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Aas B, Gribkovskaia I, Halskau Ø, Shlopak A. Routing of supply vessels to petroleum installations. INTERNATIONAL JOURNAL OF PHYSICAL DISTRIBUTION & LOGISTICS MANAGEMENT 2007. [DOI: 10.1108/09600030710734866] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Calculating exact ground states of spin glasses: A polyhedral approach. ACTA ACUST UNITED AC 2006. [DOI: 10.1007/bfb0057526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Mester DI, Ronin YI, Korostishevsky MA, Pikus VL, Glazman AE, Korol AB. Multilocus consensus genetic maps (MCGM): formulation, algorithms, and results. Comput Biol Chem 2005; 30:12-20. [PMID: 16301000 DOI: 10.1016/j.compbiolchem.2005.09.007] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2005] [Revised: 09/30/2005] [Accepted: 09/30/2005] [Indexed: 11/18/2022]
Abstract
In process of creating genetic maps different labs/research groups obtain overlapping parts of the map. Merging these parts into one integrative map is based on looking for maximum shared marker orders among the maps. Really, not all shared markers of such maps have consensus order that obstructs building of the integrative maps. In this paper we propose a new approach to build verified multilocus consensus genetic maps in which shared markers always are integrated in stable consensus order. The approach is based on combined analysis of initial mapping data rather than manipulating with previously constructed maps. We show that more effective and reliable solutions may be obtained based on "synchronized ordering" facilitated by cycles of "re-sampling-->ordering-->removing unstable markers". The proposed formulation of consensus genetic mapping can be considered as a version of traveling salesperson problem (TSP) that we refer to as synchronized-TSP. From the viewpoint of optimization, synchronized-TSP belongs to discrete constrained optimization problems. Earlier we developed new powerful and fast guided evolution strategy algorithms for some types of discrete constrained optimization. These algorithms were used here as a basis for solving more challenging problems of consensual marker ordering.
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Affiliation(s)
- D I Mester
- Institute of Evolution, University of Haifa, Haifa 31905, Israel
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Jensson P, Kristinsdottir BP, Gunnarsson HP. Optimal sequencing of tasks in an aluminium smelter casthouse. COMPUT IND 2005. [DOI: 10.1016/j.compind.2004.06.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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LAPORTE GILBERT, SALAZAR-GONZÁLEZ JUANJOSÉ, SEMET FRÉDÉRIC. Exact algorithms for the job sequencing and tool switching problem. ACTA ACUST UNITED AC 2004. [DOI: 10.1080/07408170490257871] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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ASEF-VAZIRI ARDAVAN, LAPORTE GILBERT, SRISKANDARAJAH CHELLIAH. The block layout shortest loop design problem. ACTA ACUST UNITED AC 2000. [DOI: 10.1080/07408170008967430] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Agarwala R, Applegate DL, Maglott D, Schuler GD, Schäffer AA. A fast and scalable radiation hybrid map construction and integration strategy. Genome Res 2000; 10:350-64. [PMID: 10720576 PMCID: PMC311427 DOI: 10.1101/gr.10.3.350] [Citation(s) in RCA: 124] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
This paper describes a fast and scalable strategy for constructing a radiation hybrid (RH) map from data on different RH panels. The maps on each panel are then integrated to produce a single RH map for the genome. Recurring problems in using maps from several sources are that the maps use different markers, the maps do not place the overlapping markers in same order, and the objective functions for map quality are incomparable. We use methods from combinatorial optimization to develop a strategy that addresses these issues. We show that by the standard objective functions of obligate chromosome breaks and maximum likelihood, software for the traveling salesman problem produces RH maps with better quality much more quickly than using software specifically tailored for RH mapping. We use known algorithms for the longest common subsequence problem as part of our map integration strategy. We demonstrate our methods by reconstructing and integrating maps for markers typed on the Genebridge 4 (GB4) and the Stanford G3 panels publicly available from the RH database. We compare map quality of our integrated map with published maps for GB4 panel and G3 panel by considering whether markers occur in the same order on a map and in DNA sequence contigs submitted to GenBank. We find that all of the maps are inconsistent with the sequence data for at least 50% of the contigs, but our integrated maps are more consistent. The map integration strategy not only scales to multiple RH maps but also to any maps that have comparable criteria for measuring map quality. Our software improves on current technology for doing RH mapping in areas of computation time and algorithms for considering a large number of markers for mapping. The essential impediments to producing dense high-quality RH maps are data quality and panel size, not computation.
