Abstract
Multi-objective quadratic assignment problems (mQAPs) are NP-hard problems that optimally allocate facilities to locations using a distance matrix and several flow matrices. mQAPs are often used to compare the performance of the multi-objective meta-heuristics. We generate large mQAP instances by combining small size mQAP with known local optimum. We call these instances composite mQAPs, and we show that the cost function of these mQAPs is additively decomposable. We give mild conditions for which a composite mQAP instance has known optimum solution. We generate composite mQAP instances using a set of uniform distributions that obey these conditions. Using numerical experiments we show that composite mQAPs are difficult for multi-objective meta-heuristics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Puglierin, F., Drugan, M.M., Wiering, M.: Bandit-inspired memetic algorithms for solving quadratic assignment problems. In: Proc. of CEC, pp. 2078–2085. IEEE (2013)
Drugan, M.M.: Cartesian product of scalarization functions for many-objective QAP instances with correlated flow matrices. In: Proc. of GECCO, pp. 527–534. ACM (2013)
Çela, E.: The Quadratic Assignment Problem: Theory and Algorithms. Kluwer Academic Publishers, Dordrecht (1998)
Drezner, Z., Hahn, P., Taillard, E.: Recent advances for the quadratic assignment problem with special emphasis on instances that are difficult for meta-heuristic methods. Annals of Operations Research 139(1), 65–94 (2005)
Drugan, M.: Generating QAP instances with known optimum solution and additively decomposable cost function. Journal of Combinatorial Optimization (2014)
Palubeckis, G.: An algorithm for construction of test cases for the quadratic assignment problem. Informatica, Lith. Acad. Sci. 11(3), 281–296 (2000)
Knowles, J.D., Corne, D.W.: Instance generators and test suites for the multiobjective quadratic assignment problem. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 295–310. Springer, Heidelberg (2003)
Drugan, M.M., Thierens, D.: Stochastic pareto local search: Pareto neighbourhood exploration and perturbation strategies. J. Heuristics 18(5), 727–766 (2012)
Wayne, A.: Inequalities and inversions of order. Scripta Mathematica 12(2), 164–169 (1946)
Angel, E., Zissimopoulos, V.: On the hardness of the quadratic assignment problem with metaheuristics. J. Heuristics 8(4), 399–414 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Drugan, M.M. (2014). Multi-objective Quadratic Assignment Problem Instances Generator with a Known Optimum Solution. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_55
Download citation
DOI: https://doi.org/10.1007/978-3-319-10762-2_55
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10761-5
Online ISBN: 978-3-319-10762-2
eBook Packages: Computer ScienceComputer Science (R0)