The maximally diverse grouping problem (MDGP) consists of finding a partition of a set of elements into a given number of mutually disjoint groups, while respecting the requirements of group size constraints and diversity. In this paper, we propose an iterated tabu search (ITS) algorithm for solving this problem. We report computational results on three sets of benchmark MDGP instances of size up to 960 elements and provide comparisons of ITS to five state-of-the-art heuristic methods from the literature. The results demonstrate the superiority of the ITS algorithm over alternative approaches. The source code of the algorithm is available for free download via the internet.

The goal of this paper is to discuss the tabu search (TS) meta-heuristic and its enhancement for combinatorial optimization problems. Firstly, the issues related to the principles and specific features of the standard TS are concerned. Further, a promising extension to the classical tabu search scheme is introduced. The most important component of this extension is a special kind of diversification mechanism. We give the paradigm of this new improved TS strategy, which is called an iterated tabu search (ITS). ITS was applied to the difficult combinatorial optimization problems, the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). The results of the experiments with the TSP and QAP show the high efficiency of the ITS strategy. The outstanding performance of ITS is also demonstrated by the fact that the new record-breaking solutions were found for the hard QAP instances - tai80a and tai100a.

In this paper, an efficient hybrid genetic algorithm (HGA) and its variants for the wellknown combinatorial optimization problem, the quadratic assignment problem (QAP) are discussed. In particular, we tested our algorithms on a special type of QAPs, the structured quadratic assignment problems. The results from the computational experiments on this class of problems demonstrate that HGAs allow to achieve near-optimal and (pseudo-)optimal solutions at very reasonable computation times. The obtained results also confirm that the hybrid genetic algorithms are among the most suitable heuristic approaches for this type of QAPs.

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Eccentric angular motion transfer mechanisms are analyzed in the paper. The de-balancing mass has an additional degree of freedom in these mechanisms. It was found that certain types of such mechanisms posses interesting nonlinear dynamical features when a self-resonance motion mode occurs. Such self-resonance motion mode takes place when the main driving element rotates with relatively high angular velocity, but low frequency vibrations are generated in the range of fundamental frequency of the system. Analytical, numerical and experimental investigations of nonlinear vibration excitation systems were performed. Such vibration excitation systems have high practical value as there is no necessity for complex vibration control equipment -the stability of operation is guaranteed by non-linear dynamical interactions. Laser velocity measurement system was used for experimental investigations of the dynamical properties of the system. The results of the investigations validated the results of the theoretical analysis and provide a background for developing new type of dynamical mechanisms.