Covers

This paper introduces the theory of covers for functions defined over binary variables. Covers formalize the notion of decomposability. Large complex problems are decomposed into subproblems each containing fewer variables, which can then be solved in parallel. Practical applications of the benefits from decomposition include the parallel architecture of supercomputers, the divisionalization of firms, and the decentralization of economic activity. In this introductory paper, we show how covers also shed light on the choice among public projects with complementarities. Further, covers provide a measure of complexity/decomposability with respect to contour sets, allowing for nonlinear effects which occur near the optimum to receive more weight than nonlinear effects arbitrarily located in the domain. Finally, as we demonstrate, covers can be used to analyze and to calibrate search algorithms

Landscapes and Effective Fitness

The concept of a fitness landscape arose in theoretical biology, while that of effective fitness has its origin in evolutionary computation. Both have emerged as useful conceptual tools with which to understand the dynamics of evolutionary processes, especially in the presence of complex genotype-phenotype relations. In this contribution we attempt to provide a unified discussion of these two approaches, discussing both their advantages and disadvantages in the context of some simple models. We also discuss how fitness and effective fitness change under various transformations of the configuration space of the underlying genetic model, concentrating on coarse-graining transformations and on a particular coordinate transformation that provides an appropriate basis for illuminating the structure and consequences of recombination

What makes a problem hard for a genetic algorithm? Some anomalous results and their explanation

What makes a problem easy or hard for a genetic algorithm (GA)? This question has become increasingly important as people have tried to apply the GA to ever more diverse types of problems. Much previous work on this question has studied the relationship between GA performance and the structure of a given fitness function when it is expressed as a Walsh polynomial . The work of Bethke, Goldberg, and others has produced certain theoretical results about this relationship. In this article we review these theoretical results, and then discuss a number of seemingly anomalous experimental results reported by Tanese concerning the performance of the GA on a subclass of Walsh polynomials, some members of which were expected to be easy for the GA to optimize. Tanese found that the GA was poor at optimizing all functions in this subclass, that a partitioning of a single large population into a number of smaller independent populations seemed to improve performance, and that hillelimbing outperformed both the original and partitioned forms of the GA on these functions. These results seemed to contradict several commonly held expectations about GAs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46892/1/10994_2004_Article_BF00993046.pd

A survey of techniques for characterising fitness landscapes and some possible ways forward

Real-world optimisation problems are often very complex. Metaheuristics have been successful in solving many of these problems, but the difficulty in choosing the best approach can be a huge challenge for practitioners. One approach to this dilemma is to use fitness landscape analysis to better understand problems before deciding on approaches to solving the problems. However, despite extensive research on fitness landscape analysis and a large number of developed techniques, very few techniques are used in practice. This could be because fitness landscape analysis in itself can be complex. In an attempt to make fitness landscape analysis techniques accessible, this paper provides an overview of techniques from the 1980s to the present. Attributes that are important for practical implementation are highlighted and ways of adapting techniques to be more feasible or appropriate are suggested. The survey reveals the wide range of factors that can influence problem difficulty, emphasising the need for a shift in focus away from predicting problem hardness towards measuring characteristics. It is hoped that this survey will invoke renewed interest in the field of understanding complex optimisation problems and ultimately lead to better decision making on the use of appropriate metaheuristics.http://www.elsevier.com/locate/inshb201

A probabilistic cooperative-competitive hierarchical search model.

