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Adapting and Eliminating Control Parameters
A disadvantage of control parameters is that their ¯ne-tuning is a time consuming manual task. Furthermore, ideal values for the control parameters may vary during the evolution process. For example, values that encourage exploration may be desirable initially, while values that encourage exploitation may be e®ective at a later time during the algorithm’s execution.
Three broad strategies have emerged to address the disadvantages associated with DE control parameters. The ¯rst strategy uses adaptive control parameters and is discussed in Section 2.4.4.1. The values of the control parameters are adapted using information gathered during the optimisation process or to predetermined values. The second strategy is to use self-adapting control parameters. This is discussed in Section 2.4.4.2. Parameters are incorporated into the evolution process, which results in the optimisation of the control parameters in parallel with optimising the ¯tness landscape [Eiben et al., 2000]. The third strategy is to explicitly eliminate the need to tune control parameters from the algorithm and is discussed in Section 2.4.4.3.
The computational intelligence community have not reached consensus on when an algorithm should be classi¯ed as \adaptive » and when it should be classi¯ed as \self- adaptive ». For example, Brest et al. [2006] and Qin and Suganthan [2005] describe their algorithms as \self-adaptive », while Zhang and Sanderson [2009] argue that these algo- rithms should be described as \adaptive ». The following convention is used in this thesis: Algorithms that explicitly control the values of control parameters during the optimisation process are classi¯ed as \adaptive ». For example, linearly decreasing the scale factor as a function of time (initially to encourage exploration and later to encourage exploitation) are classi¯ed as \adaptive ». Algorithms that select control parameters based on the success rate of previous values during the optimisation process are classi¯ed as \self-adaptive ».
Ideally, algorithms that adapt control parameters should reduce the number of pa- rameters, or preferably eliminate all parameters. However, the literature review presented in this section illustrates that, in practice, adaptive and self-adaptive control parameter algorithms do not in all cases reduce the number of parameters. Several approaches to adapting or eliminating DE parameters are available in the literature and are discussed in this section. Algorithms that are relevant to Chapter 6, which presents the incorporation of self-adaptive control parameters into the algorithms that are developed in this thesis, are described in more detail.
1 INTRODUCTION
1.1 Motivation
1.2 Objectives .
1.3 Methodology .
1.4 Contributions
1.5 Scope .
1.6 Thesis structure .
2 BACKGROUND
2.1 Introduction
2.2 Optimisation
2.3 Genotypic Diversity
2.4 Di®erential Evolution
2.4.1 Basic Di®erential Evolution .
2.4.2 Di®erential Evolution Schemes
2.4.3 Di®erential Evolution Control Parameters
2.4.4 Adapting and Eliminating Control Parameters .
2.4.5 Di®erential Evolution Applications .
2.5 Dynamic Environments
2.5.1 Formal De¯nition
2.5.2 Types of Dynamic Environments
2.5.3 Moving Peaks Benchmark
2.5.4 Generalised Dynamic Benchmark Generator .
2.5.5 Performance Measures for Dynamic Environments
2.6 Conclusions
3 DYNAMIC ENVIRONMENT OPTIMISATION ALGORITHMS
3.1 Introduction
3.2 Di®erential Evolution in Dynamic Environments
3.2.1 Loss of Diversit
3.2.2 Outdated Information
3.3 Related Work
3.3.1 Approaches aimed at solving Dynamic Optimisation Problems
3.3.2 Strategies used to solve Dynamic Optimisation Problems .
3.3.3 Algorithms aimed at Dynamic Optimisation Problems .
3.3.4 Summary .
3.4 Di®erential Evolution for Dynamic Optimisation Problems .
3.4.1 DynDE
3.4.2 jDE
3.5 Detecting Changes in the Environment
3.6 Conclusions
4 NOVEL EXTENSIONS TO DYNDE
4.1 Introduction
4.2 Alternative Exclusion Threshold Approach
4.3 Competitive Population Evaluation
4.4 Reinitialisation Midpoint Check
4.5 Competing Di®erential Evolution
4.6 Experimental Results
4.7 Comparison to Other Approaches
4.8 General Applicability
4.9 Conclusions
5 UNKNOWN NUMBER OF OPTIMA
5.1 Introduction
5.2 Dynamic Population Di®erential Evolution
5.3 Experimental Results
5.4 Comparison to Other Approaches .
5.5 Conclusions
6 SELF-ADAPTIVE CONTROL PARAMETERS
7 CONCLUSIONS
8 Bibliography
A Parameter dependence of jDE
B Additional Results
C Additional Results – Chapter 5
D Additional Results – Chapter 6
E List of Symbols
F List of Abbreviations
G Derived Publications
