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Stochastic Constraint Programming with And-Or Branch-and-Bound

Behrouz Babaki, Tias Guns, Luc de Raedt
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
Stochastic constraint programming was proposed as a way to formulate and solve such decision problems, involving arbitrary constraints over both decision and random variables.  ...  The resulting approach searches over the And-Or search tree directly, and we investigate tight bounds on the expected utility objective.  ...  Conclusion and Future Work We presented a novel stochastic constraint programming method with three distinguishing features: a novel bound that works on the And-Or search space directly; the use of (nontrivial  ... 
doi:10.24963/ijcai.2017/76 dblp:conf/ijcai/BabakiGR17 fatcat:bonaixzrmnhjbpokfidnuhokom

Page 7221 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
(A-IASA; Laxenburg); Ruszezynski, Andrzej (1-RTG4-MGI; Piscataway, NJ) A branch and bound method for stochastic global optimization. (English summary) Math. Programming 83 (1998), no. 3, Ser.  ...  For subproblems, defined in branch and bound methods, unbiased statistical upper and lower bounds are con- structed, and exploiting these bounds, it is shown that there exists a finite (but random) iteration  ... 

On Bridging the Gap Between Stochastic Integer Programming and MIP Solver Technologies

Gyana R. Parija, Shabbir Ahmed, Alan J. King
2004 INFORMS journal on computing  
Stochastic integer programs (SIP) represent a very difficult class of optimization problems arising from the presence of both uncertainty and discreteness in planning and decision problems.  ...  On the other hand, commercial software packages for solving deterministic integer programs have been around for quite a few years, and more recently, a package for solving stochastic linear programs has  ...  Ahmed's research has been supported in part by The Logistics Institute Asia-Pacific in Singapore and the National Science Foundation under Grant DMII-0099726.  ... 
doi:10.1287/ijoc.1020.0005 fatcat:msfqx5ybqrbo7cmzesr5m2tuee

Stochastic Constraint Programming [article]

Toby Walsh
2009 arXiv   pre-print
Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables, and compare with other approaches for decision  ...  We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures.  ...  We can therefore borrow from traditional constraint satisfaction and optimization powerful algorithmic techniques like branch and bound, constraint propagation and nogood recording.  ... 
arXiv:0903.1152v1 fatcat:lyq6id4uefb6lojov435u3jcnm

Page 1585 of Mathematical Reviews Vol. 49, Issue 4 [page]

1975 Mathematical Reviews  
A stochastic linear program with deterministic constraints and unknown ergodic stochastic processes as cost coeffi- cients is considered.  ...  They discuss a general scheme for branch and bound methods and explain its application to integer programming in detail.  ... 

Page 3994 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
Swaney, Branch and bound for global NLP: new bounding LP (1-35); Thomas G. W. Epperly and Ross E. Swaney, Branch and bound for global NLP: iterative LP algorithm & results (37-73); V.  ...  As noted in the preface, instructors would do well to start with Chapters 7 or 8 to give students some flavor of the nature of stochastic programming models.  ... 

A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems

Guglielmo Lulli, Suvrajeet Sen
2004 Management science  
In this paper we present a branch-and-price method to solve special structured multi-stage stochastic integer programming problems.  ...  We validate our method on two different versions of a multi-stage stochastic batch-sizing problem. One version adopts a recourse formulation, and the other is based on probabilistic constraints.  ...  The authors are grateful to Laszlo Ladányi and Ted Ralphs for the valuable suggestions and comments in the implementation of SP-COIN-BCP.  ... 
doi:10.1287/mnsc.1030.0164 fatcat:epvvyc2bjjduja5furoi4ct22a

Page 1388 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
(F-VER-PR; Versailles) Stochastic mathematical programs with equilibrium constraints.  ...  This paper is concerned with some recent advances in numerical methods for solving MILP problems. Exact methods include Lagrangian relaxation, branch and bound, and branch and cut.  ... 

Page 5104 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
or to prove LP optimality at a node of the branch-and- bound tree.  ...  We also discuss the relationship with Lagrangian duality.” 99¢:90075 90C15 90-02 Kall, P. (CH-ZRCH-OR; Ziirich) Bounds for and approximations to stochastic linear programs with recourse—tutorial.  ... 

Page 1769 of Mathematical Reviews Vol. , Issue 86d [page]

1986 Mathematical Reviews  
Author summary: “We present a different branch and bound al- gorithm for mixed integer programming.  ...  Unlike standard linear programming based branch and bound algorithms, where a single fractional variable (or special ordered set) is selected for prob- lem separation, the proposed method selects groups  ... 

Decomposition strategy for the stochastic pooling problem

Xiang Li, Asgeir Tomasgard, Paul I. Barton
2011 Journal of Global Optimization  
Solution of this lower bounding problem is then decomposed into a sequence of relaxed master problems, which are MILPs with much smaller sizes, and primal bounding problems, which are linear programs.  ...  The decomposition algorithm terminates finitely when the lower and upper bounds coincide (or are close enough), or infeasibility of the problem is indicated.  ...  significantly in the branch-and-bound framework.  ... 
doi:10.1007/s10898-011-9792-0 fatcat:c6vfbpsxizapnb6txvpbfih5dm

Page 4642 of Mathematical Reviews Vol. , Issue 87h [page]

1987 Mathematical Reviews  
Summary: “We review and complete the approximation results for stochastic programs with recourse.  ...  The problem is solved by a branch-and-bound method that employs the Zionts and Wallenius procedure (Zionts and J.  ... 

Page 1432 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
The author presents an algorithmic solution to mixed integer non- linear programs (MINLP) via integration of branch-and-bound techniques with an SQP solver.  ...  , bounded between lower and upper bounds, pre- sent on the right-hand side of the constraints.  ... 

Page 8247 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Summary: “Variable lower bounds in mixed integer programs are constraints with the general form x > Ly, where x is a continuous variable and y is a binary or an integer variable.  ...  For a two-stage stochastic linear program with fixed recourse and with another data random which should have smooth densities the twice continuous differentiability conditions (some of which are implicit  ... 

Page 832 of Mathematical Reviews Vol. , Issue 84b [page]

1984 Mathematical Reviews  
The problem (*) is reformulated as a stochastic programming problem with chance constraints and reduced in the usual way to a convex deterministic programming problem with linear cost function and quadratic  ...  Author’s summary: “In a branch-and-bound algorithm, a partial problem P, is terminated if the lower bound of the optimal value of P, is greater (in case all optimal solutions are sought) or not smaller  ... 
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