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Solving Large Quadratic Assignment Problems on Computational Grids
, 2000
"... The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computat ..."
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Cited by 82 (7 self)
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The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms. In this article we describe a novel approach to solve QAPs using a state-of-the-art branch-and-bound algorithm running on a federation of geographically distributed resources known as a computational grid. Solution of QAPs of unprecedented complexity, including the nug30, kra30b, and tho30 instances, is reported.
Solving Quadratic Assignment Problems Using Convex Quadratic Programming Relaxations
, 2000
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Recent Advances for the Quadratic Assignment Problem with Special Emphasis on Instances that are Difficult for Meta-Heuristic Methods
- Annals of OR
, 2005
"... This paper reports heuristic and exact solution advances for the Quadratic Assignment Problem (QAP). QAP instances frequently used in the literature are relatively well solved by heuristic approaches. Indeed, solutions at a fraction of one percent from the best known solution values are rapidly foun ..."
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Cited by 14 (1 self)
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This paper reports heuristic and exact solution advances for the Quadratic Assignment Problem (QAP). QAP instances frequently used in the literature are relatively well solved by heuristic approaches. Indeed, solutions at a fraction of one percent from the best known solution values are rapidly found by most heuristic methods. Exact methods are not able to prove optimality for these instances as soon as the problem size approaches 30 to 40. This article presents new QAP instances that are ill conditioned for many metaheuristic-based methods. However, these new instances are shown to be solved relatively well by some exact methods, since problem instances up to a size of 75 have been exactly solved. Key words: Quadratic assignment problem, local search, branch & bound, benchmarks. 1. Introduction. 1.1 The quadratic assignment problem (QAP). The QAP is a combinatorial optimization problem stated for the first time by Koopmans and Beckmann in 1957. It can be described as follows: Given two n × n matrices (aij) and(bkl), find a permutation ππππ minimizing:
Tree Elaboration Strategies In Branch and Bound Algorithms For Solving the Quadratic Assignment Problem
, 1999
"... This paper presents a new strategy for selecting nodes in a branch-and-bound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies failed on the larger size problems. The strategy is a variation of polytomic depth-first searc ..."
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Cited by 12 (3 self)
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This paper presents a new strategy for selecting nodes in a branch-and-bound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies failed on the larger size problems. The strategy is a variation of polytomic depth-first search of Mautor and Roucairol which extends a node by all assignments of an unassigned facility to unassigned locations based upon the counting of 'forbidden' locations. A forbidden location is one where the addition of the corresponding leader (linear cost) element would increase the lower bound beyond the upper bound. We learned that this fortuitous situation never occurs near the root on Nugent problems larger than 15. One has to make better estimates of the bound if the strategy is to work. We have, therefore, designed and implemented an increasingly improved set of bound calculations. The better of these bound calculations to be utilized near the root and the less accurate (poorer bounds) utilized further into the tree. The result is an effective and powerful technique for shortening the run times of problem instances in the range of size 16 to 25. Run times were decreased generally by five- or six-to-one and the number of nodes evaluated was decreased as much as 10-to-one. Later improvements in our strategy produced a better than 3-to-1 reduction in runtime so that overall improvement in run time was as high as 20-to-1 as compared to our earlier results. At the end of our paper, we compare the performance of the four most successful algorithms for exact solution of the QAP.
A Hospital Facility Layout Problem Finally Solved
, 2000
"... This paper presents a history of a difficult facility layout problem that falls into the category of the Koopmans-Beckmann variant of the Quadratic Assignment Problem (QAP), wherein 30 facilities are to be assigned to 30 locations. The problem arose in 1972 as part of the design of a German unive ..."
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Cited by 11 (1 self)
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This paper presents a history of a difficult facility layout problem that falls into the category of the Koopmans-Beckmann variant of the Quadratic Assignment Problem (QAP), wherein 30 facilities are to be assigned to 30 locations. The problem arose in 1972 as part of the design of a German university hospital, Klinikum Regensburg. This problem, known as the Krarup30a upon its inclusion in the QAPLIB library of QAP instances, has remained an important example of one of the most difficult to solve. In 1999, two approaches provided multiple optimum solutions.
