Using Quadratic Assignment Methods to Generate Initial Permutations for Least-Squares Unidimensional Scaling of Symmetric Proximity Matrices

Exact and approximate algorithms for part-machine clustering based on a relationship between interval graphs and Robinson matrices

“…Therefore, we also developed a simulated annealing heuristic for the RPP that is capable of accommodating larger test problems. The structure of the simulated annealing heuristic is closely related to those designed for related permutation problems (Heragu and Alfa, 1992;Brusco and Stahl, 2000), and the selection of algorithm Set parameters: cooling factor c = 0.9, minimum temperature t min = 0.0001, maximum temperature t max = n 2 , and temperature length TL = 100n Compute the number of temperature reductions TR = (log(t min ) --log(tmax))/log(c) Randomly generate an initial permutation, , and compute f 3 ( ) Set temp = t max Set B = For tr = 1 to TR For tl = 1 to TL Generate a neighboring solution, ′, by interchanging the objects in two randomly selected positions of parameters (cooling factor, temperature length, etc) were based on previous research as well as our own experimentation. The pseudocode for the simulated annealing heuristic is displayed in Fig.…”

Optimal Least-Squares Unidimensional Scaling: Improved Branch-and-Bound Procedures and Comparison to Dynamic Programming

“…This paper focuses on least-squares unidimensional scaling of symmetric proximity matrices, which has a long and rich history in the combinatorial data analysis literature (see Brusco and Stahl (2000) and Hubert, Arabie, and Meulman (2001, Chapter 4) for recent reviews). We assume that pairwise dissimilarity data are available for a collection of n objects, and that S = {1, 2, .…”

Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers

“…From the practical point of view, it is because of the diversified applications of the QAP. The QAP has been applied in many fields such as backboard wiring [7], typewriter keyboards and control panels design [8], scheduling [9], numerical analysis [10], storage-and-retrieval [11], and many others. More advances in theoretical aspects, solution methods and applications of the QAP can be found in [5,12,13,14,15,16,17,18].…”