Differential Evolution: A Handbook for Global Permutation-Based Combinatorial Optimization

1. Front Matter

   Pages I-XVII

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2. Motivation for Differential Evolution for Permutative—Based Combinatorial Problems

   • Godfrey Onwubolu, Donald Davendra

   Pages 1-11

3. Differential Evolution for Permutation—Based Combinatorial Problems

   • Godfrey Onwubolu, Donald Davendra

   Pages 13-34

4. Forward Backward Transformation

   • Donald Davendra, Godfrey Onwubolu

   Pages 35-80

5. Relative Position Indexing Approach

   • Daniel Lichtblau

   Pages 81-120

6. Smallest Position Value Approach

   • Fatih Tasgetiren, Angela Chen, Gunes Gencyilmaz, Said Gattoufi

   Pages 121-138

7. Discrete/Binary Approach

   • Fatih Tasgetiren, Yun-Chia Liang, Quan-Ke Pan, Ponnuthurai Suganthan

   Pages 139-162

8. Discrete Set Handling

   • Ivan Zelinka

   Pages 163-205

9. Back Matter

   Pages 207-213

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What is combinatorial optimization? Traditionally, a problem is considered to be c- binatorial if its set of feasible solutions is both ?nite and discrete, i. e. , enumerable. For example, the traveling salesman problem asks in what order a salesman should visit the cities in his territory if he wants to minimize his total mileage (see Sect. 2. 2. 2). The traveling salesman problem’s feasible solutions - permutations of city labels - c- prise a ?nite, discrete set. By contrast, Differential Evolution was originally designed to optimize functions de?ned on real spaces. Unlike combinatorial problems, the set of feasible solutions for real parameter optimization is continuous. Although Differential Evolution operates internally with ?oating-point precision, it has been applied with success to many numerical optimization problems that have t- ditionally been classi?ed as combinatorial because their feasible sets are discrete. For example, the knapsack problem’s goal is to pack objects of differing weight and value so that the knapsack’s total weight is less than a given maximum and the value of the items inside is maximized (see Sect. 2. 2. 1). The set of feasible solutions - vectors whose components are nonnegative integers - is both numerical and discrete. To handle such problems while retaining full precision, Differential Evolution copies ?oating-point - lutions to a temporary vector that, prior to being evaluated, is truncated to the nearest feasible solution, e. g. , by rounding the temporary parameters to the nearest nonnegative integer.

• Differential Evolution
• Mathematica
• Permutation
• algorithm
• algorithms
• combinatorial optimization
• computational intelligence
• evolution
• intelligence
• mutation
• optimization
• programming
• programming language
• transformation

• Richmond Hill, Canada

  Godfrey C. Onwubolu

• Department of Applied Informatics, Tomas Bata Univerzity in Zlin, Zlin, Czech Republic

  Donald Davendra

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