Our research focuses on designing and analyzing algorithms and software systems that are capable of adapting themselves to the nature of the problems in hand as well as to the specific of the computational environment and the user’s requirements. The main goal of this adaptation is to minimize the computational cost and/or to speed up designing and implementing software projects. Our methodology is drawn from classical mathematics, operational research, as well as the theory of deterministic and stochastic algorithms combined with artificial intelligence tools.
We intensely utilize analogy between various virtual and real-life processes. We perform effective simulations of continuous technological processes using graph-grammar, linguistic mechanisms. We use social metaphors to decrease the computational cost of stochastic algorithms dedicated to oil industry. We apply multi-agent systems and solutions borrowed from the potential field theory for scheduling in distributed environments.
Nowadays, our activity is concentrated on:
- hybrid algorithms (stochastic search combined with a gradient steepest descent ones) solving ill posed inverse problems in oil industry,
- exact and iterative concurrent solvers for difficult direct BV and IBV problems of acoustics and electromagnetic wave propagation in human body,
- low complexity, concurrent, graph-grammar driven exact solvers,
- exact solvers with linear and logarithmic complexity for h,p-adaptive finite element method,
- hierarchic genetic and memetic strategies in global optimization,
- low complexity projection algorithms for tomographic data.