Blackbox optimization---optimization in presence of limited knowledge about the objective function---has recently enjoyed a large increase in interest because of the demand from the practitioners. This has triggered a race for new high performance algorithms for solving large, difficult problems. Simulated annealing, genetic algorithms, tabu search are some examples. Unfortunately, each of these algorithms is creating a separate field in itself and their use in practice is often guided by personal discretion rather than scientific reasons. The primary reason behind this confusing situation is the lack of any comprehensive understanding about blackbox search. This dissertation takes a step toward clearing some of the confusion. The main objectives of this dissertation are: 1. present SEARCH (Search Envisioned As Relation & Class Hierarchizing)---an alternate perspective of blackbox optimization and its quantitative analysis that lays the foundation essential for transcending the limits of random enumerative search; 2. design and testing of the fast messy genetic algorithm. SEARCH is a general framework for understanding blackbox optimization in terms of relations,

A new mathematical representation is proposed for the configuration space structure induced by recombination which we called "P-structure". It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental "genotypes" the set of all recombinant genotypes obtainable from the parental ones. It is shown that this construction allows a Fourier-decomposition of fitness landscapes into a superposition of "elementary landscapes". This decomposition is analogous to the Fourier decomposition of fitness landscapes on mutation spaces. The elementary landscapes are obtained as eigenfunctions of a Laplacian operator defined for P-structures. For binary string recombination the elementary landscapes are exactly the p-spin functions (Walsh functions), i.e. the same as the elementary landscapes of the string point mutation spaces (i.e. the hypercube). This supports the notion of a strong homomorphisms between string mutation ...

In a previous paper (Reeves, 1995), a simple genetic algorithm (GA) was developed for finding (approximately) the minimum makespan of the n-job, m-machine permutation flowshop sequencing problem (PFSP). The performance of the algorithm was comparable to that of a naive neighbourhood search technique and a proven Simulated Annealing algorithm. However, recent results (Nowicki & Smutnicki, 1996) have demonstrated the superiority of a tabu search method in solving the PFSP. In this paper, we re-consider the implementation of a GA for this problem, and show that by taking into account the features of the landscape generated by the operators used, we are able to improve its performance significantly. 1 Introduction Finding optimal solutions to large combinatorial problems (COPs) is not in general a realistic endeavour, as has been recognized ever since the implications of the concept of computational complexity (Garey & Johnson, 1979) have been realized. One effect of this recognition has ...

Natural selection acts on genetic variation that comes from two principal sources: mutation and recombination. Because of the inherent differences between mutation and recombination, it is often assumed that they are qualitatively different ways to explore the genotype space. In this paper a new way of constructing recombination spaces is introduced and the topological features of the resulting hypergraphs are analyzed. It is shown that types which are neighbors in the point mutation space are also neighbors in the recombination space, i.e. mutation and recombination spaces are homomorphic. This implies that the shapes of the fitness functions explored by mutation and recombination are similar. However, the potential of one- and two-point recombination operators to explore the fitness landscape may differ dramatically from uniform recombination operators or mutation operators because of the limited number of recombinant types they can produce. 1 Introduction The concept of fitness lan...

This paper might have been subtitled "An algorithmicist looks at no free lunch." We use simple adversary arguments to redevelop and explore some ofthenofreelunch (NFL) theorems and perhaps extend them a little. A second goal is to clarify the relationship of NFL theorems to algorithm theory. In particular we claim that NFL puts much weaker restrictions on the claims that an evolutionary algorithm can make than does acceptance of the conjectures of traditional complexity theory. And third we take a brief look at whether the notion of natural evolution relates to optimization, and what if any the implications of evolution are for computing. In this part, we mostly try to raise questions concerning the validity of applying the genetic model to the problem of optimization. This is an informal paper -- most of the information presented is not formally proven, and is either "common knowledge" or formally proven elsewhere. Some of the claims are intuitions based on experience with algorithms, and in a more formal setting should be classi ed as conjectures. Thegoalisnotsomuch todevelop theory, asitisto perhaps persuade the reader to adopt a particular viewpoint.

Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, nearness, distance or accessibility. Landscape theory has emerged as an attempt to devise suitable mathematical structures for describing the "static" properties of landscapes as well as their influence on the dynamics of adaptation. In this review we focus on the connections of landscape theory with algebraic combinatorics and random graph theory, where exact results are available.

Genetic algorithms (GAs) are multi-dimensional and stochastic search methods, involving complex interactions among their parameters. For last two decades, researchers have been trying to understand the mechanics of GA parameter interactions by using various techniques|careful `functional ' decomposition of parameter interactions, empirical studies, and Markov chain analysis. Although the complexities in these interactions are getting clearer with such analyses, it still remains an open question in the mind of a new-comer to the eld or to a GA-practitioner as to what values of GA parameters (such as population size, choice of GA operators, operator probabilities, and others) to use in an arbitrary problem. In this paper, we investigate the performance of simple tripartite GAs on a number of simple to complex test problems from a practical standpoint. Since in a real-world situation, the overall time to run a GA is more or less dominated by the time consumed by objective function evaluations, we compare di erent GAs for a xed number of function evaluations. Based on probability calculations and simulation results, it is observed that for solving simple problems (unimodal or small modality problems) the mutation operator plays an important role, although GAs with the crossover operator alone can also solve these problems. However, the two operators (when applied alone) have two di erent working zones for the population size. For complex problems involving massive multi-modality and misleadingness (deception), the crossover operator is the key search operator. Based on these studies, it is recommended that when in doubt, the use of the crossover operator with an adequate population size is a reliable approach.

A major reason for the maintenance of a population in a Genetic Algorithm (GA) is the hope of increased performance via direct communication of information between individuals. This communication is achieved through the use of a crossover operator. If crossover is not a useful method for this exchange, the GA may not, on average, perform any better than a variety of simpler algorithms that are not population-based. A simple method for testing the usefulness of crossover for a particular problem instance is presented. This allows the identification of situations in which crossover is apparently useful but is actually only producing gains that could be obtained, or exceeded, with macromutation and no population. 1 INTRODUCTION The features of a GA that distinguish it most from other search methods are its use of a population and a crossover operator. In a GA, crossover is employed to effect direct communication between individuals in a population. The usefulness of crossover, and theref...

ABSTRACT. Fitness landscapes can be decomposed into elementary landscapes using a Fourier transform that is determined by the structure of the underlying con guration space. The amplitude spectrum obtained from the Fourier transform contains information about the ruggedness of the landscape. It can be used for classi cation and comparison purposes. We consider here three very di erent types of landscapes using both mutation and recombination to de ne the topological structure of the con guration spaces. A reliable procedure for estimating the amplitude spectra is presented. The method is based on certain correlation functions that are easily obtained from empirical studies of the landscapes.

The distinction between continuous and discontinuous transitions is a longstanding problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabilities with which of one phenotype is accessible from another through changes at the genotypic level. The shape space of RNA secondary structures is used to illustrate this approach. We show that evolutionary trajectories are continuous if and only if they follow connected paths in phenotype space.