Differential Evolution
ong>Differentialong> Evolution: 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, ong>Differentialong> 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 ong>Differentialong> 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, ong>Differentialong> 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.