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Fitness Landscape Analysis and Memetic Algorithms for the Quadratic Assignment Problem
, 1999
"... In this paper, a fitness landscape analysis for several instances of the quadratic assignment problem (QAP) is performed and the results are used to classify problem instances according to their hardness for local search heuristics and metaheuristics based on local search. The local properties of t ..."
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Cited by 62 (9 self)
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In this paper, a fitness landscape analysis for several instances of the quadratic assignment problem (QAP) is performed and the results are used to classify problem instances according to their hardness for local search heuristics and metaheuristics based on local search. The local properties of the tness landscape are studied by performing an autocorrelation analysis, while the global structure is investigated by employing a fitness distance correlation analysis. It is shown that epistasis, as expressed by the dominance of the flow and distance matrices of a QAP instance, the landscape ruggedness in terms of the correlation length of a landscape, and the correlation between fitness and distance of local optima in the landscape together are useful for predicting the performance of memetic algorithms  evolutionary algorithms incorporating local search  to a certain extent. Thus, based on these properties a favorable choice of recombination and/or mutation operators can be found.
Fitness Landscapes and Memetic Algorithm Design
 New Ideas in Optimization
, 1999
"... Introduction The notion of fitness landscapes has been introduced to describe the dynamics of evolutionary adaptation in nature [40] and has become a powerful concept in evolutionary theory. Fitness landscapes are equally well suited to describe the behavior of heuristic search methods in optimizat ..."
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Cited by 58 (7 self)
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Introduction The notion of fitness landscapes has been introduced to describe the dynamics of evolutionary adaptation in nature [40] and has become a powerful concept in evolutionary theory. Fitness landscapes are equally well suited to describe the behavior of heuristic search methods in optimization, since the process of evolution can be thought of as searching a collection of genotypes in order to find the genotype of an organism with highest fitness and thus highest chance of survival. Thinking of a heuristic search method as a strategy to "navigate" in the fitness landscape of a given optimization problem may help in predicting the performance of a heuristic search algorithm if the structure of the landscape is known in advance. Furthermore, the analysis of fitness landscapes may help in designing highly effective search algorithms. In the following we show how the analysis of fitness landscapes of combinatorial optimization problems can aid in designing the components of
Memetic Algorithms for Combinatorial Optimization Problems: Fitness Landscapes and Effective Search Strategies
, 2001
"... ..."
Fitness Landscapes, Memetic Algorithms, and Greedy Operators for Graph Bipartitioning
 Evolutionary Computation
, 2000
"... The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis ..."
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Cited by 48 (13 self)
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The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced.
A Comparison of Memetic Algorithms, Tabu Search, and Ant Colonies for the Quadratic Assignment Problem
 Proc. Congress on Evolutionary Computation, IEEE
, 1999
"... A memetic algorithm (MA), i.e. an evolutionary algorithm making use of local search, for the quadratic assignment problem is presented. A new recombination operator for realizing the approach is described, and the behavior of the MA is investigated on a set of problem instances containing between 25 ..."
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Cited by 32 (4 self)
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A memetic algorithm (MA), i.e. an evolutionary algorithm making use of local search, for the quadratic assignment problem is presented. A new recombination operator for realizing the approach is described, and the behavior of the MA is investigated on a set of problem instances containing between 25 and 100 facilities/locations. The results indicate that the proposed MA is able to produce high quality solutions quickly. A comparison of the MA with some of the currently best alternative approaches  reactive tabu search, robust tabu search and the fast ant colony system  demonstrates that the MA outperforms its competitors on all studied problem instances of practical interest. 1 Introduction The problem of assigning a set of facilities (with given flows between them) to a set of locations (with given distances between them) in such a way that the sum of the product between flows and distances is minimized is known as the facilities location problem [1] or the quadratic assignment ...
Optimization with extremal dynamics
 Physical Review Letters
"... We explore a new generalpurpose heuristic for finding highquality solutions to hard optimization problems. The method, called extremal optimization, is inspired by selforganized criticality, a concept introduced to describe emergent complexity in physical systems. Extremal optimization successive ..."
