Guided Randomness in Optimization, Volume 1.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.