메뉴 건너뛰기




Volumn 157, Issue 1, 2016, Pages 47-67

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

Author keywords

Decomposition algorithms; Lower bounding; Stochastic mixed integer programming

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; STOCHASTIC SYSTEMS;

EID: 84961989546     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-016-1000-z     Document Type: Article
Times cited : (148)

References (42)
  • 1
    • 21144438339 scopus 로고    scopus 로고
    • A finite branch and bound algorithm for two-stage stochastic integer programs
    • Ahmed, S., Tawarmalani, M., Sahinidis, N.V.: A finite branch and bound algorithm for two-stage stochastic integer programs. Math. Program. Ser. A 100(2), 355–377 (2004)
    • (2004) Math. Program. Ser. A , vol.100 , Issue.2 , pp. 355-377
    • Ahmed, S.1    Tawarmalani, M.2    Sahinidis, N.V.3
  • 2
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction method of multipliers
    • Boyd, S., Parihk, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3, 1–22 (2011)
    • (2011) Found Trends Mach Learn , vol.3 , pp. 1-22
    • Boyd, S.1    Parihk, N.2    Chu, E.3    Peleato, B.4    Eckstein, J.5
  • 3
    • 0032674969 scopus 로고    scopus 로고
    • Dual decomposition in stochastic integer programming
    • Carøe, C.C., Schultz, R.: Dual decomposition in stochastic integer programming. Oper. Res. Lett. 24(1), 37–45 (1999)
    • (1999) Oper. Res. Lett. , vol.24 , Issue.1 , pp. 37-45
    • Carøe, C.C.1    Schultz, R.2
  • 4
    • 33747623533 scopus 로고    scopus 로고
    • A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem
    • Carrión, M., Arroyo, J.M.: A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans. Power Syst. 21(3), 1371–1378 (2006)
    • (2006) IEEE Trans. Power Syst. , vol.21 , Issue.3 , pp. 1371-1378
    • Carrión, M.1    Arroyo, J.M.2
  • 6
    • 0032024334 scopus 로고    scopus 로고
    • Stochastic network interdiction
    • Cormican, K.J., Morton, D.P., Wood, R.K.: Stochastic network interdiction. Oper. Res. 46(2), 184–197 (1998)
    • (1998) Oper. Res. , vol.46 , Issue.2 , pp. 184-197
    • Cormican, K.J.1    Morton, D.P.2    Wood, R.K.3
  • 7
    • 84884698472 scopus 로고    scopus 로고
    • Scenario grouping in a progressive hedging-based meta-heuristics for stochastic network design
    • Crainic, T., Hewitt, M., Rei, W.: Scenario grouping in a progressive hedging-based meta-heuristics for stochastic network design. Comput. Oper. Res. 43, 90–99 (2014)
    • (2014) Comput. Oper. Res. , vol.43 , pp. 90-99
    • Crainic, T.1    Hewitt, M.2    Rei, W.3
  • 8
    • 0001391104 scopus 로고
    • Decomposition principle for linear programs
    • Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8(1), 101–111 (1960)
    • (1960) Oper. Res. , vol.8 , Issue.1 , pp. 101-111
    • Dantzig, G.B.1    Wolfe, P.2
  • 9
    • 84856271407 scopus 로고    scopus 로고
    • Stochastic optimization of electricity portfolios: Scenario tree modeling and risk management
    • Rebennack S, Pardalos PM, Pereira MVF, Iliadis NA, (eds), Springer, Berlin
    • Eichhorn, A., Heitsch, H., Römisch, W.: Stochastic optimization of electricity portfolios: Scenario tree modeling and risk management. In: Rebennack, S., Pardalos, P.M., Pereira, M.V.F., Iliadis, N.A. (eds.) Handbook of Power Systems II, Energy Systems, pp. 405–432. Springer, Berlin (2010). doi:10.1007/978-3-642-12686-4_15
    • (2010) Handbook of Power Systems II, Energy Systems , pp. 405-432
    • Eichhorn, A.1    Heitsch, H.2    Römisch, W.3
  • 11
    • 84866173589 scopus 로고    scopus 로고
    • Scenario cluster decomposition of the lagrangian dual in stochastic mixed 0–1 optimization
    • Escudero, L., Garn, A., Prez, G., Unzueta, A.: Scenario cluster decomposition of the lagrangian dual in stochastic mixed 0–1 optimization. Comput. Oper. Res. 40, 362–377 (2013)
    • (2013) Comput. Oper. Res. , vol.40 , pp. 362-377
    • Escudero, L.1    Garn, A.2    Prez, G.3    Unzueta, A.4
  • 12
    • 0023451776 scopus 로고
    • Lagrangean decomposition: a model yielding stronger lagrangean bounds
    • Guignard, M., Kim, S.: Lagrangean decomposition: a model yielding stronger lagrangean bounds. Math. Program. 39(2), 215–228 (1987)
    • (1987) Math. Program. , vol.39 , Issue.2 , pp. 215-228
