This is the first book devoted entirely to Differential Evolution (DE) for global permutative-based combinatorial optimization. Since its original development, DE has mainly been applied to solving problems characterized by continuous parameters. This means that only a subset of real-world problems could be solved by the original, classical DE algorithm. This book presents in detail the various permutative-based combinatorial DE formulations by their initiators in an easy-to-follow manner, through extensive illustrations and computer code. It is a valuable resource for professionals and students interested in DE in order to have full potentials of DE at their disposal as a proven optimizer. All source programs in C and Mathematica programming languages are downloadable from the website of Springer. 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 problems 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 problems goal is to pack objects of differing weight and value so that the knapsacks 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. Combinatorial optimisation is a ubiquitous discipline whose usefulness spans vast applications domains. The intrinsic complexity of most combinatorial optimisation problems makes classical methods unaffordable in many cases. To acquire practical solutions to these problems requires the use of metaheuristic approaches that trade completeness for pragmatic effectiveness. Such approaches are able to provide optimal or quasi-optimal solutions to a plethora of difficult combinatorial optimisation problems. The application of metaheuristics to combinatorial optimisation is an active field in which new theoretical developments, new algorithmic models, and new application areas are continuously emerging. This volume presents recent advances in the area of metaheuristic combinatorial optimisation, with a special focus on evolutionary computation methods. Moreover, it addresses local search methods and hybrid approaches. In this sense, the book includes cutting-edge theoretical, methodological, algorithmic and applied developments in the field, from respected experts and with a sound perspective. Motivation for differential evolution for permutative-based combinatorial problems / Godfrey C. Onwubolu, Donald Davendra Differential evolution for permutation-based combinatorial problems / Godfrey C. Onwubolu, Donald Davendra Forward backward transformation / Godfrey C. Onwubolu, Donald Davendra Relative position indexing approach / Daniel Lichtblau Smallest position value approach / Fatih Tasgetiren ... [et al.] Discrete/binary approach / Fatih Tasgetiren ... [et al.] Discrete set handling / Ivan Zelinka. Front Matter....Pages I-XVII Motivation for Differential Evolution for Permutative—Based Combinatorial Problems....Pages 1-11 Differential Evolution for Permutation—Based Combinatorial Problems....Pages 13-34 Forward Backward Transformation....Pages 35-80 Relative Position Indexing Approach....Pages 81-120 Smallest Position Value Approach....Pages 121-138 Discrete/Binary Approach....Pages 139-162 Discrete Set Handling....Pages 163-205 Back Matter....Pages 207-213
