It is often claimed that Evolutionary Algorithms are superior to other optimization techniques, in particular, in situations where not much is known about the objective function to be optimized. In contrast to that Wolpert and Macready (1997) proved that all optimization techniques have the same behavior --- on average over all f : X ! Y where X and Y are finite sets. This result is called No Free Lunch Theorem. Here different scenarios of optimization are presented. It is argued why the scenario on which the No Free Lunch Theorem is based does not model real life optimization. For more realistic scenarios it is argued why optimization techniques differ in their efficiency. For a small example this claim is proved.

The No Free Lunch theorem is reviewed and cast within a simple framework for blackbox search. A duality result which relates functions being optimized to algorithms optimizing them is obtained and is used to sharpen the No Free Lunch theorem. Observations are made concerning problem description length within the context provided by the results of this paper. It is seen that No Free Lunch results are independent from whether or not the set of functions (over which a No Free Lunch result holds) is compressible.

A measure of complexity is proposed that counts the number of local minima in any given problem representation. A special class of functions with the maximum possible number of optima is also defined. A proof is given showing that reflected Gray code induce more optima than Binary over this special class of functions; by the No Free Lunch principle, reflected Gray codes therefore induces fewer optima over all other remaining functions. 1 INTRODUCTION Over all possible functions, Gray codes and Standard Binary codes are equal in that they both cover the set of all possible bit representations [4]. In spite of this No Free Lunch result [5], applications oriented researchers have often argued for the use of Gray codes [1]. The debate as to whether Gray coding is better than Binary representations has been a classic example of where theory and practice clash. The results in this paper bring theory and practice closer together and yields new insights into the role of representati...

An overview of evolutionary algorithms is presented covering genetic algorithms, evolution strategies, genetic programming and evolutionary programming. The schema theorem is reviewed and critiqued. Gray codes, bit representations and real-valued representations are discussed for parameter optimization problems. Parallel Island models are also reviewed, and the evaluation of evolutionary algorithms is discussed.

Abstract. The sharpened No-Free-Lunch-theorem (NFL-theorem) states that, regardless of the performance measure, the performance of all optimization algorithms averaged uniformly over any finite set F of functions is equal if and only if F is closed under permutation (c.u.p.). In this paper, we first summarize some consequences of this theorem, which have been proven recently: The number of subsets c.u.p. can be neglected compared to the total number of possible subsets. In particular, problem classes relevant in practice are not likely to be c.u.p. The average number of evaluations needed to find a desirable (e.g., optimal) solution can be calculated independent of the optimization algorithm in certain scenarios. Second, as the main result, the NFL-theorem is extended. Necessary and sufficient conditions for NFL-results to hold are given for arbitrary distributions of target functions. This yields the most general NFL-theorem for optimization presented so far. Mathematics Subject Classifications (2000): 90C27, 68T20. Key words: evolutionary computation, No-Free-Lunch theorem.

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, OE, designed to provide one measure of complexity with respect to a simple genetic algorithm

Many organisations now routinely gather vast and ever-increasing amounts of data in the ordinary course of their business. While much of this information is collected for day-to-day operational reasons, many businesses are now realising that this data has much additional value for improving operational processes. Large databases can form the basis of decision support systems, often based around a data warehouse. Such systems may then be used for a variety of applications such as trend spotting, pattern recognition, behavioral modeling and customer worth assessment. Against this backdrop, the term data mining is used to refer to the process of searching through a large volume of data to discover interesting and useful information. The authors have traditionally sought to divide data mining into three types or levels---undirected or pure data mining, where the system is left almost entirely unconstrained to discover patterns in the data free of prejudices from the user; directed data mi...

When a function is mapped onto a bit representation, the structure of the fitness landscape can change dramatically. Techniques such as Delta Coding have tried to dynamically adapt the representation during the search process in hopes of making the problem easier for a genetic algorithm to solve.

Introduction This tutorial reviews basic concepts in complexity theory, as well as various No Free Lunch results and how these results relate to computational complexity. The tutorial explain basic concepts in an informal fashion that illuminates key concepts. "No Free Lunch" theorems for search can be summarized by the following result: another when its performance is averaged over all possible discrete functions. Note that "No Free Lunch" is often referred to simply as NFL within the heuristic search community (despite copyrights and trademarks held by the National Football League). No Free Lunch relates to complexity theory in as much as complexity theory addresses the time and space costs of algorithms; complexity theory is also concerned with key classes of problems, such as the class of NP -Complete problems that are also of interest to researchers designing search algorithms. 2. Complexity, P and NP The complexity classes denoted by P and NP are the most famous (or notor

Most evolutionary algorithms use a fixed representation space. This complicates their application to many problem domains, especially when there are dependencies between problem variables (e.g. problems naturally defined over permutations). This paper presents a method for specifying algorithms with respect to abstract representations, making them completely independent of any actual representation or problem domain. It also defines a procedure for generating a concrete representation from an explicit characterisation of a problem domain which captures beliefs about its structure. This allows arbitrary algorithms to be applied to arbitrary problems yielding well-specified search strategies suitable for implementation. The process is illustrated by showing how identical algorithms can be applied to both the TSP and real parameter optimisation to yield familiar (but superficially very different) concrete search strategies.