A measure of search difficulty, fitness distance correlation (FDC), is introduced and examined in relation to genetic algorithm (GA) performance. In many cases, this correlation can be used to predict the performance of a GA on problems with known global maxima. It correctly classifies easy deceptive problems as easy and difficult non-deceptive problems as difficult, indicates when Gray coding will prove better than binary coding, and is consistent with the surprises encountered when GAs were used on the Tanese and royal road functions. The FDC measure is a consequence of an investigation into the connection between GAs and heuristic search. 1 INTRODUCTION A correspondence between evolutionary algorithms and heuristic state space search is developed in (Jones, 1995b). This is based on a model of fitness landscapes as directed, labeled graphs that are closely related to the state spaces employed in heuristic search. We examine one aspect of this correspondence, the relationship between...

Niching methods extend genetic algorithms to domains that require the location and maintenance of multiple solutions. Such domains include classification and machine learning, multimodal function optimization, multiobjective function optimization, and simulation of complex and adaptive systems. This study presents a comprehensive treatment of niching methods and the related topic of population diversity. Its purpose is to analyze existing niching methods and to design improved niching methods. To achieve this purpose, it first develops a general framework for the modelling of niching methods, and then applies this framework to construct models of individual niching methods, specifically crowding and sharing methods. Using a constructed model of crowding, this study determines why crowding methods over the last two decades have not made effective niching methods. A series of tests and design modifications results in the development of a highly effective form of crowding, called determin...

The problem of complex adaptations is studied in two largely disconnected research traditions: evolutionary biology and evolutionary computer science. This paper summarizes the results from both areas and compares their implications. In evolutionary computer science it was found that the Darwinian process of mutation, recombination and selection is not universally effective in improving complex systems like computer programs or chip designs. For adaptation to occur, these systems must possess "evolvability", i.e. the ability of random variations to sometimes produce improvement. It was found that evolvability critically depends on the way genetic variation maps onto phenotypic variation, an issue known as the representation problem. The genotype-phenotype map determines the variability of characters, which is the propensity to vary. Variability needs to be distinguished from variation, which are the actually realized differences between individuals. The genotype-phenotype map is the ...

Genetic algorithms rely on two genetic operators - crossover and mutation. Although there exists a large body of conventional wisdom concerning the roles of crossover and mutation, these roles have not been captured in a theoretical fashion. For example, it has never been theoretically shown that mutation is in some sense "less powerful" than crossover or vice versa. This paper provides some answers to these questions by theoretically demonstrating that there are some important characteristics of each operator that are not captured by the other.

In this paper we investigate genetic algorithms where more than two parents are involved in the recombination operation. In particular, we introduce gene scanning as a reproduction mechanism that generalizes classical crossovers, such as n-point crossover or uniform crossover, and is applicable to an arbitrary number (two or more) of parents. We performed extensive tests for optimizing numerical functions, the TSP and graph coloring to observe the effect of different numbers of parents. The experiments show that 2-parent recombination is outperformed when using more parents on the classical DeJong functions. For the other problems the results are not conclusive, in some cases 2 parents are optimal, while in some others more parents are better. 1. Introduction A fact in nature is that the creation of new individuals always occurs through either asexual (one parent) or sexual (two parents) reproduction. It hardly ever puzzles people why the number of parents is restricted to one or two....

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The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced.

In this paper, we develop techniques based on evolvability statistics of the fitness landscape surrounding sampled solutions. Averaging the measures over a sample of equal fitness solutions allows us to build up fitness evolvability portraits of the fitness landscape, which we show can be used to compare both the ruggedness and neutrality in a set of tunably rugged and tunably neutral landscapes. We further show that the techniques can be used with solution samples collected through both random sampling of the landscapes and online sampling during optimization. Finally, we apply the techniques to two real evolutionary electronics search spaces and highlight differences between the two search spaces, comparing with the time taken to find good solutions through search.

In an earlier paper we examined the relationship between genetic algorithms (GAs) and traditional methods of experimental design. This was motivated by an investigation into the problems caused by epistasis in the implementation and application of GAs to optimization problems. We showed how this viewpoint enables us to gain further insights into the determination of epistatic effects, and into the value of different forms of encoding a problem for a GA solution. We also demonstrated the equivalence of this approach toWalsh transform analysis. In this paper we consider further the question of whether the epistasis metric actually gives a good prediction of the ease or difficulty of solution of a given problem by a GA. Our original analysis assumed, as does the rest of the related literature, knowledge of the complete solution space. In practice, we only ever sample a fraction of all possible solutions, and this raises significant questions which are the subject of...

. We use the one-dimensional nearest neighbor interaction functions (NNIs) to show how the presence of symmetry in a fitness function greatly influences the convergence behavior of the simple genetic algorithm (SGA). The effect of symmetry on the SGA supports the statement that it is not the amount of interaction present in a fitness function, measured e.g. by Davidor's epistasis variance and the experimental design techniques introduced by Reeves and Wright, which is important, but the kind of interaction. The NNI functions exhibit a minimal amount of second order interaction, are trivial to optimize deterministically and yet show a wide range of SGA behavior. They have been extensively studied in statistical physics; results from this field explain the negative effect of symmetry on the convergence behavior of the SGA. This note intends to introduce them to the GA-community. Introduction One factor influencing the convergence behavior of the simple genetic algorithm (SGA) is the pre...