Partition-based decomposition algorithms for two-stage Stochastic integer programs with continuous recourse

In this paper, we propose partition-based decomposition algorithms for solving two-stage stochastic integer program with continuous recourse. The partition-based decomposition method enhance the classical decomposition methods (such as Benders decomposition) by utilizing the inexact cuts (coarse cuts) induced by a scenario partition. Coarse cut generation can be much less expensive than the standard Benders cuts, when the partition size is relatively small compared to the total number of scenarios. We conduct an extensive computational study to illustrate the advantage of the proposed partition-based decomposition algorithms compared with the state-of-the-art approaches.

[1]  Gilbert Laporte,et al.  Benders Decomposition for Large-Scale Uncapacitated Hub Location , 2011, Oper. Res..

[2]  Yongjia Song,et al.  Adaptive Partition-Based Level Decomposition Methods for Solving Two-Stage Stochastic Programs with Fixed Recourse , 2018, INFORMS J. Comput..

[3]  James R. Luedtke,et al.  An Adaptive Partition-Based Approach for Solving Two-Stage Stochastic Programs with Fixed Recourse , 2015, SIAM J. Optim..

[4]  Víctor M. Albornoz,et al.  A two‐stage stochastic integer programming model for a thermal power system expansion , 2004 .

[5]  Yurii Nesterov,et al.  New variants of bundle methods , 1995, Math. Program..

[6]  Claudia A. Sagastizábal,et al.  Level bundle methods for oracles with on-demand accuracy , 2014, Optim. Methods Softw..

[7]  Suvrajeet Sen Subgradient decomposition and differentiability of the recourse function of a two stage stochastic linear program , 1993, Oper. Res. Lett..

[8]  Sanjeeb Dash,et al.  Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse , 2017, INFORMS J. Comput..

[9]  A. Ruszczynski,et al.  Accelerating the regularized decomposition method for two stage stochastic linear problems , 1997 .

[10]  Alexander Shapiro,et al.  Lectures on Stochastic Programming: Modeling and Theory , 2009 .

[11]  François V. Louveaux,et al.  Discrete stochastic location models , 1986 .

[12]  Jacek Gondzio,et al.  Building and Solving Large-Scale Stochastic Programs on an Affordable Distributed Computing System , 2000, Ann. Oper. Res..

[13]  Leena Suhl,et al.  Applying oracles of on-demand accuracy in two-stage stochastic programming - A computational study , 2014, Eur. J. Oper. Res..

[14]  Rafael Palacios,et al.  Analysis of stochastic problem decomposition algorithms in computational grids , 2009, Ann. Oper. Res..

[15]  Eduardo Moreno,et al.  A primal-dual aggregation algorithm for minimizing conditional value-at-risk in linear programs , 2014, Comput. Optim. Appl..

[16]  Alexander Shapiro,et al.  The empirical behavior of sampling methods for stochastic programming , 2006, Ann. Oper. Res..

[17]  R. Wets,et al.  L-SHAPED LINEAR PROGRAMS WITH APPLICATIONS TO OPTIMAL CONTROL AND STOCHASTIC PROGRAMMING. , 1969 .

[18]  Daniel Bienstock,et al.  Solving LP Relaxations of Large-Scale Precedence Constrained Problems , 2010, IPCO.

[19]  Gaël Varoquaux,et al.  The NumPy Array: A Structure for Efficient Numerical Computation , 2011, Computing in Science & Engineering.

[20]  Gautam Mitra,et al.  A computational study of a solver system for processing two-stage stochastic LPs with enhanced Benders decomposition , 2012, Math. Program. Comput..

[21]  Sanjay Mehrotra,et al.  A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management , 2015, Oper. Res..

[22]  J. F. Benders Partitioning procedures for solving mixed-variables programming problems , 1962 .

[23]  Julia L. Higle,et al.  Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse , 1991, Math. Oper. Res..

[24]  Susana Scheimberg,et al.  Inexact Bundle Methods for Two-Stage Stochastic Programming , 2011, SIAM J. Optim..

[25]  Marianthi G. Ierapetritou,et al.  Accelerating Benders method using covering cut bundle generation , 2010, Int. Trans. Oper. Res..

[26]  James R. Luedtke,et al.  Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty , 2017, Manag. Sci..

[27]  Achim Koberstein,et al.  Dynamic sequencing and cut consolidation for the parallel hybrid-cut nested L-shaped method , 2013, Eur. J. Oper. Res..

[28]  Jean Charles Gilbert,et al.  Numerical Optimization: Theoretical and Practical Aspects , 2003 .

[29]  Andrzej Ruszczynski,et al.  A regularized decomposition method for minimizing a sum of polyhedral functions , 1986, Math. Program..

[30]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[31]  Lewis Ntaimo,et al.  Adaptive multicut aggregation for two-stage stochastic linear programs with recourse , 2010, Eur. J. Oper. Res..

[32]  Hanif D. Sherali,et al.  Two-stage workforce planning under demand fluctuations and uncertainty , 2009, J. Oper. Res. Soc..