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A Complex Search Technique for Solving the Quadratic Assignment Problem
Ider Tseveendorj,Catherine Roucairol,Bazarragchaa Barsbold,Enkhbat Rentsen,Bertrand Le Cun,Francois Galea 한국멀티미디어학회 2009 한국멀티미디어학회 국제학술대회 Vol.2009 No.-
An algorithm recently developed by Enkhbat et al. based on continuous relaxation of the quadratic assignment problem generates suboptimal solution of good quality on average giving no sufficient enough verification on global optimality of the generated solution, whereas a branch and bound method provides a solution with verified global optimality, taking on input an upper bound close to global optimality. In this research we investigated possibility for combining these two techniques, so that firstly upper bound is obtained from the relaxed problem using a continuous global optimization, then a branch and bound procedure is taken to solve the problem completely.
An integrative model for the identification of key players of cancer networks
Amgalan, Bayarbaatar,Tseveendorj, Ider,Lee, Hyunju Elsevier 2018 Applied mathematical modelling Vol.58 No.-
<P><B>Abstract</B></P> <P>Uncovering miscoordination in a biological network is essential for the understanding of cellular malfunctions in cancer. Integrative analysis across multiple cellular levels may provide an opportunity to elucidate the miscoordination between the regulatory mechanisms in cancer cells.</P> <P>Here, we propose an integrative model for the identification of key players of the cancer-activated Multi-Type Interaction (MTI) gene network (KPOCN). To measure the functional associations between genes, using DNA copy number aberrations (CNAs) and gene expressions (GEs), we constructed three interacting weighted graphs: GEs affected by CNAs, CNAs by CNAs, and GEs by GEs. These three weighted graphs were mapped onto a single graph, in order to construct a MTI gene network by using their optimal combination. Finally, the effect of a single gene was determined by using the centrality and betweenness of node scores in the MTI network.</P> <P>We first tested KPOCN using simulated datasets, and afterward, we applied this model to the real breast cancer datasets. KPOCN was shown to identify successfully key regulators with their corresponding response variables (targets) when using the simulated data, and identified well-known breast cancer oncogenes. These results demonstrated that our model can be used for an efficient identification of key genes that affect cancer development. Source codes are available at http://gcancer.org/KPOCN.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A computational method for identification of cancer driver genes is proposed. </LI> <LI> Non-differentiable convex optimization identifies relationships between genes. </LI> <LI> Contributions of genomic data to cancer are formulated by convex maximization. </LI> <LI> Gene expression, copy number, and gene interaction are used to analyze breast cancer. </LI> </UL> </P>
A hybrid method to solve the multi-objective combinatorial auctions
CHAHRAZAD ADICHE,M EZIANE AIDER 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.1
In this paper, we present a hybrid method for solving the multiitem multi-unit Winner Determination Problem of Combinatorial Auctions in the multi-attribute (multi-objective) context. Indeed, the bids may concern several specications of the item, involving not only its price, but also its quality, the delivery conditions, the delivery deadlines, the risk of not being paid after a bid has been accepted and so on. The problem is intractable and is equivalent to a Multi-Objective Multi-Constraint Knapsack Problem, a well known NP-Hard Problem. We propose a hybrid method, based on the Multi-Objective Branchand- Bound approach and the Random Walk Tabu Search metaheuristic. The Multi-Objective Branch-and-Bound used here is referred to be the process of the principal research. We present a novel rule to automatically rank bids while taking into account the Decision Makers's (DM's) preferences on objectives that are most relevant. A fuzzy dominance relation, on the discrete set of weight vectors, is then computed and used to rank bids and select a feasible solution (a subset of accepted bids). Numerical experiments are reported on data sets available in the literature, in the case of three objective functions, three items and the number of bids varying from 10 to 50. The obtained results show the eciency of our Extended Multi-Objective Branch-and-Bound method that outperforms the existing Multi-Objective Branch-and-Bound methods both in terms of CPU time and ratio of dominated partial solutions. Furthermore, the hybrid method generates a larger number of ecient bids in reasonable time for all instances.