by Wong Yin Bun, Terence.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 99-104).Abstract also in Chinese.List of Figures --- p.ixList of Tables --- p.xiChapter I --- Preliminary --- p.1Chapter 1 --- Introduction --- p.2Chapter 1.1 --- Thesis themes --- p.4Chapter 1.1.1 --- Dynamical view of landscape --- p.4Chapter 1.1.2 --- Bottom-up self-feedback algorithm with memory --- p.4Chapter 1.1.3 --- Cooperation and competition --- p.5Chapter 1.1.4 --- Contributions to genetic algorithms --- p.5Chapter 1.2 --- Thesis outline --- p.5Chapter 1.3 --- Contribution at a glance --- p.6Chapter 1.3.1 --- Problem --- p.6Chapter 1.3.2 --- Approach --- p.7Chapter 1.3.3 --- Contributions --- p.7Chapter 2 --- Background --- p.8Chapter 2.1 --- Iterative stochastic searching algorithms --- p.8Chapter 2.1.1 --- The algorithm --- p.8Chapter 2.1.2 --- Stochasticity --- p.10Chapter 2.2 --- Fitness landscapes and its relation to neighborhood --- p.12Chapter 2.2.1 --- Direct searching --- p.12Chapter 2.2.2 --- Exploration and exploitation --- p.12Chapter 2.2.3 --- Fitness landscapes --- p.13Chapter 2.2.4 --- Neighborhood --- p.16Chapter 2.3 --- Species formation methods --- p.17Chapter 2.3.1 --- Crowding methods --- p.17Chapter 2.3.2 --- Deterministic crowding --- p.18Chapter 2.3.3 --- Sharing method --- p.18Chapter 2.3.4 --- Dynamic niching --- p.19Chapter 2.4 --- Summary --- p.21Chapter II --- Probabilistic Binary Hierarchical Search --- p.22Chapter 3 --- The basic algorithm --- p.23Chapter 3.1 --- Introduction --- p.23Chapter 3.2 --- Search space reduction with binary hierarchy --- p.25Chapter 3.3 --- Search space modeling --- p.26Chapter 3.4 --- The information processing cycle --- p.29Chapter 3.4.1 --- Local searching agents --- p.29Chapter 3.4.2 --- Global environment --- p.30Chapter 3.4.3 --- Cooperative refinement and feedback --- p.33Chapter 3.5 --- Enhancement features --- p.34Chapter 3.5.1 --- Fitness scaling --- p.34Chapter 3.5.2 --- Elitism --- p.35Chapter 3.6 --- Illustration of the algorithm behavior --- p.36Chapter 3.6.1 --- Test problem --- p.36Chapter 3.6.2 --- Performance study --- p.38Chapter 3.6.3 --- Benchmark tests --- p.45Chapter 3.7 --- Discussion and analysis --- p.45Chapter 3.7.1 --- Hierarchy of partitions --- p.45Chapter 3.7.2 --- Availability of global information --- p.47Chapter 3.7.3 --- Adaptation --- p.47Chapter 3.8 --- Summary --- p.48Chapter III --- Cooperation and Competition --- p.50Chapter 4 --- High-dimensionality --- p.51Chapter 4.1 --- Introduction --- p.51Chapter 4.1.1 --- The challenge of high-dimensionality --- p.51Chapter 4.1.2 --- Cooperation - A solution to high-dimensionality --- p.52Chapter 4.2 --- Probabilistic Cooperative Binary Hierarchical Search --- p.52Chapter 4.2.1 --- Decoupling --- p.52Chapter 4.2.2 --- Cooperative fitness --- p.53Chapter 4.2.3 --- The cooperative model --- p.54Chapter 4.3 --- Empirical performance study --- p.56Chapter 4.3.1 --- pBHS versus pcBHS --- p.56Chapter 4.3.2 --- Scaling behavior of pcBHS --- p.60Chapter 4.3.3 --- Benchmark test --- p.62Chapter 4.4 --- Summary --- p.63Chapter 5 --- Deception --- p.65Chapter 5.1 --- Introduction --- p.65Chapter 5.1.1 --- The challenge of deceptiveness --- p.65Chapter 5.1.2 --- Competition: A solution to deception --- p.67Chapter 5.2 --- Probabilistic cooperative-competitive binary hierarchical search --- p.67Chapter 5.2.1 --- Overview --- p.68Chapter 5.2.2 --- The cooperative-competitive model --- p.68Chapter 5.3 --- Empirical performance study --- p.70Chapter 5.3.1 --- Goldberg's deceptive function --- p.70Chapter 5.3.2 --- "Shekel family - S5, S7, and S10" --- p.73Chapter 5.4 --- Summary --- p.74Chapter IV --- Finale --- p.78Chapter 6 --- A new genetic operator --- p.79Chapter 6.1 --- Introduction --- p.79Chapter 6.2 --- Variants of the integration --- p.80Chapter 6.2.1 --- Fixed-fraction-of-all --- p.83Chapter 6.2.2 --- Fixed-fraction-of-best --- p.83Chapter 6.2.3 --- Best-from-both --- p.84Chapter 6.3 --- Empricial performance study --- p.84Chapter 6.4 --- Summary --- p.88Chapter 7 --- Conclusion and Future work --- p.89Chapter A --- The pBHS Algorithm --- p.91Chapter A.1 --- Overview --- p.91Chapter A.2 --- Details --- p.91Chapter B --- Test problems --- p.96Bibliography --- p.9

