Abstract
A implementation of the distributed Dang and Ye’s fixed-point algorithm, which is a new alternative algorithm for integer programming, is developed in this paper. This fixed-point algorithm is derived from an increasing mapping which satisfies certain properties. A classical problem, which is called market split problem, has been solved by this distributed implementation. It is shown that this implementation is effective in numerical results. Besides, it can be used to other similar integer problems.
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References
Gary, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. WH Freeman & Co., San Francisco (1979)
Gomory, R.E.: Outline of an algorithm for integer solutions to linear programs. Bull. Am. Math. Soc. 64(5), 275–278 (1958)
Land, A.H., Doig, A.G.: An automatic method of solving discrete programming problems. Econometrica: J. Econometric Soc. 28, 497–520 (1960)
Scarf, H.E.: Neighborhood systems for production sets with indivisibilities. Econometrica: J. Econometric Soc. 54, 507–532 (1986)
Jünger, M., Liebling, T., Naddef, D., Nemhauser, G., Pulleyblank, W., Rerhard, G., Rinaldi, G., Wolsey, L.: 50 Years of Integer Programming 1958–2008. Springer, Berlin (2010)
Dang, C.: An increasing-mapping approach to integer programming based on lexicographic ordering and linear programming. In: The Ninth International Symposium on Operations Research and Its Applications, Chengdu-jiuzhaigou, China (2010)
Dang, C., Ye, Y.: A fixed point iterative approach to integer programming and its distributed computation. Fixed Point Theor. Appl. 2015(1), 1–15 (2015)
Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1998)
Message Passing Interface Forum: MPI: A message-passing interfacestandard, version 2.2 (2009). http://www.mpiforum.org/docs/mpi-2.2/mpi22-report.pdf
Cornuéjols, G., Dawande, M.: A class of hard small 01 programs. In: Integer Programming and Combinatorial Optimization, pp. 284–293 (1998)
Aardal, K., Bixby, R.E., Hurkens, C.A., Lenstra, A.K., Smeltink, J.W.: Market split and basis reduction: towards a solution of the Cornuéjols-Dawande instances. INFORMS J. Comput. 12(3), 192–202 (2000)
Wu, Z., Dang, C., Zhu, C.: Solving the market split problem using a distributed computation approach. In: IEEE International Conference on Information and Automation, Yinchuan, China, pp. 1252–1257 (2013)
Acknowledgment
The authors are very grateful to the reviewers for their valuable suggestions and comments. This work was partially supported by National Nature Science Foundation of China under grants 71471091 and 71271119, Research Foundation of USTS under grants No. XKQ201517.
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Wu, Z., Shi, Q., Yu, Y., Xia, H., Yang, H. (2016). Implementation of the Distributed Fixed-Point Algorithm and Its Application. In: Chen, J., Nakamori, Y., Yue, W., Tang, X. (eds) Knowledge and Systems Sciences. KSS 2016. Communications in Computer and Information Science, vol 660. Springer, Singapore. https://doi.org/10.1007/978-981-10-2857-1_15
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DOI: https://doi.org/10.1007/978-981-10-2857-1_15
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