Informatica

Given a set of objects with profits (any, even negative, numbers) assigned not only to separate objects but also to pairs of them, the unconstrained binary quadratic optimization problem consists in finding a subset of objects for which the overall profit is maximized. In this paper, an iterated tabu search algorithm for solving this problem is proposed. Computational results for problem instances of size up to 7000 variables (objects) are reported and comparisons with other up-to-date heuristic methods are provided.

In this paper we present an algorithm for generating quadratic assignment problem (QAP) instances with known provably optimal solution. The flow matrix of such instances is constructed from the matrices corresponding to special graphs whose size may reach the dimension of the problem. In this respect, the algorithm generalizes some existing algorithms based on the iterative selection of triangles only. The set of instances which can be produced by the algorithm is NP-hard. Using multi-start descent heuristic for the QAP, we compare experimentally such test cases against those created by several existing generators and against Nugent-type problems from the QAPLIB as well.

In this paper we define a class of edge-weighted graphs having nonnegatively valued bisections. We show experimentally that complete such graphs with more than three vertices and also some special graphs with only positive edges can be applied to improve the existing lower bounds for a version of the quadratic assignment problem, namely with a matrix composed of rectilinear distances between points in the Euclidean space.

In this paper, we present two heuristics for solving the unconstrained quadratic 0–1 programming problem. First heuristic realizes the steepest ascent from the centre of the hypercube, while the second constructs a series of solutions and chooses the best of them. In order to evaluate their worst-case behaviour We define the performance ratio K which uses the objective function value at the reference point x=1/2. We show for both heuristics that K is bounded by 1 from above and this bound is sharp. Finally, we report on the results of a computational study with proposed and local improvement heuristics.

This paper briefly reviews some of the recent results on the problems and algorithms for their solution in quadratic 0-1 optimization. First, the complexity of problems is discussed. Next, some exact algorithms and heuristics are mentioned. Finally, results in the analysis of the algorithms for 0-1 quadratic problems are summarized. The papers written in Russian are considered more thoroughly here.