Adaptive scaling of evolvable systems

Neo-Darwinian evolution is an established natural inspiration for computational optimisation with a diverse range of forms. A particular feature of models such as Genetic Algorithms (GA) [18, 12] is the incremental combination of partial solutions distributed within a population of solutions. This mechanism in principle allows certain problems to be solved which would not be amenable to a simple local search. Such problems require these partial solutions, generally known as building-blocks, to be handled without disruption. The traditional means for this is a combination of a suitable chromosome ordering with a sympathetic recombination operator. More advanced algorithms attempt to adapt to accommodate these dependencies during the search. The recent approach of Estimation of Distribution Algorithms (EDA) aims to directly infer a probabilistic model of a promising population distribution from a sample of fitter solutions [23]. This model is then sampled to generate a new solution set. A symbiotic view of evolution is behind the recent development of the Compositional Search Evolutionary Algorithms (CSEA) [49, 19, 8] which build up an incremental model of variable dependencies conditional on a series of tests. Building-blocks are retained as explicit genetic structures and conditionally joined to form higher-order structures. These have been shown to be effective on special classes of hierarchical problems but are unproven on less tightly-structured problems. We propose that there exists a simple yet powerful combination of the above approaches: the persistent, adapting dependency model of a compositional pool with the expressive and compact variable weighting of probabilistic models. We review and deconstruct some of the key methods above for the purpose of determining their individual drawbacks and their common principles. By this reasoned approach we aim to arrive at a unifying framework that can adaptively scale to span a range of problem structure classes. This is implemented in a novel algorithm called the Transitional Evolutionary Algorithm (TEA). This is empirically validated in an incremental manner, verifying the various facets of the TEA and comparing it with related algorithms for an increasingly structured series of benchmark problems. This prompts some refinements to result in a simple and general algorithm that is nevertheless competitive with state-of-the-art methods

Covers

This paper introduces the theory of covers for functions defined over binary variables. Covers formalize the notion of decomposability. Large complex problems are decomposed into subproblems each containing fewer variables, which can then be solved in parallel. Practical applications of the benefits from decomposition include the parallel architecture of supercomputers, the divisionalization of firms, and the decentralization of economic activity. In this introductory paper, we show how covers also shed light on the choice among public projects with complementarities. Further, covers provide a measure of complexity/decomposability with respect to contour sets, allowing for nonlinear effects which occur near the optimum to receive more weight than nonlinear effects arbitrarily located in the domain. Finally, as we demonstrate, covers can be used to analyze and to calibrate search algorithms

Multi-agent evolutionary systems for the generation of complex virtual worlds

Modern films, games and virtual reality applications are dependent on convincing computer graphics. Highly complex models are a requirement for the successful delivery of many scenes and environments. While workflows such as rendering, compositing and animation have been streamlined to accommodate increasing demands, modelling complex models is still a laborious task. This paper introduces the computational benefits of an Interactive Genetic Algorithm (IGA) to computer graphics modelling while compensating the effects of user fatigue, a common issue with Interactive Evolutionary Computation. An intelligent agent is used in conjunction with an IGA that offers the potential to reduce the effects of user fatigue by learning from the choices made by the human designer and directing the search accordingly. This workflow accelerates the layout and distribution of basic elements to form complex models. It captures the designer's intent through interaction, and encourages playful discovery