Iterative Optimizers

Book description

Almost every month, a new optimization algorithm is proposed, often accompanied by the claim that it is superior to all those that came before it. However, this claim is generally based on the algorithm's performance on a specific set of test cases, which are not necessarily representative of the types of problems the algorithm will face in real life.

This book presents the theoretical analysis and practical methods (along with source codes) necessary to estimate the difficulty of problems in a test set, as well as to build bespoke test sets consisting of problems with varied difficulties.

The book formally establishes a typology of optimization problems, from which a reliable test set can be deduced. At the same time, it highlights how classic test sets are skewed in favor of different classes of problems, and how, as a result, optimizers that have performed well on test problems may perform poorly in real life scenarios.

Table of contents

  1. Cover
  2. Preface
    1. The Essentials
  3. Introduction
    1. Reading guide
  4. 1 Some Definitions
    1. 1.1. Continuous case vs discrete case: when a theorem no longer holds
    2. 1.2. Landscape
  5. 2 Difficulty of the Difficulty
    1. 2.1. Effort and budgets
    2. 2.2. Acceptable solution
    3. 2.3. Difficulty vs complexity
    4. 2.4. Normalized roughness
    5. 2.5. Measure δr,ε
    6. 2.6. Measure δ0
    7. 2.7. Measures non-NisB
    8. 2.8. Perceived difficulty
  6. 3 Landscape Typology
    1. 3.1. Reliable functions, misleading and neutral
    2. 3.2. Plateaus
    3. 3.3. Multimodal functions
    4. 3.4. Unimodal functions
  7. 4 LandGener
    1. 4.1. Examples
    2. 4.2. Generated files
    3. 4.3. Regular landscape
  8. 5 Test Cases
    1. 5.1. Structure of a representative test case
    2. 5.2. CEC 2005
    3. 5.3. CEC 2011
  9. 6 Difficulty vs Dimension
    1. 6.1. Rosenbrock function
    2. 6.2. Griewank function
    3. 6.3. Example of the normalized paraboloid
    4. 6.4. Normalized bi-paraboloid
    5. 6.5. Difficulty δ0 and dimension
  10. 7 Exploitation and Exploration vs Difficulty
    1. 7.1. Exploitation, an incomplete definition
    2. 7.2. Rigorous definitions
    3. 7.3. Balance profile
  11. 8 The Explo2 Algorithm
    1. 8.1. The algorithm
    2. 8.2. Subjective numerical summary of a distribution of results
  12. 9 Balance and Perceived Difficulty
    1. 9.1. Constant profile-based experiments
    2. 9.2. Calculated difficulty vs perceived difficulty
  13. Appendix
    1. A.1. Pigeonhole principle and monotonicity
    2. A.2. Similarities between optimizers
    3. A.3. Optimizer signature
    4. A.4. Non-NisB difficulties of a unimodal function
    5. A.5. A few test functions
    6. A.6. Equivalent functions
    7. A.7. Examples of deceptive functions
    8. A.8. Empirical rules for a measure of difficulty
    9. A.9. Optimizer effectiveness
    10. A.10. Explo2+
    11. A.11. Greedy
    12. A.12. Source codes
    13. A.13. LandGener landscapes
  14. References
  15. Index
  16. End User License Agreement

Product information

  • Title: Iterative Optimizers
  • Author(s): Maurice Clerc
  • Release date: April 2019
  • Publisher(s): Wiley-ISTE
  • ISBN: 9781786304094