Gobov D. Mathematical models and metaheuristics algorithms for solving optimization problem in permutation space.

The mathematical models of combinatorial optimization problem (COP) and numerical methods of solving such problems are the objects of the research. The purpose of dissertation work is a development and validation of new mathematical models and metaheuristics algorithms for solving optimization problem in permutation space, their practical realization and approbation in applied areas. In the process of the research the methods of mathematical modeling, theory of choice and decision-making, probability theory, methods of statistical treatment of information were used. Scientific novelty: a new probabilistic search pattern in neighborhood for stochastic local search algorithms is proposed, new computing circuits of accelerated probabilistic modeling method (G2-algorithm) and variable neighborhood local search method (VNSG-algorithm) are developed, for G2-algorithm rate of convergence estimation is theoretically proved; to solve COP in permutation space new metaheuristics algorithms based on H-method, G2- and VNSG-algorithms are developed; new metaheuristic model-oriented methods for solving COP - multi-agent H-method are proposed; mathematical model for join order problem and set of approximate algorithms are developed; efficiency of proposed algorithms for solved one class of allocation problem is analyzed. Degree of introduction: developed models and methods were used at designed computer-aided system "State Budget" for Ministry of Finance, integrated control system of the enterprise for agroindustrial holding "Landgut-Ukraine", and at application of automated system "Express-UZM" on the Ukrainian Railways. Application domain: solving optimization problems in arbitrary locally finite spaces, designing complex automated system.