    • Guignard, M.1    Kim, S.2
  • 13
    • 84928571408 scopus 로고    scopus 로고
    • Integration of progressive hedging and dual decomposition in stochastic integer programs
    • Guo, G., Hackebeil, G., Ryan, S., Watson, J., Woodruff, D.: Integration of progressive hedging and dual decomposition in stochastic integer programs. Oper. Res. Lett. 43, 311–316 (2015)
    • (2015) Oper. Res. Lett. , vol.43 , pp. 311-316
    • Guo, G.1    Hackebeil, G.2    Ryan, S.3    Watson, J.4    Woodruff, D.5
  • 14
    • 84864524056 scopus 로고    scopus 로고
    • Pyomo: Modeling and solving mathematical programs in Python
    • Hart, W., Watson, J., Woodruff, D.: Pyomo: Modeling and solving mathematical programs in Python. Math. Program. Comput. 3(3), 219–260 (2011)
    • (2011) Math. Program. Comput , vol.3 , Issue.3 , pp. 219-260
    • Hart, W.1    Watson, J.2    Woodruff, D.3
  • 15
    • 18744366655 scopus 로고    scopus 로고
    • A decomposition algorithm applied to planning the interdiction of stochastic networks
    • Held, H., Hemmecke, R., Woodruff, D.L.: A decomposition algorithm applied to planning the interdiction of stochastic networks. Naval Res. Logist. (NRL) 52(4), 321–328 (2005)
    • (2005) Naval Res. Logist. (NRL) , vol.52 , Issue.4 , pp. 321-328
    • Held, H.1    Hemmecke, R.2    Woodruff, D.L.3
  • 17
    • 55349100212 scopus 로고    scopus 로고
    • Reformulation and sampling to solve a stochastic network interdiction problem
    • Janjarassuk, U., Linderoth, J.: Reformulation and sampling to solve a stochastic network interdiction problem. Networks 52(3), 120–132 (2008)
    • (2008) Networks , vol.52 , Issue.3 , pp. 120-132
    • Janjarassuk, U.1    Linderoth, J.2
  • 18
    • 34248677663 scopus 로고    scopus 로고
    • Evaluation of scenario-generation methods for stochastic programming
    • Kaut, M., Wallace, S.: Evaluation of scenario-generation methods for stochastic programming. Pac. J. Optim. 3(2), 257–271 (2007)
    • (2007) Pac. J. Optim. , vol.3 , Issue.2 , pp. 257-271
    • Kaut, M.1    Wallace, S.2
  • 19
    • 0030235440 scopus 로고    scopus 로고
    • Progressive hedging and tabu search applied to mixed integer (0, 1) multistage stochastic programming
    • Løkketangen, A., Woodruff, D.L.: Progressive hedging and tabu search applied to mixed integer (0, 1) multistage stochastic programming. J. Heuristics 2, 111–128 (1996)
    • (1996) J. Heuristics , vol.2 , pp. 111-128
    • Løkketangen, A.1    Woodruff, D.L.2
  • 20
    • 84874929547 scopus 로고    scopus 로고
    • On parallelizing dual decomposition in stochastic integer programming
    • Lubin, M., Martin, K., Petra, C., Sandıkçı, B.: On parallelizing dual decomposition in stochastic integer programming. Oper. Res. Lett. 41(3), 252–258 (2013)
    • (2013) Oper. Res. Lett. , vol.41 , Issue.3 , pp. 252-258
    • Lubin, M.1    Martin, K.2    Petra, C.3    Sandıkçı, B.4
  • 21
    • 3142535226 scopus 로고    scopus 로고
    • A branch-and-price algorithm for multistage stochastic integer programming with application to stochastic batch-sizing problems
    • Lulli, G., Sen, S.: A branch-and-price algorithm for multistage stochastic integer programming with application to stochastic batch-sizing problems. Manag. Sci. 50(6), 786–796 (2004)
    • (2004) Manag. Sci. , vol.50 , Issue.6 , pp. 786-796
    • Lulli, G.1    Sen, S.2
  • 23
    • 34250417328 scopus 로고
    • On the existence of optimal solutions to integer and mixed-integer programming problems
    • Meyer, R.R.: On the existence of optimal solutions to integer and mixed-integer programming problems. Math. Program. 7(1), 223–235 (1974)
    • (1974) Math. Program. , vol.7 , Issue.1 , pp. 223-235
    • Meyer, R.R.1
  • 24
    • 84886085924 scopus 로고    scopus 로고
    • Tight and compact MILP formulation for the thermal unit commitment problem
    • Morales-Espana, G., Latorre, J.M., Ramos, A.: Tight and compact MILP formulation for the thermal unit commitment problem. IEEE Trans. Power Syst. 21, 4897–4908 (2013)
    • (2013) IEEE Trans. Power Syst. , vol.21 , pp. 4897-4908
    • Morales-Espana, G.1    Latorre, J.M.2    Ramos, A.3
  • 25
    • 0006115292 scopus 로고
    • Applying the progressive hedging algorithm to stochastic generalized networks
