The choice of a representation i.e. the definition of the search space, is of vital importance in all Evolutionary Optimization processes. In the context of Topological Optimum Design in Structural Mechanics, this paper investigates possible representations for evolutionary shape design.

It is known that the performance of a genetic algorithm depends on the survival environment and the reproducibility of building blocks. In this paper, we propose a new encoding/crossover scheme that uses genic distance which explicitly defines the distance between each pair of genes in the chromosome. It pursues both relatively high survival probabilities of more epistatic gene groups and diverse crossover operators for the high creativity of new schemata. The experimental results on benchmark traveling salesman problems showed remarkable improvement in tour cost and running time over state-of-the-art genetic algorithms for the problem. 1

The problem of the identification of mechanical inclusion is theoretically ill-posed, and to-date numerical algorithms have demonstrated to be inaccurate and unstable. On the other hand, Evolutionary Algorithms provide a general approach to inverse problem solving. However, great care must be taken during the implementation: The choice of the representation, which determines the search space, is critical. Three representations are presented and discussed. Whereas the straightforward mesh-dependent representation suffers strong limitations, both mesh-independent representation provide outstanding results on simple instances of the identification problem, including experimental robustness in presence of noise.

Abstract. The building block hypothesis implies that the epistatic property of a given problem must be connected well to the linkage property of the employed representation and crossover operator in the design of genetic algorithms. A good handling of building blocks has much to do with topological linkages of genes in the chromosome. In this paper, we provide a taxonomy of the approaches that exploit topological linkages of genes. They are classified into three models: static linkage model, adaptive linkage model, and evolvable linkage model. We also provide an overview on the chromosomal structures, encodings, and operators supporting each of the models. 1

Evolutionary Algorithms provide a general approach to inverse problem solving: As optimization methods, they only require the computation of values of the function to optimize. Thus, the only prerequisite to efficiently handle inverse problems is a good numerical model of the direct problem, and a representation for potential solutions. The identification of mechanical inclusion, even in the linear elasticity framework, is a difficult problem, theoretically ill-posed: Evolutionary Algorithms are in that context a good tentative choice for a robust numerical method, as standard deterministic algorithms have proven inaccurate and unstable. However, great attention must be given to the implementation. The representation, which determines the search space, is critical for a successful application of Evolutionary Algorithms to any problem. Two original representations are presented for the inclusion identification problem, together with the associated evolution operators (crossover and muta...

Genetic algorithms (GAs) are believed to exploit the synergy between different traversals of the solution space that are afforded by crossover and mutation operators. While dozens of different crossovers are known, comparatively little attention has been devoted to improving performance by using multiple crossover operators within a given GA implementation. Here, we examine various aspects of combining different crossovers; we demonstrate that mixtures of crossovers can outperform any single crossover, and that choosing appropriate mixing proportions is critical for good performance. We conjecture that good crossover mixtures are characterized by "balance" in the crossovers' respective influences in the population, and explore three adaptive strategies for mixing crossovers. 1 Introduction The crossover and mutation operators of genetic algorithms (GAs) navigate the solution space in synergetic ways: crossover generates new solutions by combining traits of already-visited solutions, w...

Many problems to be solved in geophysical processing can be expressed in terms of identification of spatial geological models : given a function OE applied to a geological model fl, producing a result R, the problem is to find fl such that OE(fl ) = R , where R is the expected result : a seismogram, a pressure curve, a seismic cross-section etc. The presented research deals with the joint use of evolutionary algorithms and Voronoi diagrams to address some non-parametric instances of identification problems in geophysics, i.e. without a priori hypothesis about the geometrical layout of possible solutions. In this paper, a first application in velocity determination for seismic imaging demonstrates the ability of this approach to identify both the geometry and the velocities of the underground from experimental seismograms. 1 Introduction 1.1 The geophysical problem A seismic experiment starts with an artificial explosion at some point near the surface. Elastic waves propagate thr...

This paper reviews and summarizes existing linkage learning techniques for genetic and evolutionary algorithms in the literature. It first introduces the definition of linkage in both biological systems and genetic algorithms. Then, it discusses the importance for genetic and evolutionary algorithms to be capable of learning linkage, which is referred to as the relationship between decision variables. Existing linkage learning methods proposed in the literature are reviewed according to different facets of genetic and evolutionary algorithms, including the means to distinguish between good linkage and bad linkage, the methods to express or represent linkage, and the ways to store linkage information. Studies related to these linkage learning methods and techniques are also investigated in this survey. 1

Abstract. As a preprocessing for genetic algorithms, static reordering helps genetic algorithms effectively create and preserve high-quality schemata, and consequently improves the performance of genetic algorithms. In this paper, we propose a static reordering method independent of problem-specific knowledge. One of the novel features of our reordering method is that it is applicable to any problem with no information about the problem. The proposed method constructs a weighted complete graph from the gene distances calculated from solutions with relatively high fitnesses, transforms them into a gene-interaction graph, and finds a gene rearrangement. Extensive experimental results showed significant improvement for a number of applications. 1

This paper presents an Evolutionary approach to problems of shape optimization and identification: the aim is to find a partition of a given design domain of the 2D-plane or the 3D-space into two subsets (e.g. material and void for the Optimal Design problems). The central issue of this paper is the representation of such repartition suitable for its evolutionary optimization, and its dependency with respect to the problem at hand.