching in SPEA2
        3.1.3 Implementation of Subpopulation Searching in IBEA
    3.2 Experimental Settings
        3.2.1 Parameters of SPEA2
        3.2.2 Parameters of SPEA2 with Subpopulation Searching
        3.2.3 Parameters of IBEA
        3.2.4 Parameters of IBEA with Subpopulation Searching
    3.3 Experimental Results
        3.3.1 Comparison between SPEA2 and SPEA2 with Subpopulation Searching
        3.3.2 Comparison between IBEA and IBEA with Subpopulation Searching
        3.3.3 The Effect of the Number of Subpopulations
    3.4 Summary
Chapter 4 Neighborhood Anchor
    4.1 The Proposed Method
        4.1.1 The Basic Idea of The Neighborhood Anchor
        4.1.2 Implementation of Neighborhood Anchor in SPEA2
        4.1.3 Implementation of Neighborhood Anchor in IBEA
    4.2 Experimental Settings
        4.2.1 Parameters of SPEA2 and IBEA
        4.2.2 Parameters of SPEA2 with Neighborhood Anchor
        4.2.3 Parameters of IBEA with Neighborhood Anchor
    4.3 Experimental Results for Neighborhood Anchor
        4.3.1 Comparison between SPEA2 and SPEA2 with Neighborhood Anchor
        4.3.2 Comparison between IBEA and IBEA with Neighborhood Anchor
    4.4 Summary
Chapter 5 Comparison between DNEA and Our Best Algorithm
    5.1 Experimental Settings
    5.2 Experimental Results
        5.2.1 Quantitative Analysis
        5.2.2 Visual Examination
    5.3 Discussion
    5.4 Summary
Conclusions
References
Acknowledgements


【參考文獻(xiàn)】：
期刊論文
[1]A self-organizing multimodal multi-objective pigeon-inspired optimization algorithm[J]. Yi HU,Jie WANG,Jing LIANG,Kunjie YU,Hui SONG,Qianqian GUO,Caitong YUE,Yanli WANG.  Science China（Information Sciences）. 2019(07)



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