Above are papers related to the following paper: [Paper_ID] Paper #1109208. 	[Title] Walsh Functions and Predicting Problem Complexity [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131116. 	[Title] 3 Representation Issues in Neighborhood Search and Evolutionary Algorithms [Abstract] Evolutionary Algorithms are often presented as general purpose search methods. Yet, we also know that no search method is better than another over all possible problems and that in fact there is often a good deal of problem specific information involved in the choice of problem representation and search operators. In this paper we explore some very general properties of representations as they relate to neighborhood search methods. In particular, we looked at the expected number of local optima under a neighborhood search operator when averaged overall possible representations. The number of local optima under a neighborhood search operator for standard Binary and standard binary reflected Gray codes is developed and explored as one measure of problem complexity. We also relate number of local optima to another metric, , designed to provide one measure of complexity with respect to a simple genetic algorithm. Choosing a good representation is a vital component of solving any search problem. However, choosing a good representation for a problem is as difficult as choosing a good search algorithm for a problem. Wolpert and Macready's (1995) No Free Lunch (NFL) theorem proves that no search algorithm is better than any other over all possible discrete functions. Radcliffe and Surry (1995) extend these notions to also cover the idea that all representations are equivalent when their behavior is considered on average over all possible functions. To understand these results, we first outline some of the simple assumptions behind this theorem. First, assume the optimization problem is discrete; this describes all combinatorial optimization problems-and really all optimization problems being solved on computers since computers have finite precision. Second, we ignore the fact that we can resample points in the space. The "No Free Lunch" result can be stated as follows: Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #148341. 	[Title] Nonlinearity, Hyperplane Ranking and the Simple Genetic Algorithm [Abstract] Several metrics are used in empirical studies to explore the mechanisms of convergence of genetic algorithms. The metric is designed to measure the consistency of an arbitrary ranking of hyperplanes in a partition with respect to a target string. Walsh coefficients can be calculated for small functions in order to characterize sources of linear and nonlinear interactions. A simple deception measure is also developed to look closely at the effects of increasing nonlinearity of functions. Correlations between the metric and deception measure are discussed and relationships between and convergence behavior of a simple genetic algorithm are studied over large sets of functions with varying degrees of nonlinearity. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #263069. 	[Title] Hyperplane Ranking in Simple Genetic Algorithms [Abstract] We examine the role of hyperplane ranking during search performed by a simple genetic algorithm. We also develop a metric for measuring the degree of ranking that exists with respect to static measurements taken directly from the function, as well as the measurement of dynamic ranking of hyperplanes during genetic search. We show that the degree of dynamic ranking induced by a simple genetic algorithm is highly correlated with the degree of static ranking that is inherent in the function, especially during the initial genera tions of search. Please summarise all the given information.

Paper #1109208 has the title `Walsh Functions and Predicting Problem Complexity  
` and the abstract ` 
`.
Question: Which category should Paper #1109208 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1109208 has the title `Walsh Functions and Predicting Problem Complexity  
` and the abstract ` 
`.
Question: Which category should Paper #1109208 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Genetic_Algorithms