The use of the ``golden section'' rule in probability modeling algorithms. (Q2739943)

This paper deals with the quadratic assignment problem in combinatorial formulation. Let \(X\) be the space of all permutations of integers \(\{1,\ldots,n\}\). The goal function is given by \(f(x)= \sum\limits_{i=1}^{n}\sum\limits_{j=1}^{n}c_{ij}d_{x_{i}x_{j}}, x\in X\), where \((c_{ij})_{n\times n}\), \((d_{ij})_{n\times n}\) are given matrices, \(c_{ij}\geq 0, d_{ij}\geq 0\). We must find permutation \(\underline {x}\in X\) such that \(\underline {x}=\arg\,\min\{f(x):x\in X\}\). The algorithm using the ``golden cut'' rule is proposed for solution of the considered quadratic assignment problem. Results of the computing test are presented.