For almost two decades the question of whether tabu search (TS) or simulated annealing (SA) performs better for the quadratic assignment problem has been unresolved. To answer this question satisfactorily, we compare performance at various values of targeted solution quality, running each heuristic at its optimal number of iterations for each target. We find that for a number of varied problem ...

We derive a new semidefinite programming bound for the maximum k-section problem. For k = 2 (i.e. for maximum bisection), the new bound is least as strong as the well-known bound by Frieze and Jerrum [A. Frieze and M. Jerrum. Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION. Algorithmica, 18(1): 67–81, 1997]. For k ≥ 3 the new bound dominates a bound of Karish and Rendl [S.E. K...

The quadratic assignment problem (QAP) maybe was for a long time the one among the prominent NP-hard combinatorial optimization problems about which the fewest polyhedral results had been known. Recent work of Rijal (1995) and Padberg and Rijal (1996) has on the one hand yielded some basic facts about the associated quadratic assignment polytope, but has on the other hand shown that \naive" inv...

We analyze a special case of the maximum quadratic assignment problem where one matrix is a monotone anti-Monge matrix and the other matrix has a multi-layered structure that is built on top of certain Toeplitz matrices. As an application of our main result, we derive a (simple and concise) alternative proof for a recent result on the scheduling problem of maximizing the variance of job complet...

This paper addresses the application of the principles of feedback and self-controlling software to the tabu search algorithm. We introduce two new reaction strategies for the tabu search algorithm. The first strategy treats the tabu search algorithm as a target system to be controlled and uses a control-theoretic approach to adjust the algorithm parameters that affect search intensification. T...

Curriculum design is a highly important activity for the academic institutions. It is discussed in literature as a balancing academic curriculum problem (BACP). The BACP schedules courses to different semesters, while balancing the total workload per period. BACP model involves precedence relations, but the related courses are not necessarily assigned to closest periods. The Relevance Based Cur...

Recent developments in fitness landscape analysis include the study of Local Optima Networks (LON) and applications of the Elementary Landscapes theory. This paper represents a first step at combining these two tools to explore their ability to forecast the performance of search algorithms. We base our analysis on the Quadratic Assignment Problem (QAP) and conduct a large statistical study over...

Mappings that preserve neighbourhood relationships are relevant in bothpractical and biological contexts. It is important to be clear about precisely what preserving neighbourhoods could mean. We give a definition of a “perfectly neighbourhood preserving” map, which we call a topographic homeomorphism, and prove that this has certain desirable properties. When a topographic homeomorphism does n...

The Quadratic Assignment Problem (QAP) has remained one of the great challenges in combinatorial optimization. It is still considered a computationally nontrivial task to solve modest size problems, say of size n = 20: The QAPLIB was rst published in 1991, in order to provide a uni ed testbed for QAP, accessible to the scienti c community. It consisted of virtually all QAP instances that were a...

The facility layout problem has generally been formulated as a quadratic assignment problem, where the interacting facilities are assigned to the various sites. In this paper a different approach, based on assigning distances between pairs of sites to pairs of facilities, is taken. A network formulation and analysis of this problem is provided. An algorithm, composed of three phases, is develop...