A simple greedy algorithm for a class of shuttle transportation problems
Greedy algorithms for combinatorial optimization problems are typically direct and efficient, but hard to prove optimality. The paper presents a special class of transportation problems where a supplier sends goods to a set of customers, returning to the source after each delivery. We show that thes...
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| Published in | Optimization letters Vol. 3; no. 4; pp. 491 - 497 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer-Verlag
01.09.2009
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1862-4472 1862-4480 |
| DOI | 10.1007/s11590-009-0126-9 |
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| Abstract | Greedy algorithms for combinatorial optimization problems are typically direct and efficient, but hard to prove optimality. The paper presents a special class of transportation problems where a supplier sends goods to a set of customers, returning to the source after each delivery. We show that these problems with different objective functions share a common structural property, and therefore a simple but powerful generic greedy algorithm yields optimal solutions for all of them. |
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| AbstractList | Greedy algorithms for combinatorial optimization problems are typically direct and efficient, but hard to prove optimality. The paper presents a special class of transportation problems where a supplier sends goods to a set of customers, returning to the source after each delivery. We show that these problems with different objective functions share a common structural property, and therefore a simple but powerful generic greedy algorithm yields optimal solutions for all of them. |
| Author | Xu, Chuanqing Xue, Jinyun Zheng, Yujun |
| Author_xml | – sequence: 1 givenname: Yujun surname: Zheng fullname: Zheng, Yujun email: yujun.zheng@computer.org organization: Institute of Software, Chinese Academy of Sciences – sequence: 2 givenname: Chuanqing surname: Xu fullname: Xu, Chuanqing organization: Academy of Armored Force Engineering – sequence: 3 givenname: Jinyun surname: Xue fullname: Xue, Jinyun organization: Provincial Key Lab of High-Performance Computing, Jiangxi Normal University |
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| Cites_doi | 10.1287/trsc.14.2.130 10.1007/BF01584082 10.1007/978-3-540-71549-8_6 10.1287/mnsc.4.2.191 10.1016/0377-2217(95)00050-X 10.1016/0167-6377(84)90067-1 |
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| Issue | 4 |
| Keywords | Shuttle transportation problems Greedy algorithm Combinatorial optimization |
| Language | English |
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| References | AlsuwaiyelM.H.Algorithms Design Techniques and Analysis1992SingaporeWorld Scientific Publishing BellmanB.Notes on the theory of dynamic programming transportation modelsManag. Sci.195841911950995.9061910.1287/mnsc.4.2.191 ZhengY.WangJ.XueJ.Agent based framework for emergency rescue and assistance planningLect. Notes Comput. Sci.20074430708110.1007/978-3-540-71549-8_6 EdmondsJ.Matroids and the greedy algorithmMath. Prog.1971117123610.1007/BF01584082297357 CormenT.H.LeisersonC.E.RivestR.L.SteinC.Introduction to Algorithm, vol. 22001New YorkMcGraw-Hill LuenbergerD.G.Linear and Nonlinear Programming, vol. 21984ReadingAddison-Wesley GendreauM.LaporteG.SeguinR.Stochastic vehicle routingEuro. J. Oper. Res.1996883120913.9009410.1016/0377-2217(95)00050-X PsaraftisH.N.A dynamic programming solution the single vehicle many-to-many immediate request dial-a-ride problemTrans. Sci.19801413015410.1287/trsc.14.2.130 SzwarcW.PosnerM.E.The tridiagonal transportation problemOper. Res. Lett.1984325300531.9007010.1016/0167-6377(84)90067-1748610 D.G. Luenberger (126_CR6) 1984 Y. Zheng (126_CR9) 2007; 4430 H.N. Psaraftis (126_CR7) 1980; 14 W. Szwarc (126_CR8) 1984; 3 M.H. Alsuwaiyel (126_CR1) 1992 T.H. Cormen (126_CR3) 2001 B. Bellman (126_CR2) 1958; 4 J. Edmonds (126_CR4) 1971; 1 M. Gendreau (126_CR5) 1996; 88 |
| References_xml | – reference: ZhengY.WangJ.XueJ.Agent based framework for emergency rescue and assistance planningLect. Notes Comput. Sci.20074430708110.1007/978-3-540-71549-8_6 – reference: BellmanB.Notes on the theory of dynamic programming transportation modelsManag. Sci.195841911950995.9061910.1287/mnsc.4.2.191 – reference: PsaraftisH.N.A dynamic programming solution the single vehicle many-to-many immediate request dial-a-ride problemTrans. Sci.19801413015410.1287/trsc.14.2.130 – reference: EdmondsJ.Matroids and the greedy algorithmMath. Prog.1971117123610.1007/BF01584082297357 – reference: LuenbergerD.G.Linear and Nonlinear Programming, vol. 21984ReadingAddison-Wesley – reference: SzwarcW.PosnerM.E.The tridiagonal transportation problemOper. Res. Lett.1984325300531.9007010.1016/0167-6377(84)90067-1748610 – reference: GendreauM.LaporteG.SeguinR.Stochastic vehicle routingEuro. J. Oper. Res.1996883120913.9009410.1016/0377-2217(95)00050-X – reference: CormenT.H.LeisersonC.E.RivestR.L.SteinC.Introduction to Algorithm, vol. 22001New YorkMcGraw-Hill – reference: AlsuwaiyelM.H.Algorithms Design Techniques and Analysis1992SingaporeWorld Scientific Publishing – volume: 14 start-page: 130 year: 1980 ident: 126_CR7 publication-title: Trans. Sci. doi: 10.1287/trsc.14.2.130 – volume: 1 start-page: 171 year: 1971 ident: 126_CR4 publication-title: Math. Prog. doi: 10.1007/BF01584082 – volume-title: Introduction to Algorithm, vol. 2 year: 2001 ident: 126_CR3 – volume-title: Linear and Nonlinear Programming, vol. 2 year: 1984 ident: 126_CR6 – volume: 4430 start-page: 70 year: 2007 ident: 126_CR9 publication-title: Lect. Notes Comput. Sci. doi: 10.1007/978-3-540-71549-8_6 – volume: 4 start-page: 191 year: 1958 ident: 126_CR2 publication-title: Manag. Sci. doi: 10.1287/mnsc.4.2.191 – volume-title: Algorithms Design Techniques and Analysis year: 1992 ident: 126_CR1 – volume: 88 start-page: 3 year: 1996 ident: 126_CR5 publication-title: Euro. J. Oper. Res. doi: 10.1016/0377-2217(95)00050-X – volume: 3 start-page: 25 year: 1984 ident: 126_CR8 publication-title: Oper. Res. Lett. doi: 10.1016/0167-6377(84)90067-1 |
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| SubjectTerms | Computational Intelligence Mathematics Mathematics and Statistics Numerical and Computational Physics Operations Research/Decision Theory Optimization Original Paper Simulation |
| Title | A simple greedy algorithm for a class of shuttle transportation problems |
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