Generating QAP instances with known optimum solution and additively decomposable cost function

Abstract

Link to publication Citation for published version (APA):Drugan, M. M. (2015). Generating QAP instances with known optimum solution and additively decomposable cost function. Journal of Combinatorial Optimization, 30(4), 1138-1172. DOI: 10.1007 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract Quadratic assignment problems (QAPs) is a NP-hard combinatorial optimization problem. QAPs are often used to compare the performance of meta-heuristics. In this paper, we propose a QAP problem instance generator that can be used for benchmarking for heuristic algorithms. Our QAP generator combines small size QAPs with known optimum solution into a larger size QAP instance. We call these instances composite QAPs (cQAPs), and we show that the cost function of cQAPs is additively decomposable. We give mild conditions for which a cQAP instance has known optimum solution. We generate cQAP instances using uniform distributions with different bounds for the component QAPs and for the rest of the cQAP elements. Numerical and analytical techniques that measure the difficulty of the cQAP instances in comparison with other QAPs from the literature are introduced. These methods point out that some cQAP instances are difficult for local search with many local optimum of various values, low epistasis and non-trivial asymptotic behaviour.

Nonequilibrium Monte Carlo for unfreezing variables in hard combinatorial optimization

“…In the first class, we studied random 4-SAT problems with 5000 variables deep into the rigidity regime. In the second class we benchmarked our algorithm on random QAP instances, with sizes ranging from 256 to 1600 binary variables [55], as well as some industrial instances from the QAPLIB public library [56]. We also applied NMC algorithm to other combinatorial optimization problems with various dimensionality and structure.…”

A great deluge and tabu search hybrid with two-stage memory support for quadratic assignment problem

“…Quadratic assignment problem belongs to the class of NP-hard combinatorial optimization problems and the largest instances that can be solved with exact algorithms are limited to instances of size around 30 [19][20][21]. Hence, the only feasible way to deal with the solution of large QAP instances is to use heuristic approaches which guarantee to reach a locally optimal solution in reasonable computation times.…”

“…Table 14 illustrates the APD scores for the final set of QAP instances containing the difficult drexx problems. Unfortunately, only one algorithm is found in literature with scores of some of (8) 0.175 (14) 5.915 10.100 Tai75e02 4.165 (8) 0.339 (14) 8.751 Tai75e03 1.081 (14) 0.000 (20) 2.681 Tai75e04 1.005 (16) 0.030 (19) 3.705 Tai75e05 1.412 (11) 0.000 (20) 2.412 Tai75e06 2.115 (10) 0.000 (20) 4.005 Tai75e07 4.662 (7) 0.136 (17) 8.015 Tai75e08…”

“…3.951 (8) 0.059 (19) 8.523 Tai75e09 1.051 (15) 0.000 (20) 4.798 Tai75e10 2.910 (10) 0.149 (19) 5.740 Tai75e11 1.021 (16) 0.000 (20) 3.721 Tai75e12 4.619 (7) 0.000 (20) 8.196 Tai75e13 2.922 (11) 0.000 (20) 5.123 Tai75e14 1.601 (12) 0.000 (20) 3.659 Tai75e15…”

“…1.374 (14) 0.053 (19) 2.743 tai125e01 7.751 15.600 0.000 (10) 0.000 (20) the drexx problems. It is observed that the proposed TMSGD-QAP algorithm solved all drexx problem of size 30 and below optimally in all 10 trials.…”