Abstract: Many contemporary problems in biomedicine, biophysics, and bioinformatics, as well as in numerous other fields of engineering and social sciences, can be reduced to mathematical modeling based on graph theory. Mathematical modeling is generally interpreted as the act of representing a real-world system through mathematical formulations and equations, aiming to develop and implement a model that facilitates subsequent analysis, design, and system optimization. The aim of this paper is to demonstrate, through an illustrative account of the synergy between graph theory and peptide analysis, how combinatorial optimization enables the resolution of complex biophysical problems in a computationally elegant and efficient manner. Due to their importance in analyzing and predicting peptide properties, the proposed model focuses on constructing a smaller yet representative subset of amino acid scales. To this end, a Variable Neighborhood Search (VNS) approach is employed – a contemporary metaheuristic in the field of combinatorial optimization.

Keywords: graph theory, dominating set, amino-acid scales, combinatorial optimization, variable neighborhood search

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