Overview
- Presents a complete introduction to differential evolution
- Includes the continuous space DE formulation and the permutative-based combinatorial DE formulation
Part of the book series: Studies in Computational Intelligence (SCI, volume 175)
Buy print copy
About this book
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.
Similar content being viewed by others
Keywords
Table of contents (7 chapters)
-
Front Matter
-
Back Matter
Editors and Affiliations
Bibliographic Information
Book Title: Differential Evolution: A Handbook for Global Permutation-Based Combinatorial Optimization
Editors: Godfrey C. Onwubolu, Donald Davendra
Series Title: Studies in Computational Intelligence
DOI: https://doi.org/10.1007/978-3-540-92151-6
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Hardcover ISBN: 978-3-540-92150-9Published: 13 January 2009
Softcover ISBN: 978-3-662-51892-2Published: 30 April 2017
eBook ISBN: 978-3-540-92151-6Published: 23 December 2008
Series ISSN: 1860-949X
Series E-ISSN: 1860-9503
Edition Number: 1
Number of Pages: XVII, 213
Topics: Mathematical and Computational Engineering, Artificial Intelligence, Applications of Mathematics