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609
A comparative analysis of selection schemes used in genetic algorithms
 Foundations of Genetic Algorithms
, 1991
"... This paper considers a number of selection schemes commonly used in modern genetic algorithms. Specifically, proportionate reproduction, ranking selection, tournament selection, and Genitor (or «steady state") selection are compared on the basis of solutions to deterministic difference or d ..."
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Cited by 514 (31 self)
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This paper considers a number of selection schemes commonly used in modern genetic algorithms. Specifically, proportionate reproduction, ranking selection, tournament selection, and Genitor (or «steady state&quot;) selection are compared on the basis of solutions to deterministic difference or differential equations, which are verified through computer simulations. The analysis provides convenient approximate or exact solutions as well as useful convergence time and growth ratio estimates. The paper recommends practical application of the analyses and suggests a number of paths for more detailed analytical investigation of selection techniques. Keywords: proportionate selection, ranking selection, tournament selection, Genitor, takeover time, time complexity, growth ratio. 1
An Overview of Evolutionary Algorithms in Multiobjective Optimization
 Evolutionary Computation
, 1995
"... The application of evolutionary algorithms (EAs) in multiobjective optimization is currently receiving growing interest from researchers with various backgrounds. Most research in this area has understandably concentrated on the selection stage of EAs, due to the need to integrate vectorial performa ..."
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Cited by 485 (13 self)
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The application of evolutionary algorithms (EAs) in multiobjective optimization is currently receiving growing interest from researchers with various backgrounds. Most research in this area has understandably concentrated on the selection stage of EAs, due to the need to integrate vectorial performance measures with the inherently scalar way in which EAs reward individual performance, i.e., number of offspring. In this review, current multiobjective evolutionary approaches are discussed, ranging from the conventional analytical aggregation of the different objectives into a single function to a number of populationbased approaches and the more recent ranking schemes based on the definition of Paretooptimality. The sensitivity of different methods to
Predictive Models for the Breeder Genetic Algorithm  I. Continuous Parameter Optimization
 EVOLUTIONARY COMPUTATION
, 1993
"... In this paper a new genetic algorithm called the Breeder Genetic Algorithm (BGA) is introduced. The BGA is based on artificial selection similar to that used by human breeders. A predictive model for the BGA is presented which is derived from quantitative genetics. The model is used to predict t ..."
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Cited by 394 (25 self)
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In this paper a new genetic algorithm called the Breeder Genetic Algorithm (BGA) is introduced. The BGA is based on artificial selection similar to that used by human breeders. A predictive model for the BGA is presented which is derived from quantitative genetics. The model is used to predict the behavior of the BGA for simple test functions. Different mutation schemes are compared by computing the expected progress to the solution. The numerical performance of the BGA is demonstrated on a test suite of multimodal functions. The number of function evaluations needed to locate the optimum scales only as n ln(n) where n is the number of parameters. Results up to n = 1000 are reported.
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 353 (12 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.
Approximating the nondominated front using the Pareto Archived Evolution Strategy
 EVOLUTIONARY COMPUTATION
, 2000
"... We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its ..."
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Cited by 320 (19 self)
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We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1 + 1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1 + 1)PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some realworld applications when local search seems superior to or competitive with populationbased methods. We introduce (1 + λ) and (μ  λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.
A Genetic Algorithm Tutorial
 Statistics and Computing
, 1994
"... This tutorial covers the canonical genetic algorithm as well as more experimental forms of genetic algorithms, including parallel island models and parallel cellular genetic algorithms. The tutorial also illustrates genetic search byhyperplane sampling. The theoretical foundations of genetic algorit ..."
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Cited by 319 (5 self)
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This tutorial covers the canonical genetic algorithm as well as more experimental forms of genetic algorithms, including parallel island models and parallel cellular genetic algorithms. The tutorial also illustrates genetic search byhyperplane sampling. The theoretical foundations of genetic algorithms are reviewed, include the schema theorem as well as recently developed exact models of the canonical genetic algorithm.
Metaheuristics in combinatorial optimization: Overview and conceptual comparison
 ACM COMPUTING SURVEYS
, 2003
"... The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important meta ..."
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Cited by 299 (16 self)
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The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.
Evolutionary computation: Comments on the history and current state
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 1997
"... Evolutionary computation has started to receive significant attention during the last decade, although the origins can be traced back to the late 1950’s. This article surveys the history as well as the current state of this rapidly growing field. We describe the purpose, the general structure, and ..."
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Cited by 275 (0 self)
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Evolutionary computation has started to receive significant attention during the last decade, although the origins can be traced back to the late 1950’s. This article surveys the history as well as the current state of this rapidly growing field. We describe the purpose, the general structure, and the working principles of different approaches, including genetic algorithms (GA) [with links to genetic programming (GP) and classifier systems (CS)], evolution strategies (ES), and evolutionary programming (EP) by analysis and comparison of their most important constituents (i.e., representations, variation operators, reproduction, and selection mechanism). Finally, we give a brief overview on the manifold of application domains, although this necessarily must remain incomplete.
Strongly Typed Genetic Programming
 Evolutionary Computation
, 1994
"... Genetic programming is a powerful method for automatically generating computer programs via the process of natural selection [Koza 92]. However, it has the limitation known as "closure", i.e. that all the variables, constants, arguments for functions, and values returned from functions m ..."
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Cited by 274 (1 self)
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Genetic programming is a powerful method for automatically generating computer programs via the process of natural selection [Koza 92]. However, it has the limitation known as "closure", i.e. that all the variables, constants, arguments for functions, and values returned from functions must be of the same data type. To correct this deficiency, we introduce a variation of genetic programming called "strongly typed" genetic programming(STGP). In STGP, variables, constants, arguments, and returned values can be of any data type with the provision that the data type for each such value be specified beforehand. This allows the initialization process and the genetic operators to only generate syntactically correct parse trees. Key concepts for STGP are generic functions, which are not true strongly typed functions but rather templates for classes of such functions, and generic data types, which are analogous. To illustrate STGP, we present four examples involving vector/matrix manip...
Linkage Learning via Probabilistic Modeling in the ECGA
, 1999
"... The goal of linkage learning, or building block identification, is the creation of a more effective genetic algorithm (GA). This paper explores the relationship between the linkagelearning problem and that of learning probability distributions over multivariate spaces. Herein, it is argued that th ..."
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Cited by 231 (4 self)
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The goal of linkage learning, or building block identification, is the creation of a more effective genetic algorithm (GA). This paper explores the relationship between the linkagelearning problem and that of learning probability distributions over multivariate spaces. Herein, it is argued that these problems are equivalent. Using a simple but effective approach to learning distributions, and by implication linkage, this paper reveals the existence of GAlike algorithms that are potentially orders of magnitude faster and more accurate than the simple GA. I. Introduction Linkage learning in genetic algorithms (GAs) is the identification of building blocks to be conserved under crossover. Theoretical studies have shown that if an effective linkagelearning GA were developed, it would hold significant advantages over the simple GA (2). Therefore, the task of developing such an algorithm has drawn significant attention. Past approaches to developing such an algorithm have focused on ev...