Breakout local search for the quadratic assignment problem
- Applied Mathematics and Computation
"... The quadratic assignment problem (QAP) is one of the most studied combinatorial optimization problems with various practical applications. In this paper, we present Breakout Local Search (BLS) for solving QAP. BLS explores the search space by a joint use of local search and adaptive perturbation str ..."
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Cited by 8 (4 self)
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The quadratic assignment problem (QAP) is one of the most studied combinatorial optimization problems with various practical applications. In this paper, we present Breakout Local Search (BLS) for solving QAP. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Experimental evalua-tions on the set of QAPLIB benchmark instances show that the proposed approach is able to attain current best-known results for all but two instances with an average computing time of less than 4.5 hours. Comparisons are also provided to show the competitiveness of the proposed approach with respect to the best-performing QAP algorithms from the literature.
A Low-Dimensional Semidefinite Relaxation for the Quadratic Assignment Problem
"... doi 10.1287/moor.1090.0419 ..."
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A Study of Quadratic Assignment Problem Instances That Are Difficult for Meta-Heuristic Methods
"... The quadratic assignment instances frequently used in the literature are relatively well solved by heuristic approaches. Indeed, solutions at a fraction of one percent from the best known solution values are rapidly found by most heuristic methods. Exact methods are not able to prove optimality for ..."
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Cited by 6 (0 self)
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The quadratic assignment instances frequently used in the literature are relatively well solved by heuristic approaches. Indeed, solutions at a fraction of one percent from the best known solution values are rapidly found by most heuristic methods. Exact methods are not able to prove optimality for these instances as soon as the problem size approaches 30 to 40. This article presents new QAP instances that are ill conditioned for many metaheuristic-based methods. However, these new instances are shown to be solved relatively well by some exact methods since problem instances up to a size of 75 have been exactly solved.
Estimation of distribution algorithm with 2-opt local search for the quadratic assignment problem
- Towards a New Evolutionary Computation. Advances in Estimation of Distribution Algorithm
, 2006
"... Abstract. This chapter proposes a combination of estimation of distribution algorithm (EDA) and the 2-opt local search algorithm (EDA/LS) for the quadratic assignment problem (QAP). In EDA/LS, a new operator, called guided mutation, is employed for generating new solutions. This operator uses both g ..."
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Cited by 6 (1 self)
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Abstract. This chapter proposes a combination of estimation of distribution algorithm (EDA) and the 2-opt local search algorithm (EDA/LS) for the quadratic assignment problem (QAP). In EDA/LS, a new operator, called guided mutation, is employed for generating new solutions. This operator uses both global statistical information collected from the previous search and the location information of solutions found so far. The 2-opt local search algorithm is applied to each new solution generated by guided mutation. A restart strategy based on statistical information is used when the search is trapped in a local area. Experimental results on a set of QAP test instances show that EDA/LS is comparable with the memetic algorithm of Merz and Freisleben and outperforms estimation of distribution algorithm with guided local search (EDA/GLS). The proximate optimality principle on the QAP is verified experimentally to justify the rationale behind heuristics (including EDA/GLS) for the QAP. 1
The Steinberg Wiring Problem
, 2001
"... this paper was written we learned of a previously unreleased technical report by M. Nystrom [35] that describes the solution of the ste36b/c problems. Nystrom used a distributed B&B algorithm based on the GLB, implemented on 22 200 MHz Pentium Pro CPUs. The serial time to solve the ste36b/c inst ..."
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Cited by 5 (0 self)
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this paper was written we learned of a previously unreleased technical report by M. Nystrom [35] that describes the solution of the ste36b/c problems. Nystrom used a distributed B&B algorithm based on the GLB, implemented on 22 200 MHz Pentium Pro CPUs. The serial time to solve the ste36b/c instances on one of these CPUs is estimated to be approximately 60 days/200 days, respectively. (The time for ste36c is substantially higher because this problem was solved using an initial incumbent value of +1.) "wiring" 2001/12/19 page 13 i i i i i i i i 13 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 0 3 6 9 12 15 18 21 24 27 30 33 Level Figure 4. Distribution of nodes in solution of ste36a 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 3 6 9 12 15 18 21 24 27 30 33 Level 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0 Rel. Gap Cum. Hrs
