Informatica

This paper investigates the problem of partitioning a complete weighted graph into complete subgraphs, each having the same number of vertices, with the objective of minimizing the sum of edge weights of the resulting subgraphs. This NP-complete problem arises in many applications such as assignment and scheduling-related group partitioning problems and micro-aggregation techniques. In this paper, we present a mathematical programming model and propose a complementary column generation approach to solve the resulting model. A dual based lower bounding feature is also introduced to curtail the notorious tailing-off effects often induced when using column generation methods. Computational results are presented for a wide range of test problems.

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.

The problem of parameter clustering on the basis of their correlation matrix is considered. The convergence in probability of parameter clustering based on the simulated annealing is investigated theoretically.

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 deal with the problem of extremal parameter grouping. The problem formulation, the algorithms of parameter grouping and the fields of implementation are presented. The deterministic algorithms of extremal parameter grouping often find the local maximum of the functional, characterizing the quality of a partition. The problem has been formulated as a problem of combinatorial optimization and attempted to be solved using the simulated annealing strategy. The algorithms, realizing such a strategy and devoted to the solving of the problem concerned, are proposed and investigated.