    • Mulvey, J.M., Vladimirou, H.: Applying the progressive hedging algorithm to stochastic generalized networks. Ann. Oper. Res. 31, 399–424 (1991)
    • (1991) Ann. Oper. Res. , vol.31 , pp. 399-424
    • Mulvey, J.M.1    Vladimirou, H.2
  • 26
    • 84986946902 scopus 로고
    • Solving multistage stochastic networks: an appplication of scenario aggregation
    • Mulvey, J.M., Vladimirou, H.: Solving multistage stochastic networks: an appplication of scenario aggregation. Networks 21, 619–643 (1991)
    • (1991) Networks , vol.21 , pp. 619-643
    • Mulvey, J.M.1    Vladimirou, H.2
  • 28
    • 25444471863 scopus 로고    scopus 로고
    • The million-variable march for stochastic combinatorial optimization
    • Ntaimo, L., Sen, S.: The million-variable march for stochastic combinatorial optimization. J. Glob. Optim. 32, 385–400 (2005)
    • (2005) J. Glob. Optim. , vol.32 , pp. 385-400
    • Ntaimo, L.1    Sen, S.2
  • 29
    • 84880066582 scopus 로고    scopus 로고
    • Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network
    • Papavasiliou, A., Oren, S.S.: Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network. Oper. Res. 61(3), 578–592 (2013)
    • (2013) Oper. Res. , vol.61 , Issue.3 , pp. 578-592
    • Papavasiliou, A.1    Oren, S.S.2
  • 31
    • 0000514655 scopus 로고    scopus 로고
    • Scenarios and policy aggregation in optimization under uncertainty
    • Rockafellar, R.T., Wets, R.J.B.: Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16(1), 119–147 (2004)
    • (2004) Math. Oper. Res. , vol.16 , Issue.1 , pp. 119-147
    • Rockafellar, R.T.1    Wets, R.J.B.2
  • 34
    • 13544260501 scopus 로고    scopus 로고
    • A stochastic programming approach for supply chain network design under uncertainty
    • Santoso, T., Ahmed, S., Goetschalckx, M., Shapiro, A.: A stochastic programming approach for supply chain network design under uncertainty. Eur. J. Oper. Res. 167(1), 96–115 (2005)
    • (2005) Eur. J. Oper. Res. , vol.167 , Issue.1 , pp. 96-115
    • Santoso, T.1    Ahmed, S.2    Goetschalckx, M.3    Shapiro, A.4
  • 36
    • 34748842567 scopus 로고    scopus 로고
    • Dynamic testing of wholesale power market designs: an open-source agent-based framework
    • Sun, J., Tesfatsion, L.: Dynamic testing of wholesale power market designs: an open-source agent-based framework. Comput. Econ. 30(3), 291–327 (2007)
    • (2007) Comput. Econ. , vol.30 , Issue.3 , pp. 291-327
    • Sun, J.1    Tesfatsion, L.2
  • 37
    • 0030215880 scopus 로고    scopus 로고
    • A stochastic model for the unit commitment problem
    • Takriti, S., Birge, J.R., Long, E.: A stochastic model for the unit commitment problem. IEEE Trans. Power Syst. 11(3), 1497–1508 (1996)
    • (1996) IEEE Trans. Power Syst. , vol.11 , Issue.3 , pp. 1497-1508
    • Takriti, S.1    Birge, J.R.2    Long, E.3
  • 38
    • 84964690141 scopus 로고    scopus 로고
    • van der Vlerk, M.H.: Stochastic integer programming bibliography. (1996–2007)
    • van der Vlerk, M.H.: Stochastic integer programming bibliography. http://www.eco.rug.nl/mally/biblio/sip.html (1996–2007)
  • 39
    • 84864520668 scopus 로고    scopus 로고
    • PySP: Modeling and solving stochastic programs in Python
    • Watson, J., Woodruff, D., Hart, W.: PySP: Modeling and solving stochastic programs in Python. Math. Program. Comput. 4(2), 109–149 (2012)
    • (2012) Math. Program. Comput , vol.4 , Issue.2 , pp. 109-149
    • Watson, J.1    Woodruff, D.2    Hart, W.3
  • 40
    • 80053098461 scopus 로고    scopus 로고
    • Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems
    • Watson, J.P., Woodruff, D.L.: Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Comput. Manag. Sci. 8(4), 355–370 (2011)
    • (2011) Comput. Manag. Sci. , vol.8 , Issue.4 , pp. 355-370
    • Watson, J.P.1    Woodruff, D.L.2
  • 42
    • 0008044781 scopus 로고
    • The aggregation principle in scenario analysis and stochastic optimization
    • Wallace SW, (ed), Springer, Berlin
    • Wets, R.J.B.: The aggregation principle in scenario analysis and stochastic optimization. In: Wallace, S.W. (ed.) Algorithms and Model Formulations in Mathematical Programming, pp. 91–113. Springer, Berlin (1989)
    • (1989) Algorithms and Model Formulations in Mathematical Programming , pp. 91-113
    • Wets, R.J.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.