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Cited by 31 (2 self)
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We explore a new generalpurpose heuristic for finding highquality solutions to hard optimization problems. The method, called extremal optimization, is inspired by selforganized criticality, a concept introduced to describe emergent complexity in physical systems. Extremal optimization successively replaces extremely undesirable variables of a single suboptimal solution with new, random ones. Large fluctuations ensue, that efficiently explore many local optima. With only one adjustable parameter, the heuristic’s performance has proven competitive with more elaborate methods, especially near phase transitions which are believed to coincide with the hardest instances. We use extremal optimization to elucidate the phase transition in the 3coloring problem, and we provide independent confirmation of previously reported extrapolations for the groundstate energy of±J spin glasses in d = 3 and 4. PACS number(s): 02.60.Pn, 05.65.+b, 75.10.Nr, 64.60.Cn. Many natural systems have, without any centralized organizing facility, developed into complex structures that optimize their use of resources in sophisticated ways [1]. Biological evolution has formed efficient
Nature’s way of optimizing
 Artificial Intelligence
, 2000
"... We propose a generalpurpose method for finding highquality solutions to hard optimization problems, inspired by selforganizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely undesirable components of suboptimal solutions. Drawing upon ..."
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Cited by 25 (5 self)
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We propose a generalpurpose method for finding highquality solutions to hard optimization problems, inspired by selforganizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely undesirable components of suboptimal solutions. Drawing upon models used to simulate farfromequilibrium dynamics, it complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. With only one adjustable parameter, its performance proves competitive with, and often superior to, more elaborate stochastic optimization procedures. We demonstrate it here on two classic hard optimization problems: graph partitioning and the traveling salesman problem. 1 In nature, highly specialized, complex structures often emerge when their most inefficient components are selectively driven to extinction. Evolution, for example, progresses by selecting against the few most poorly adapted species, rather than by expressly breeding those species best adapted to their environment [1]. To describe the dynamics of systems with
Genetic Algorithms for Binary Quadratic Programming
 in GECCO1999: Proceedings of the Genetic and Evolutionary Computation Conference
, 1999
"... In this paper, genetic algorithms for the unconstrained binary quadratic programming problem (BQP) are presented. It is shown that for small problems a simple genetic algorithm with uniform crossover is sufficient to find optimum or bestknown solutions in short time, while for problems with a high ..."
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Cited by 23 (7 self)
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In this paper, genetic algorithms for the unconstrained binary quadratic programming problem (BQP) are presented. It is shown that for small problems a simple genetic algorithm with uniform crossover is sufficient to find optimum or bestknown solutions in short time, while for problems with a high number of variables (n 200) it is essential to incorporate local search to arrive at highquality solutions. A hybrid genetic algorithm incorporating local search is tested on 40 problem instances of sizes containing between n = 200 and n = 2500. The results of the computer experiments show that the approach is comparable to alternative heuristics such as tabu search for small instances and superior to tabu search and simulated annealing for large instances. New best solutions could be found for 14 large problem instances. 1 INTRODUCTION In the unconstrained binary quadratic programming problem (BQP), a symmetric rational n \Theta n matrix Q = (q ij ) is given, and a binary vector of leng...
Efficiency of Local Search with Multiple Local Optima
 SIAM J. Discr. Math., Vol
, 2000
"... Abstract. The first contribution of this paper is a theoretical investigation of combinatorial optimization problems. Their landscapes are specified by the set of neighborhoods of all points of the search space. The aim of the paper consists of the estimation of the number N of local optima and the ..."
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Cited by 11 (0 self)
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Abstract. The first contribution of this paper is a theoretical investigation of combinatorial optimization problems. Their landscapes are specified by the set of neighborhoods of all points of the search space. The aim of the paper consists of the estimation of the number N of local optima and the distributions of the sizes (αj) of their attraction basins. For different types of landscapes we give precise estimates of the size of the random sample that ensures that at least one point lies in each attraction basin. A practical methodology is then proposed for identifying these quantities (N and (αj) distributions) for an unknown landscape, given a random sample of starting points and a local steepest ascent search. This methodology can be applied to any landscape specified with a modification operator and provides bounds on search complexity to detect all local optima. Experiments demonstrate the efficiency of this methodology for guiding the choice of modification operators, eventually leading to the design of problemdependent optimization heuristics.