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On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts  Towards Memetic Algorithms
, 1989
"... Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could ..."
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Cited by 186 (10 self)
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Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could possibly enumerate 10 9 tours per second on a computer it would thus take roughly 10 639 years of computing to establish the optimality of this tour by exhaustive enumeration." This quote shows the real difficulty of a combinatorial optimization problem. The huge number of configurations is the primary difficulty when dealing with one of these problems. The quote belongs to M.W Padberg and M. Grotschel, Chap. 9., "Polyhedral computations", from the book The Traveling Salesman Problem: A Guided tour of Combinatorial Optimization [124]. It is interesting to compare the number of configurations of realworld problems in combinatorial optimization with those large numbers arising in Cosmol...
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/
PseudoBoolean Optimization
 DISCRETE APPLIED MATHEMATICS
, 2001
"... This survey examines the state of the art of a variety of problems related to pseudoBoolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudoBoolean optimization, the specially important case of ..."
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Cited by 110 (4 self)
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This survey examines the state of the art of a variety of problems related to pseudoBoolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudoBoolean optimization, the specially important case of quadratic pseudoBoolean optimization (to which every pseudoBoolean optimization can be reduced), several other important special classes, and approximation algorithms.
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.
Semidefinite Programming Relaxations For The Quadratic Assignment Problem
, 1998
"... Semidefinite programming (SDP) relaxations for the quadratic assignment problem (QAP) are derived using the dual of the (homogenized) Lagrangian dual of appropriate equivalent representations of QAP. These relaxations result in the interesting, special, case where only the dual problem of the SDP re ..."
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Cited by 72 (25 self)
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Semidefinite programming (SDP) relaxations for the quadratic assignment problem (QAP) are derived using the dual of the (homogenized) Lagrangian dual of appropriate equivalent representations of QAP. These relaxations result in the interesting, special, case where only the dual problem of the SDP relaxation has strict interior, i.e. the Slater constraint qualification always fails for the primal problem. Although there is no duality gap in theory, this indicates that the relaxation cannot be solved in a numerically stable way. By exploring the geometrical structure of the relaxation, we are able to find projected SDP relaxations. These new relaxations, and their duals, satisfy the Slater constraint qualification, and so can be solved numerically using primaldual interiorpoint methods. For one of our models, a preconditioned conjugate gradient method is used for solving the large linear systems which arise when finding the Newton direction. The preconditioner is found by exploiting th...
A New Lower Bound via Projection for the Quadratic Assignment Problem
 Mathematics of Operations Research
, 1992
"... New lower bounds for the quadratic assignment problem QAP are presented. These bounds are based on the orthogonal relaxation of QAP. The additional improvement is obtained by making efficient use of a tractable representation of orthogonal matrices having constant row and column sums. The new bound ..."
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Cited by 53 (17 self)
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New lower bounds for the quadratic assignment problem QAP are presented. These bounds are based on the orthogonal relaxation of QAP. The additional improvement is obtained by making efficient use of a tractable representation of orthogonal matrices having constant row and column sums. The new bound is easy to implement and often provides high quality bounds under an acceptable computational effort. Key Words: quadratic assignment problem, lower bounds, relaxations, orthogonal projection, eigenvalue bounds. 0 The authors would like to thank the Natural Sciences and Engineering Research Council of Canada and the Austrian Science Foundatation (FWF) for their support. 1 Introduction The Quadratic Assignment Problem QAP is a generic model for various problems arising e.g. in location theory, VLSI design, facility layout, keyboard design and many other areas, see [1] for a recent survey on the QAP. Formally the QAP consists of minimizing f(X) = tr(AXB t + C)X t over the set of permu...
Exact And Approximate Nondeterministic TreeSearch Procedures For The Quadratic Assignment Problem
, 1998
"... This paper introduces two new techniques for solving the Quadratic Assignment Problem. The first is a heuristic technique, defined in accordance to the Ant System metaphor, and includes as a distinctive feature the use of a new lower bound at each constructive step. The second is a branch and bound ..."
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Cited by 46 (5 self)
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This paper introduces two new techniques for solving the Quadratic Assignment Problem. The first is a heuristic technique, defined in accordance to the Ant System metaphor, and includes as a distinctive feature the use of a new lower bound at each constructive step. The second is a branch and bound exact approach, containing some elements introduced in the Ant algorithm. Computational results prove the effectiveness of both approaches.
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...
Using combinatorial optimization within maxproduct belief propagation
 Advances in Neural Information Processing Systems (NIPS
, 2007
"... In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or closetooptimal assignment can be found very efficiently using combinatorial optimization algorithms: cert ..."
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Cited by 39 (6 self)
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In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or closetooptimal assignment can be found very efficiently using combinatorial optimization algorithms: certain MRFs with mutual exclusion constraints can be solved using bipartite matching, and MRFs with regular potentials can be solved using minimum cut methods. However, these solutions do not apply to the many MRFs that contain such tractable components as subnetworks, but also other noncomplying potentials. In this paper, we present a new method, called COMPOSE, for exploiting combinatorial optimization for subnetworks within the context of a maxproduct belief propagation algorithm. COMPOSE uses combinatorial optimization for computing exact maxmarginals for an entire subnetwork; these can then be used for inference in the context of the network as a whole. We describe highly efficient methods for computing maxmarginals for subnetworks corresponding both to bipartite matchings and to regular networks. We present results on both synthetic and real networks encoding correspondence problems between images, which involve both matching constraints and pairwise geometric constraints. We compare to a range of current methods, showing that the ability of COMPOSE to transmit information globally across the network leads to improved convergence, decreased running time, and higherscoring assignments. 1