# Decomposition strategy for the stochastic pooling problem

@article{Li2012DecompositionSF, title={Decomposition strategy for the stochastic pooling problem}, author={Xiang Li and Asgeir Tomasgard and Paul I. Barton}, journal={Journal of Global Optimization}, year={2012}, volume={54}, pages={765-790} }

The stochastic pooling problem is a type of stochastic mixed-integer bilinear program arising in the integrated design and operation of various important industrial networks, such as gasoline blending, natural gas production and transportation, water treatment, etc. This paper presents a rigorous decomposition method for the stochastic pooling problem, which guarantees finding an $${\epsilon}$$ -optimal solution with a finite number of iterations. By convexification of the bilinear terms, the…

## 36 Citations

### Models and Solution Methods for the Pooling Problem

- Computer Science
- 2012

This thesis develops a new formulation that proves to be stronger than other formulations based on proportion variables for the standard pooling problem, and proposes a multi-commodity flow formulation and proves its strength over formulations from the literature.

### Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities

- MathematicsOper. Res.
- 2016

This new reformulation method can be used for linear stochastic inequalities and will also significantly improve the solution of such joint chance-constrained problems.

### Relaxations and discretizations for the pooling problem

- Computer ScienceJ. Glob. Optim.
- 2017

This paper assimilates the vast literature on this problem that is dispersed over different areas and gives new insights on prevalent techniques and presents new ideas for computing dual bounds on the global optimum by solving high-dimensional linear programs.

### Robust Optimization for the Pooling Problem

- MathematicsIndustrial & Engineering Chemistry Research
- 2019

This paper compares the computational efficiency of reformulation and cutting plane approaches for three commonly used uncertainty set geometries on 14 pooling problem instances and demonstrates how accounting for uncertainty changes the optimal solution.

### An Efficient Solution Algorithm for Large-Scale Stochastic Mixed-Integer Linear Programs1

- Computer Science
- 2012

A decomposition strategy is developed that exploits the underlying structure of two-stage stochastic programming formulations with mixed-integer linear programming (MILP) recourse problems to solve capacity planning problems in the pharmaceutical industry.

### A finite ϵ -convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables

- Computer ScienceJ. Glob. Optim.
- 2019

A generalized Benders decomposition-based branch and bound algorithm (GBDBAB) to solve two-stage convex mixed- binary nonlinear stochastic programs with mixed-binary variables in both first and second-stage decisions is proposed.

### A Distributed Algorithm for Large-scale Stochastic Optimization Problems

- Computer Science
- 2016

The non-convex generalized Benders decomposition method is parallelizable and that it scales well in a distributed computing environment and the results suggests that the method has potential in terms of parallelization, but that it is essential to keep the parallelizable portion of the algorithm large.

### Sample average approximation for stochastic nonconvex mixed integer nonlinear programming via outer-approximation

- Computer ScienceOptimization and Engineering
- 2020

The proposed SAAOA algorithm works well for the special case of pure binary first stage variables and continuous stage two variables since in this case the nonconvex NLPs can be solved for each scenario independently.

### A generalized global optimization formulation of the pooling problem with processing facilities and composite quality constraints

- Computer Science
- 2016

A generalized formulation of the pooling problem that can solve the more general test cases and compare the performance of the bilinear formulation in BARON with discretizations solved as a Mixed Integer Linear Program using CPLEX.

## References

SHOWING 1-10 OF 55 REFERENCES

### Pooling Problem: Alternate Formulations and Solution Methods

- BusinessManag. Sci.
- 2004

This paper investigates how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem and considers two standard models: One is based primarily on flow variables, and the other relies on the proportion of flows entering pools.

### A new reformulation-linearization technique for bilinear programming problems

- Computer Science, MathematicsJ. Glob. Optim.
- 1992

This paper is concerned with the development of an algorithm for general bilinear programming problems, and develops a new Reformulation-Linearization Technique (RLT) for this problem, and imbeds it within a provably convergent branch-and-bound algorithm.

### Global optimization of nonlinear generalized disjunctive programming with bilinear equality constraints: applications to process networks

- Computer ScienceComput. Chem. Eng.
- 2003

### Global Optimization of Large-Scale Generalized Pooling Problems: Quadratically Constrained MINLP Models

- Computer Science
- 2010

This work addresses five instantiations of the generalized pooling problem to global optimality by introducing a quadratically constrained MINLP model formulation that reduces the number of bilinear terms and a branch-and-bound algorithm suited to address the combinatorial complex of wastewater treatment.

### Stochastic pooling problem for natural gas production network design and operation under uncertainty

- Engineering
- 2011

Product quality and uncertainty are two important issues in the design and operation of natural gas production networks. This paper presents a stochastic pooling problem optimization formulation to…

### Solving mixed integer nonlinear programs by outer approximation

- MathematicsMath. Program.
- 1994

An alternative approach is considered to the difficulties caused by infeasibility in outer approximation, in which exact penalty functions are used to solve the NLP subproblems.

### Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs

- Computer Science, MathematicsMath. Program.
- 2004

A rigorous decomposition approach to solve separable mixed-integer nonlinear programs where the participating functions are nonconvex is presented and numerical results are compared with currently available algorithms for example problems, illuminating the potential benefits of the proposed algorithm.

### A Lagrangian Approach to the Pooling Problem

- Computer Science
- 1999

It is proved that, for the multiple-quality case, the Lagrangian approach provides tighter lower bounds than the standard linear-programming relaxations used in global optimization algorithms.

### A global optimization algorithm (GOP) for certain classes of nonconvex NLPs—I. Theory

- Computer Science, Mathematics
- 1990

### Primal-Relaxed Dual Global Optimization Approach

- Computer Science, Mathematics

A deterministic global optimization approach is proposed for nonconvex constrained nonlinear programming problems that converts the original problem into primal and relaxed dual subproblems that provide valid upper and lower bounds respectively on the global optimum.