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67
The Reactive Tabu Search
, 1993
"... this paper the concept of chaotic attractor is used only as an example of a dynamic behavior that could a#ect the search process, we summarize the main characteristics and refer to [13] for a detailed theoretical analysis. Chaotic attractors are characterized by a "contraction of the areas", so that ..."
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Cited by 222 (25 self)
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this paper the concept of chaotic attractor is used only as an example of a dynamic behavior that could a#ect the search process, we summarize the main characteristics and refer to [13] for a detailed theoretical analysis. Chaotic attractors are characterized by a "contraction of the areas", so that trajectories starting with di#erent initial conditions will be compressed in a limited area of the configuration space, and by a "sensitive dependence upon the initial conditions", so that di#erent trajectories will diverge. For an analytical characterization of this sensitive dependence, it is convenient to introduce the concept of Lyapunov exponent. Let us consider the function g that maps the point at step n
QAPLIB  A Quadratic Assignment Problem Library
, 1996
"... This report, the data and also most of the best feasible solutions are available via World Wide Web. The URLs of the QAPLIB Home Page are http://www.opt.math.tugraz.ac.at/qaplib/ ..."
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Cited by 163 (6 self)
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This report, the data and also most of the best feasible solutions are available via World Wide Web. The URLs of the QAPLIB Home Page are http://www.opt.math.tugraz.ac.at/qaplib/
Generating Software Test Data by Evolution
 IEEE Transactions on Software Engineering
, 1997
"... This paper discusses the use of genetic algorithms (GAs) for automatic software test data generation. This research extends previous work on dynamic test data generation where the problem of test data generation is reduced to one of minimizing a function [Miller and Spooner, 1976, Korel, 1990]. In o ..."
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Cited by 130 (2 self)
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This paper discusses the use of genetic algorithms (GAs) for automatic software test data generation. This research extends previous work on dynamic test data generation where the problem of test data generation is reduced to one of minimizing a function [Miller and Spooner, 1976, Korel, 1990]. In our work, the function is minimized by using one of two genetic algorithms in place of the local minimization techniques used in earlier research. We describe the implementation of our GAbased system, and examine the effectiveness of this approach on a number of programs, one of which is significantly larger than those for which results have previously been reported in the literature. We also examine the effect of program complexity on the test data generation problem by executing our system on a number of synthetic programs that have varying complexities. 1 Introduction An important aspect of software testing involves judging how well a series of test inputs tests a piece of code. Usuall...
The Quadratic Assignment Problem
 HANDBOOK OF COMBINATORIAL OPTIMIZATION, P. PARDALOS AND D.Z. DU, EDS.
, 1998
"... This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, an ..."
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Cited by 110 (3 self)
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This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.Z. Du, eds.
Very LargeScale Neighborhood Search for the Quadratic Assignment Problem
 DISCRETE APPLIED MATHEMATICS
, 2002
"... The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NPhard, and can be solved to optimality only for fairly small size instances ..."
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Cited by 108 (11 self)
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The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NPhard, and can be solved to optimality only for fairly small size instances (typically, n < 25). Neighborhood search algorithms are the most popular heuristic algorithms to solve larger size instances of the QAP. The most extensively used neighborhood structure for the QAP is the 2exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities and thus has size O(n²). Previous efforts to explore larger size neighborhoods (such as 3exchange or 4exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very largescale neighborhood (VLSN) search algorithms where the size of the neighborhood is very large and we propose a novel search procedure to heuristically enumerate good neighbors. Our search procedure relies on the concept of improvement graph which allows us to evaluate neighbors much faster than the existing methods. We present extensive computational results of our algorithms on standard benchmark instances. These investigations reveal that very largescale neighborhood search algorithms give consistently better solutions compared the popular 2exchange neighborhood algorithms considering both the solution time and solution accuracy.
Tabu Search: A Tutorial
 Interfaces
, 1990
"... Tabu search is a "higher level " heuristic procedure for solving optimization problems, designed to guide other methods (or their component processes) to escape the trap of local optimality. Tabu search has obtained optimal and near optimal solutions to a wide variety of classical and practical prob ..."
