Combinatorial global optimization (8 Ergebnisse)

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Zustand: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | 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.…

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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

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Zustand: Sehr gut. Zustand: Sehr gut | Seiten: 372 | Sprache: Englisch | Produktart: Bücher | Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans-Williamson relaxation of the maximum cut problem, and the Du-Hwang solution of the Gilbert-Pollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on "Combinatorial and Global Optimization" held at Crete, Greece.…