Guided Randomness in Optimization, Volume 1
Published on 4. May 2015
316 pages
978-1-119-13644-6 (ISBN)
Description
The performance of an algorithm used depends on the GNA. This book focuses on the comparison of optimizers, it defines a stress-outcome approach which can be derived all the classic criteria (median, average, etc.) and other more sophisticated. Source-codes used for the examples are also presented, this allows a reflection on the "superfluous chance," succinctly explaining why and how the stochastic aspect of optimization could be avoided in some cases.
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Maurice Clerc
Guided Randomness in Optimization, Volume 1
Book
06/2015
1st Edition
Wiley-ISTE
€164.50
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05/2015
Wiley
€173.48
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Person
Maurice Clerc is recognized as one of the foremost PSO specialists in the world. A former France Telecom Research and Development engineer, he maintains his research activities as a consultant for the XPS (eXtended Particle Swarm) project.
Content
- Cover
- Title Page
- Copyright
- Contents
- Preface
- About this book
- Organization of the book
- Tools
- Key points
- Contact the author
- Introduction
- PART 1: Randomness in Optimization
- 1: Necessary Risk
- 1.1. No better than random search
- 1.1.1. Uniform random search
- 1.1.2. Sequential search
- 1.1.3. Partial gradient
- 1.2. Better or worse than random search
- 1.2.1. Positive correlation problems
- 1.2.2. Negative correlation problems
- 2: Random Number Generators (RNGs)
- 2.1. Generator types
- 2.2. True randomness
- 2.3. Simulated randomness
- 2.3.1. KISS
- 2.3.2. Mersenne-Twister
- 2.4. Simplified randomness
- 2.4.1. Linear congruential generators
- 2.4.2. Additive
- 2.4.3. Multiplicative
- 2.5. Guided randomness
- 2.5.1. Gaussian
- 2.5.2. Bell
- 2.5.3. Cauchy
- 2.5.4. Lévy
- 2.5.5. Log-normal
- 2.5.6. Composite distributions
- 3: The Effects of Randomness
- 3.1. Initialization
- 3.1.1. Uniform randomness
- 3.1.2. Low divergence
- 3.1.3. No Man's Land techniques
- 3.2. Movement
- 3.3. Distribution of the Next Possible Positions (DNPP)
- 3.4. Confinement, constraints and repairs
- 3.4.1. Strict confinement
- 3.4.2. Random confinement
- 3.4.3. Moderate confinement
- 3.4.4. Reverse
- 3.4.5. Reflection-diffusion
- 3.5. Strategy selection
- PART 2: Optimizer Comparison
- Introduction to Part 2
- 4: Algorithms and Optimizers
- 4.1. The Minimaliste algorithm
- 4.1.1. General description
- 4.1.2. Minimaliste in practice
- 4.1.3. Use of randomness
- 4.2. PSO
- 4.2.1. Description
- 4.2.2. Use of randomness
- 4.3. APS
- 4.3.1. Description
- 4.3.2. Uses of randomness
- 4.4. Applications of randomness
- 5: Performance Criteria
- 5.1. Eff-Res: construction and properties
- 5.1.1. Simple example using random search
- 5.2. Criteria and measurements
- 5.2.1. Objective criteria
- 5.2.1.1. Result probabilities
- 5.2.1.2. Effort probabilities
- 5.2.1.3. Mean result of an effort
- 5.2.1.4. Median result of an effort
- 5.2.1.5. Normalized efficiency
- 5.2.1.6. Mean and median cost
- 5.2.2. Semi-subjective criteria
- 5.2.2.1. Fragmentation of effort
- 5.2.2.2. Result quality and success rate
- 5.2.2.3. Global quality
- 5.3. Practical construction of an Eff-Res
- 5.3.1. Detailed example: (Minimaliste, Alpine 2D)
- 5.3.2. Qualitative interpretations
- 5.4. Conclusion
- 6: Comparing Optimizers
- 6.1. Data collection and preprocessing
- 6.2. Critical analysis of comparisons
- 6.2.1. Influence of criteria and the number of attempts
- 6.2.2. Influence of effort levels
- 6.2.3. Global comparison
- 6.2.4. Influence of the RNG
- 6.3. Uncertainty in statistical analysis
- 6.3.1. Independence of tests
- 6.3.2. Confidence threshold
- 6.3.3. Success rate
- 6.4. Remarks on test sets
- 6.4.1. Analysis grid
- 6.4.2. Representativity
- 6.5. Precision and prudence
- PART 3: Appendices
- 7: Mathematical Notions
- 7.1. Sets closed under permutations
- 7.2. Drawing with or without repetition
- 7.3. Properties of the Additive and Multiplicative generators
- 7.3.1. Additive
- 7.3.2. Multiplicative
- 8: Biases and Signatures
- 8.1. The impossible plateau
- 8.2. Optimizer signatures
- 9: A Pseudo-Scientific Article
- 9.1. Article
- 9.2. Criticism
- 10: Common Mistakes
- 11: Unnecessary Randomness? List-based Optimizers
- 11.1. Truncated lists
- 11.2. Semi-empirical lists
- 11.3. Micro-robots
- 12: Problems
- 12.1. Deceptive 1 (Flash)
- 12.2. Deceptive 2 (Comb)
- 12.3. Deceptive 3 (Brush)
- 12.4. Alpine
- 12.5. Rosenbrock
- 12.6. Pressure vessel
- 12.7. Sphere
- 12.8. Traveling salesman: six cities
- 12.9. Traveling salesman: fourteen cities (Burma 14)
- 12.10. Tripod
- 12.11. Gear train
- 13: Source Codes
- 13.1. Random generation and sampling
- 13.1.1. Preamble for Scilab codes
- 13.1.2. Drawing of a pseudo-random number, according to options
- 13.1.3. True randomness
- 13.1.4. Guided randomness
- 13.1.4.1. Approximation of the Lévy distribution
- 13.1.5. Uniform initializations (continuous, combinatorial)
- 13.1.6. Regular initializations (Sobol, Halton)
- 13.1.7. No Man's Land techniques
- 13.1.8. Sampling
- 13.1.9. Movements and confinements
- 13.2. Useful tools
- 13.3. Combinatorial operations
- 13.4. Random algorithm
- 13.5. Minimaliste algorithm
- 13.6. SPSO algorithm
- 13.7. APS algorithm
- 13.8. µPSO algorithm
- 13.9. Problems
- 13.9.1. Problem definitions
- 13.9.2. Problem landscape
- 13.10. Treatment of results
- 13.10.1. Quality (including curves)
- 13.10.2. Other criteria (including curves)
- 13.10.3. Construction of an Eff-Res
- 13.11. Treatment of the Eff-Res
- 13.11.1. Graphic representation
- 13.11.2. Interpolation
- 13.11.3. Performance criteria (including curves)
- 13.12. Histograms, polar diagrams
- 13.13. Other figures
- 13.14. Tests (bias, correlation)
- Bibliography
- Index