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Affiliation(s)
- R Agarwala
- National Center for Biotechnology Information (NCBI), National Institutes of Health (NIH), Bethesda, Maryland 20894, USA
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Desrosiers J, Dumas Y, Solomon MM, Soumis F. Chapter 2 Time constrained routing and scheduling. HANDBOOKS IN OPERATIONS RESEARCH AND MANAGEMENT SCIENCE 1995. [DOI: 10.1016/s0927-0507(05)80106-9] [Citation(s) in RCA: 269] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Jünger M, Reinelt G, Rinaldi G. Chapter 4 The traveling salesman problem. HANDBOOKS IN OPERATIONS RESEARCH AND MANAGEMENT SCIENCE 1995. [DOI: 10.1016/s0927-0507(05)80121-5] [Citation(s) in RCA: 105] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Pekny J, Miller D, Kudva G. An exact algorithm for resource constrained sequencing with application to production scheduling under an aggregate deadline. Comput Chem Eng 1993. [DOI: 10.1016/0098-1354(93)80055-r] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Edan Y, Flash T, Peiper U, Shmulevich I, Sarig Y. Near-minimum-time task planning for fruit-picking robots. ACTA ACUST UNITED AC 1991. [DOI: 10.1109/70.68069] [Citation(s) in RCA: 61] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Nemhauser GL, Wolsey LA. Chapter VI Integer programming. ACTA ACUST UNITED AC 1989. [DOI: 10.1016/s0927-0507(89)01007-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
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Nemhauser G, Wolsey L. Maximizing Submodular Set Functions: Formulations and Analysis of Algorithms. NORTH-HOLLAND MATHEMATICS STUDIES 1981. [DOI: 10.1016/s0304-0208(08)73471-6] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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Grötschel M. On the symmetric travelling salesman problem: Solution of a 120-city problem. MATHEMATICAL PROGRAMMING STUDIES 1980. [DOI: 10.1007/bfb0120887] [Citation(s) in RCA: 64] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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On the symmetric travelling salesman problem: A computational study. MATHEMATICAL PROGRAMMING STUDIES 1980. [DOI: 10.1007/bfb0120888] [Citation(s) in RCA: 83] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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Burkard RE. Travelling Salesman and Assignment Problems: A Survey. DISCRETE OPTIMIZATION I, PROCEEDINGS OF THE ADVANCED RESEARCH INSTITUTE ON DISCRETE OPTIMIZATION AND SYSTEMS APPLICATIONS OF THE SYSTEMS SCIENCE PANEL OF NATO AND OF THE DISCRETE OPTIMIZATION SYMPOSIUM 1979. [DOI: 10.1016/s0167-5060(08)70827-6] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Grötschel M, Padberg MW. On the Symmetric Travelling Salesman Problem: Theory and Computation. ACTA ACUST UNITED AC 1978. [DOI: 10.1007/978-3-642-95322-4_12] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2023]
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Computational Performance of Three Subtour Elimination Algorithms for Solving Asymmetric Traveling Salesman Problems. STUDIES IN INTEGER PROGRAMMING 1977. [DOI: 10.1016/s0167-5060(08)70755-6] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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Camerini PM, Fratta L, Maffioli F. On improving relaxation methods by modified gradient techniques. NONDIFFERENTIABLE OPTIMIZATION 1975. [DOI: 10.1007/bfb0120697] [Citation(s) in RCA: 179] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Zur Oberflächenstruktur des Travelling Salesman Polytopen. ACTA ACUST UNITED AC 1974. [DOI: 10.1007/978-3-642-52074-7_17] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Tillman FA, Hering RW. A study of a look-ahead procedure for solving the multiterminal delivery problem. ACTA ACUST UNITED AC 1971. [DOI: 10.1016/0041-1647(71)90023-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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