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38
The Schema Theorem and Price's Theorem
 FOUNDATIONS OF GENETIC ALGORITHMS
, 1995
"... Holland's Schema Theorem is widely taken to be the foundation for explanations of the power of genetic algorithms (GAs). Yet some dissent has been expressed as to its implications. Here, dissenting arguments are reviewed and elaborated upon, explaining why the Schema Theorem has no implicati ..."
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Cited by 101 (3 self)
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Holland's Schema Theorem is widely taken to be the foundation for explanations of the power of genetic algorithms (GAs). Yet some dissent has been expressed as to its implications. Here, dissenting arguments are reviewed and elaborated upon, explaining why the Schema Theorem has no implications for how well a GA is performing. Interpretations of the Schema Theorem have implicitly assumed that a correlation exists between parent and offspring fitnesses, and this assumption is made explicit in results based on Price's Covariance and Selection Theorem. Schemata do not play a part in the performance theorems derived for representations and operators in general. However, schemata reemerge when recombination operators are used. Using Geiringer's recombination distribution representation of recombination operators, a "missing" schema theorem is derived which makes explicit the intuition for when a GA should perform well. Finally, the method of "adaptive landscape" analysis is exa...
A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman Problems
 In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation
, 1996
"... The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and ..."
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Cited by 87 (12 self)
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The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and genetic algorithms are used to search the space of local optima in order to find the global optimum. New genetic operators for realizing the proposed approach are described, and the quality and efficiency of the solutions obtained for a set of symmetric and asymmetric TSP instances are discussed. The results indicate that it is possible to arrive at high quality solutions in reasonable time. I. Introduction In the Traveling Salesman Problem (TSP) [18], [27], a number of cities with distances between them is given and the task is to find the minimumlength closed tour that visits each city once and returns to its starting point. A symmetric TSP (STSP) is one where the distance between any...
New Genetic Local Search Operators for the Traveling Salesman Problem
, 1996
"... Abstract. In this paper, an approach is presented to incorporate problem speci c knowledge into a genetic algorithm which is used to compute nearoptimum solutions to traveling salesman problems (TSP). The approach is based on using a tour construction heuristic for generating the initial population ..."
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Cited by 61 (11 self)
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Abstract. In this paper, an approach is presented to incorporate problem speci c knowledge into a genetic algorithm which is used to compute nearoptimum solutions to traveling salesman problems (TSP). The approach is based on using a tour construction heuristic for generating the initial population, a tour improvement heuristic for nding local optima in a given TSP search space, and new genetic operators for e ectively searching the space of local optima in order to nd the global optimum. The quality and e ciency of solutions obtained for a set of TSP instances containing between 318 and 1400 cities are presented. 1
Memetic Algorithms for Combinatorial Optimization Problems: Fitness Landscapes and Effective Search Strategies
, 2001
"... ..."
What makes a problem GPhard? analysis of a tunably difficult problem in genetic programming. Genetic Programming and Evolvable Machines
, 2001
"... This paper addresses the issue of what makes a problem GPhard by considering the binomial3 problem. In the process, we discuss the efficacy of the metaphor of an adaptive fitness landscape to explain what is GPhard. We show that for at least this problem, the metaphor is misleading. 1 ..."
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Cited by 42 (7 self)
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This paper addresses the issue of what makes a problem GPhard by considering the binomial3 problem. In the process, we discuss the efficacy of the metaphor of an adaptive fitness landscape to explain what is GPhard. We show that for at least this problem, the metaphor is misleading. 1
Memetic Algorithms for the Traveling Salesman Problem
 Complex Systems
, 1997
"... this paper, the tness landscapes of several instances of the traveling salesman problem (TSP) are investigated to illustrate why MAs are wellsuited for nding nearoptimum tours for the TSP. It is shown that recombination{based MAs can exploit the correlation structure of the landscape. A comparis ..."
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Cited by 36 (8 self)
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this paper, the tness landscapes of several instances of the traveling salesman problem (TSP) are investigated to illustrate why MAs are wellsuited for nding nearoptimum tours for the TSP. It is shown that recombination{based MAs can exploit the correlation structure of the landscape. A comparison of several recombination operators { including a new generic recombination operator { reveals that when using the sophisticated Lin{Kernighan local search, the performance dierence of the MAs is small. However, the most important property of eective recombination operators is shown to be respectfulness. In experiments it is shown that our MAs with generic recombination are among the best evolutionary algorithms for the TSP. In particular, optimum solutions could be found up to a problem size of 3795, and for large instances up to 85,900 cities, nearoptimum solutions could be found in a reasonable amount of time
NonRedundant Genetic Coding of Neural Networks
 In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation
, 1996
"... Feedforward neural networks have a number of functional equivalent symmetries that make them difficult to optimise with genetic recombination operators. Although this problem has received considerable attention in the past, the proposed solutions have all a heuristic nature. Here we discuss a neural ..."
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Cited by 17 (2 self)
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Feedforward neural networks have a number of functional equivalent symmetries that make them difficult to optimise with genetic recombination operators. Although this problem has received considerable attention in the past, the proposed solutions have all a heuristic nature. Here we discuss a neural network genotype representation that completely eliminates the functional redundancies by transforming each neural network to its canonical form. This transformation is computationally extremely simple since it only requires flipping the sign of some of the weights, followed by sorting the hidden neurons according to their bias. We have compared the redundant and the nonredundant representation on the basis of their crossover correlation coefficient. As expected the redundancy elimination results in a much higher crossover correlation coefficient, which shows that more information is now transmitted from the parents to the children. Finally, experimental results are given for the two spirals classification problem.
The Traveling Salesrep Problem, Edge Assembly Crossover, and 2opt
 of Lecture Notes in Computer Science
, 1998
"... Abstract. Optimal results for the Traveling Salesrep Problem have been reported on problems with up to 3038 cities using a GA with Edge Assembly Crossover (EAX). This paper rst attempts to independently replicate these results on Padberg's 532 city problem. We then evaluate the performance cont ..."
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Cited by 17 (0 self)
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Abstract. Optimal results for the Traveling Salesrep Problem have been reported on problems with up to 3038 cities using a GA with Edge Assembly Crossover (EAX). This paper rst attempts to independently replicate these results on Padberg's 532 city problem. We then evaluate the performance contribution of the various algorithm components. The incorporation of 2opt into the EAX GA is also explored. Finally, comparative results are presented for a populationbased form of 2opt that uses partial restarts. 1
How fitness structure affects subsolution acquisition in genetic programming
 Proceedings of the Third Annual Genetic Programming Conference
, 1998
"... We define fitness structure in genetic programming to be the mapping between the subprograms of a program and their respective fitness values. This paper shows how various fitness structures of a problem with independent subsolutions relate to the acquisition of subsolutions. The rate of subsolution ..."
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Cited by 15 (1 self)
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We define fitness structure in genetic programming to be the mapping between the subprograms of a program and their respective fitness values. This paper shows how various fitness structures of a problem with independent subsolutions relate to the acquisition of subsolutions. The rate of subsolution acquisition is found to be directly correlated with fitness structure whether that structure is uniform, linear or exponential. An understanding of fitness structure provides partial insight into the complicated relationship between fitness function and the outcome of genetic programming's search.
Advanced Correlation Analysis of Operators for the Traveling Salesman Problem
 in Parallel Problem Solving from Nature  Proceedings of the third Workshop, PPSN III, (H.P. Schwefel and
, 1994
"... An extension to the correlation analysis of Manderick et al. ..."
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Cited by 13 (0 self)
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An extension to the correlation analysis of Manderick et al.