Abstract: The paper introduces a new taxonomy of ill-posed parametric inverse problems, formulated as global optimization ones. It systematizes irremediable problems, which appear quite often in real life but cannot be solved using the regularization method. The paper shows also a new way of solving irremediable inverse problems by a complex memetic approach including genetic computation with adoptive accuracy, random sample clustering and a sophisticated local approximation of misfit plateau region. Finally, we use a benchmark function featuring cross-shaped plateau to discuss some factors that influence the quality of plateau shape approximation.

Abstract: Memetic agent-based paradigm, which combines evolutionary computation and local search techniques in one of promising meta-heuristics for solving large and hard discrete problem such as Low Autocorrellation Binary Sequence (LABS) or optimal Golomb-ruler (OGR). In the paper as a follow-up of the previous research, a short concept of hybrid agent-based evolutionary systems platform, which spreads computations among CPU and GPU is shortly introduced. The main part of the paper presents an efficient parallel GPU implementation of LABS local optimization strategy. As a means for comparison, speed-up between GPU implementation and CPU sequential and parallel versions are shown. This constitutes a promising step toward building hybrid platform that combines evolutionary meta-heuristics with highly efficient local optimization of chosen discrete problems.

Abstract: We present a discrete entropy inequality that exhibits versatile uses in convection dominated problems. Much like the thermodynamic entropy inequality, the sign of this so-called discrete entropy production allows us to determine unphysical regions in the numerical solution without any a-priori knowledge of the solution. Further, the sign of the discrete production also functions as an excellent indicator for mesh adaptation in convection-diffusion and other singular perturbation problems. We also show preliminary results for how the operator can be used to derive robust schemes for convection dominated problems. All the above applications i.e. (a) Detecting unphysical numerical behavior, (b) mesh adaptation and (c) stabilization, are robust in that they are achieved without any ad-hoc, user introduced, parameters making the applications robust. We show a range of numerical results that exhibit the effcacy of the operator.

Abstract: This paper presents an idea of a multi-agent decision support system. Agent-based technology allows for decentralized problem solving and creating complex decision support systems, mixing various processing techniques, such as simulation, reasoning and machine learning and allows for distributed knowledge. Our main contribution is an agent-based architecture for decision support systems which is an agent-based implementation of a labeled deductive system. Such approach allows to decompose an inference algorithm into separate modules and distribute knowledge base into parts. The system is tested on a domain of material choice support for casting.