Mathematical Modelas and Optimization Methods on Large-Scale Systems

This project will consider mathematical modeling and then developing methods to solve following real world large-scale optimization problems: mixed-integer linear (MIP) and nonlinear programming (MINLP), discrete and continuous location, hub location, optimization on networks and graphs, optimization on telecommunication and optical networks, job assignment, data clustering, data mining etc. Since large-scale optimization models cannot be solved exactly in the reasonable time, we mostly deal with heuristic approach. We will focus our research efforts in the development of the following metaheuristics (or framework for building heuristics): Variable Neighborhood Search (VNS), Genetic Algorithms, Tabu Search, Memetic Algorithms, Bee Colony Algorithms, etc. A parallelization of the developed methods is also being planned in order to be executed on multiprocessor computers. The so-called matheuristics (model-based heuristics) has attracted many researches recently. Following this trend, we plan to combine VNS with other mathematical programming commercial solvers. Besides solving MIP and MINLP, we also plan to develop efficient methods for getting initial solution. The second group of researches is related to the examination of mechanical properties of materials. Stochastic nature of rate-strengthening and brittle rupture is to be addressed statistically by using a large number of computer simulations.