Integer Optimization Heuristics

Abstract

Práca sa zameriava na celočíselné optimalizačné heuristiky, t.j. algoritmy nezávislé na riešenej úlohe, ktoré nie sú exaktné, ale často sú jedinou schodnou cestou riešenia NP taokých úloh.This thesis focuses on integer optimization heuristics, i.e. problem-independent methods which are not exact but often are the only feasible way of solving NP-hard problems. To contribute to scientific exactness in the assessment of their performance, novel time complexity measures are developed. Most importantly, quantile-based measures are presented as a preferred alternative to traditional approaches based on their theoretical groundings and promising results. Furthermore, to address hardly predictable performance on a specific problem, i.e. to improve heuristic performance on selected problems, three original heuristics using characteristics of Lévy flights, competitiveness, and the mean field theory are developed. Lastly, in order to validate the performance of the novel heuristics on practical problems, multiple objective functions are developed as well. Among others, submodel selection in generalized regression model analysis is developed and serves as the theoretical grounding for successful application in fractography and biomedicine, as demonstrated in the thesis case studies.