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Cited by 91 (2 self)
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Tabu search is a "higher level " heuristic procedure for solving optimization problems, designed to guide other methods (or their component processes) to escape the trap of local optimality. Tabu search has obtained optimal and near optimal solutions to a wide variety of classical and practical problems in applications ranging from scheduling to telecommunications and from character recognition to neural networks. It uses flexible structures memory (to permit search information to be exploited more thoroughly than by rigid memory systems or memoryless systems), conditions for strategically constraining and freeing the search process (embodied in tabu restrictions and aspiration criteria), and memory functions of varying time spans for intensifying and diversifying the search (reinforcing attributes historically found good and driving the search into new regions). Tabu search can be integrated with branchandbound and cutting plane procedures, and it has the ability to start with a simple implementation that can be upgraded over time to incorporate more advanced or specialized elements. T abu search is a metaheuristic that can to prevent them from becoming trapped at be superimposed on other procedures locally optimal solutions. The method can
Genetic Hybrids for the Quadratic Assignment Problem
 DIMACS Series in Mathematics and Theoretical Computer Science
, 1993
"... . A new hybrid procedure that combines genetic operators to existing heuristics is proposed to solve the Quadratic Assignment Problem (QAP). Genetic operators are found to improve the performance of both local search and tabu search. Some guidelines are also given to design good hybrid schemes. Thes ..."
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Cited by 89 (0 self)
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. A new hybrid procedure that combines genetic operators to existing heuristics is proposed to solve the Quadratic Assignment Problem (QAP). Genetic operators are found to improve the performance of both local search and tabu search. Some guidelines are also given to design good hybrid schemes. These hybrid algorithms are then used to improve on the best known solutions of many test problems in the literature. 1. Introduction The quadratic assignment problem (QAP) can be stated as: min OE2P (n) n X i=1 n X j=1 a ij b OE(i)OE(j) ; where A = (a ij ) and B = (b kl ) are two n \Theta n matrices and P (n) is the set of all permutations of f1; :::; ng. Matrix A is often referred to as a distance matrix between sites, and B as a flow matrix between objects. In most cases, the matrices A and B are symmetrical with a null diagonal. A permutation may then be interpreted as an assignment of objects to sites with a quadratic cost associated to it. There are many applications that can be fo...
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.
Edward,“Guided Local Search
, 1995
"... Abstract Combinatorial explosion problem is a well known phenomenon that prevents complete algorithms from solving many reallife combinatorial optimization problems. In many situations, heuristic search methods are needed. This chapter describes the principles of Guided Local Search (GLS) and Fast ..."
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Cited by 56 (5 self)
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Abstract Combinatorial explosion problem is a well known phenomenon that prevents complete algorithms from solving many reallife combinatorial optimization problems. In many situations, heuristic search methods are needed. This chapter describes the principles of Guided Local Search (GLS) and Fast Local Search (FLS) and surveys their applications. GLS is a penaltybased metaheuristic algorithm that sits on top of other local search algorithms, with the aim to improve their efficiency and robustness. FLS is a way of reducing the size of the neighbourhood to improve the efficiency of local search. The chapter also provides guidance for implementing and using GLS and FLS. Four problems, representative of general application categories, are examined with detailed information provided on how to build a GLSbased method in each case.
A Greedy Genetic Algorithm for the Quadratic Assignment Problem
 Computers and Operations Research
, 1997
"... The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. In this paper, we suggest a genetic algorithm for the QAP and report its computational behavior. The genetic algorithm incorporates many greedy principles in ..."
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Cited by 43 (2 self)
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The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. In this paper, we suggest a genetic algorithm for the QAP and report its computational behavior. The genetic algorithm incorporates many greedy principles in its design and, hence, is called the greedy genetic algorithm. The ideas we incorporate in the greedy genetic algorithm include (i) generating the initial population using a randomized construction heuristic; (ii) new crossover schemes; (iii) a special purpose immigration scheme that promotes diversity; (iv) periodic local optimization of a subset of the population; (v) tournamenting among different populations; and (vi) an overall design that attempts to strike a balance between diversity and a bias towards fitter individuals. We test our algorithm on all the benchmark instances of QAPLIB, a wellknown library of QAP instances. Out of the 132 total instances in QAPLIB of varied sizes, the g...