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40
PopulationBased Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning
, 1994
"... Genetic algorithms (GAs) are biologically motivated adaptive systems which have been used, with varying degrees of success, for function optimization. In this study, an abstraction of the basic genetic algorithm, the Equilibrium Genetic Algorithm (EGA), and the GA in turn, are reconsidered within th ..."
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Cited by 298 (11 self)
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Genetic algorithms (GAs) are biologically motivated adaptive systems which have been used, with varying degrees of success, for function optimization. In this study, an abstraction of the basic genetic algorithm, the Equilibrium Genetic Algorithm (EGA), and the GA in turn, are reconsidered within the framework of competitive learning. This new perspective reveals a number of different possibilities for performance improvements. This paper explores populationbased incremental learning (PBIL), a method of combining the mechanisms of a generational genetic algorithm with simple competitive learning. The combination of these two methods reveals a tool which is far simpler than a GA, and which outperforms a GA on large set of optimization problems in terms of both speed and accuracy. This paper presents an empirical analysis of where the proposed technique will outperform genetic algorithms, and describes a class of problems in which a genetic algorithm may be able to perform better. Extensions to this algorithm are discussed and analyzed. PBIL and extensions are compared with a standard GA on twelve problems, including standard numerical optimization functions, traditional GA test suite problems, and NPComplete problems.
Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms
 Proceedings of the Sixth International Conference on Genetic Algorithms
, 1995
"... 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 deceptiv ..."
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Cited by 204 (5 self)
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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 nondeceptive 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 for Genetic Algorithms
, 1995
"... 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 ..."
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Cited by 191 (1 self)
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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...
Simulated Binary Crossover for Continuous Search Space
, 1994
"... The success of binarycoded genetic algorithms (GAs) in problems having discrete search space largely depends on the coding used to represent the problem variables and on the crossover operator that propagates buildingblocks from parent strings to children strings. In solving optimization problems ..."
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Cited by 126 (26 self)
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The success of binarycoded genetic algorithms (GAs) in problems having discrete search space largely depends on the coding used to represent the problem variables and on the crossover operator that propagates buildingblocks from parent strings to children strings. In solving optimization problems having continuous search space, binarycoded GAs discretize the search space by using a coding of the problem variables in binary strings. However, the coding of realvalued variables in finitelength strings causes a number of difficultiesinability to achieve arbitrary precision in the obtained solution, fixed mapping of problem variables, inherent Hamming cliff problem associated with the binary coding, and processing of Holland's schemata in continuous search space. Although, a number of realcoded GAs are developed to solve optimization problems having a continuous search space, the search powers of these crossover operators are not adequate. In this paper, the search power of a cross...
Relative BuildingBlock Fitness and the BuildingBlock Hypothesis
, 1993
"... The buildingblock hypothesis states that the GA works well when short, loworder, highlyfit schemas recombine to form even more highly fit higherorder schemas. The ability to produce fitter and fitter partial solutions by combining building blocks is believed to be a primary source of the GA's se ..."
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Cited by 125 (2 self)
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The buildingblock hypothesis states that the GA works well when short, loworder, highlyfit schemas recombine to form even more highly fit higherorder schemas. The ability to produce fitter and fitter partial solutions by combining building blocks is believed to be a primary source of the GA's search power, but the GA research community currently lacks precise and quantitative descriptions of how schema processing actually takes place during the typical evolution of a GA search. Another open problem is to characterize in detail the types of fitness landscapes for which crossover will be an effective operator. In this paper we first describe a class of fitness landscapes (the "Royal Road" functions) that we have designed to investigate these questions. We then present some unexpected experimental results concerning the GA's performance on simple instances of these landscapes, in which we vary the strength of reinforcement from "stepping stones"fit intermediateorder schemas obtain...
Fitness Variance of Formae and Performance Prediction
, 1994
"... Representation is widely recognised as a key determinant of performance in evolutionary computation. The development of families of representationindependentoperators allows the formulation of formal representationindependent evolutionary algorithms. These formal algorithms can be instantiated ..."
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Cited by 61 (7 self)
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Representation is widely recognised as a key determinant of performance in evolutionary computation. The development of families of representationindependentoperators allows the formulation of formal representationindependent evolutionary algorithms. These formal algorithms can be instantiated for particular search problems by selecting a suitable representation. The performance of different representations, in the context of any given formal representationindependent algorithm, can then be measured. Simple analyses suggest that fitness variance of formae (generalised schemata) for the chosen representation might act as a performance predictor for evolutionary algorithms. This hypothesis is tested and supported through studies of four different representations for the travelling salesrep problem (TSP) in the context of both formal representationindependentgenetic algorithms and corresponding memetic algorithms. 1 Motivation The subject of this paper is representation i...
Building Better Test Functions
 Proceedings of the Sixth International Conference on Genetic Algorithms
, 1995
"... We introduce basic guidelines for developing test suites for evolutionary algorithms and examine common test functions in terms of these guidelines. Two methods of designing test functions are introduced which address specific issues relevant to comparative studies of evolutionary algorithms. ..."
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Cited by 54 (5 self)
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We introduce basic guidelines for developing test suites for evolutionary algorithms and examine common test functions in terms of these guidelines. Two methods of designing test functions are introduced which address specific issues relevant to comparative studies of evolutionary algorithms. The first method produces representation invariant functions.
How Mutation and Selection Solve Long Path Problems in Polynomial Expected Time
, 1996
"... It is shown by means of Markov chain analysis that unimodal binary long path problems can be solved by mutation and elitist selection in a polynomially bounded number of trials on average. 1 Unimodality of Binary Functions The notion of unimodal functions usually appears in the theory of optimizati ..."
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Cited by 52 (2 self)
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It is shown by means of Markov chain analysis that unimodal binary long path problems can be solved by mutation and elitist selection in a polynomially bounded number of trials on average. 1 Unimodality of Binary Functions The notion of unimodal functions usually appears in the theory of optimization in IR 1 . Elster et al. (1977), pp. 228230, provide a precise definition that is specialized to functions in IR 1 whereas the definition in Bronstein and Semendjajew (1988), p. 137, for functions in IR ` with ` 1 presupposes differentiability. Here, the following definition for functions over IB ` will be used: Definition 1 Let f be a realvalued function with domain IB ` where IB = f0; 1g. A point x 2 IB ` is called a local solution of f if f(x ) f(x) for all x 2 fy 2 IB ` : k y \Gamma x k 1 = 1g (1) where k x k 1 = P ` i=1 j x i j is the Hamming norm. If the inequality in (1) is strict, then x is termed a strictly local solution. The value f(x ) at a...
An Empirical Comparison of Seven Iterative and Evolutionary Function Optimization Heuristics
, 1995
"... This report is a repository for the results obtained from a large scale empirical comparison of seven iterative and evolutionbased optimization heuristics. Twentyseven static optimization problems, spanning six sets of problem classes which are commonly explored in genetic algorithm literature, ..."
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Cited by 50 (7 self)
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This report is a repository for the results obtained from a large scale empirical comparison of seven iterative and evolutionbased optimization heuristics. Twentyseven static optimization problems, spanning six sets of problem classes which are commonly explored in genetic algorithm literature, are examined. The problem sets include jobshop scheduling, traveling salesman, knapsack, binpacking, neural network weight optimization, and standard numerical optimization. The search spaces in these problems range from 2^368 to 2^2040. The results indicate that using genetic algorithms for the optimization of static functions does not yield a benefit, in terms of the final answer obtained, over simpler optimization heuristics. Descriptions of the algorithms tested and the encodings of the problems are described in detail for reproducibility.