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Assignment problems in logistics
Janez Povh, 2008, original scientific article

Abstract: We consider two classical problems from location theory which may serve as theoretical models for several logistic problems where one wants to assign elements of a set A to elements of a set B such that some linear or quadratic function attains its minimum. It turns out that linear objective function yields a linear assignment problem, which can be solved easily by several primal-dual methods like Hungarian method, Shortest augmenting path method etc. On the other hand, taking quadratic objective function into account makes the problem much harder. The resulting quadratic assignment problem is a very useful model but also very tough problem from theoretical and practical point of view. We list several well-known applications of these models and also the most effective methods to solve the problem. However, it is still a challenging task to solve this problem to optimality when the size of underlying sets A and B is greater than 25 and currently impossible task when the size is greater than 35.
Keywords: quadratic assignment problem, linear assignment problem, branch and bound algorithm, heuristics
Published: 05.06.2012; Views: 936; Downloads: 60
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Copositive and semidefinite relaxations of the quadratic assignment problem
Janez Povh, Franz Rendl, 2009, original scientific article

Abstract: Semidefinite relaxations of the quadratic assignment problem (QAP) have recently turned out to provide good approximations to the optimal value of QAP. We take a systematic look at various conic relaxations of QAP. We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it is hard to optimize over this cone, we also look at tractable approximations and compare with several relaxations from the literature. We show that several of the well-studied models are in fact equivalent. It is still a challenging task to solve the strongest of these models to reasonable accuracy on instances of moderate size.
Keywords: matematično programiranje, problem kvadratičnega prirejanja, kopozitivno programiranje, semidefinitna poenostavitev, quadratic assignment problem, copositive programming, semidefinite relaxations, lift-and-project relaxations
Published: 10.07.2015; Views: 499; Downloads: 63
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Community structure and the evolution of interdisciplinarity in Slovenia's scientific collaboration network
Borut Lužar, Zoran Levnajić, Janez Povh, Matjaž Perc, 2014, original scientific article

Abstract: Interaction among the scientific disciplines is of vital importance in modern science. Focusing on the case of Slovenia, we study the dynamics of interdisciplinary sciences from 1960 to 2010. Our approach relies on quantifying the interdisciplinarity of research communities detected in the coauthorship network of Slovenian scientists over time. Examining the evolution of the community structure, we find that the frequency of interdisciplinary research is only proportional with the overall growth of the network. Although marginal improvements in favor of interdisciplinarity are inferable during the 70s and 80s, the overall trends during the past 20 years are constant and indicative of stalemate. We conclude that the flow of knowledge between different fields of research in Slovenia is in need of further stimulation.
Keywords: community structure, interdisciplinarity, scientific collaboration, research funding, Slovenia
Published: 19.06.2017; Views: 319; Downloads: 227
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Paralelni razveji in omeji algoritem BiqMac Solver
Alen Vegi Kalamar, 2018, master's thesis

Abstract: Problem maksimalnega prereza je primer NP težkega problema. To pomeni, da ne poznamo učinkovitega polinomskega algoritma za reševanje problema za poljuben graf in domnevamo, da tudi ne obstaja. Kljub temu obstajajo pristopi, kako reševati problem do optimalnosti. V kolikor poznamo učinkovite hevristike in poenostavitve problema, je primeren pristop algoritem razveji in omeji. Rendl, Rinaldi in Wiegele so z uporabo različnih poenostavitev, dualne teorije, aproksimacijskih algoritmov in hevristik razvili učinkovit algoritem razveji in omeji z imenom BiqMac Solver, ki optimalno reši problem maksimalnega prereza tudi za večje grafe. Zaradi strukture je algoritem primeren, da ga implementiramo za paralelno izvajanje. Namen magistrskega dela je predstavitev algoritma BiqMac in njegova paralelna implementacija.
Keywords: maksimalen prerez grafa, semidefinitno programiranje, hevristike, algoritem razveji in omeji, paralelno računanje
Published: 04.10.2018; Views: 333; Downloads: 60
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