Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems

Jain, Vipul; Grossmann, Ignacio E.

doi:10.1287/ijoc.13.4.258.9733

Cited by 342 publications

(219 citation statements)

References 27 publications

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“…a coloring problem) but in a generic case, the master problem take the form of a feasibility problem where the cuts added can be seen as expl(z ≥ z * ) ⇒ z ≥ z * . Figure 1 presents our algorithm 4 . It has been implemented as a library of the Java version of the PaLM solver embedded within the choco (see http://choco.sf.net) constraints solver.…”

Section: Decomposition Schemementioning

confidence: 99%

“…3 It is also the case for linear duality as any dual solution is a bound for the primal. 4 Line 8 is used in the case of P 0 and P y whereas lines 5, 11, 13, and 14 concerns Pxy.…”

Section: A Benders Decomposition Algorithm For Cpmentioning

confidence: 99%

“…input : an initial solution to the master problem y, (1) begin (2) repeat (3) Cut = ∅ (4) for each sub-problem spb k do (5) Pxy : update upper bound of spb k with computeUb(k) using {z, szi, ∀i < k}) (6) solve spb k on (y, x k ) to optimality (7) add its inconsistency (if spb k is infeasible)/optimality explanation to Cut (8) P 0 , P y : spb k+1 = S i≤k,i>k spbi, with k , the last infeasible sub-problem. Pxy : Cut = computeCut(Cut)…”

Section: A Benders Decomposition Algorithm For Cpmentioning

confidence: 99%

“…It is often introduced as a basis for models and techniques using the complementary strengths of constraint programming and optimization techniques. Hybridization schemes have appeared recently and provided interesting computational results [4,5,7,8]. They have been extended [2,3,6] to take into account other kinds of sub-problems and not only the classical linear programming ones.…”

Section: Introductionmentioning

confidence: 99%

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Integrating Benders Decomposition Within Constraint Programming

Cambazard

Jussien

2005

Principles and Practice of Constraint Programming - CP 2005

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Section: Decomposition Schemementioning

confidence: 99%

“…3 It is also the case for linear duality as any dual solution is a bound for the primal. 4 Line 8 is used in the case of P 0 and P y whereas lines 5, 11, 13, and 14 concerns Pxy.…”

Section: A Benders Decomposition Algorithm For Cpmentioning

confidence: 99%

Section: A Benders Decomposition Algorithm For Cpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Integrating Benders Decomposition Within Constraint Programming

Cambazard

Jussien

2005

Principles and Practice of Constraint Programming - CP 2005

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“…This results in hybrid approaches (see, for instance, [32] and [37]), i.e., in a language and algorithms combining elements from both communities. This may have a great impact on supply chain problems and scheduling.…”

Section: Conclusion and Summarymentioning

confidence: 99%

Planning and scheduling in the process industry

Kallrath¹

2002

OR Spectrum

311

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Since there has been tremendous progress in planning and scheduling in the process industry during the last 20 years, it might be worthwhile to give an overview of the current state-of-the-art of planning and scheduling problems in the chemical process industry. This is the purpose of the current review which has the following structure: we start with some conceptional thoughts and some comments on special features of planning and scheduling problems in the process industry. In Section 2 the focus is on planning problems while in Section 3 different types of scheduling problems are discussed. Section 4 presents some solution approaches especially those applied to a benchmark problem which has received considerable interest during the last years. Section 5 allows a short view into the future of planning and scheduling. In the appendix we describe the WestenbergerKallrath problem which has already been used extensively as a benchmark problem for planning and scheduling in the process industry.

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Advances in Logic‐Based Optimization Approaches to Process Integration and Supply Chain Management

Grossmann¹

2005

Chemical Engineering

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Optimization as an enabling technology has been one of the big success stories in process systems engineering. In this paper we present a review on recent research work in the area of logic-based discrete/continuous optimization. In particular, recent advances are presented in the modeling and solution of nonlinear mixed-integer and generalized disjunctive programming, global optimization and constraint programming. The impact of these techniques is illustrated with several examples in the areas of process integration and supply chain management.. where f(x, y) is the objective function (e.g. cost), h(x, y) = 0 are the equations that describe the performance of the system (material balances, production rates), and g(x,y) ≤ 0 are inequalities that define the specifications or constraints for feasible plans and schedules. The variables x are continuous and generally correspond to state variables, while y are the discrete variables, which generally are restricted to take 0-1 values to define for instance the assignments of equipment and sequencing of tasks. Problem (MIP) corresponds to a mixed-integer nonlinear program (MINLP) when any of the functions involved are nonlinear. If all functions are linear it corresponds to a mixed-integer linear program (MILP). If there are no 0-1 variables, the problem (MIP) reduces to a nonlinear program (NLP) or linear program (LP) depending on whether or not the functions are linear.It should be noted that (MIP) problems, and their special cases, may be regarded as steady-state models. Hence, one important extension is the case of dynamic models, which in the case of discrete time models gives rise to multiperiod optimization problems, while for the case of continuous time it gives rise to optimal control problems that contain differential-algebraic equation (DAE) models.Mathematical programming, and optimization in general, have found extensive use in process systems engineering. A major reason for this is that in these problems there are often many alternative solutions, and hence, it is often not easy to find the optimal solution. Furthermore, in many cases the economics is such that finding the optimum solution translates into large savings. Therefore, there might be a large economic penalty to just sticking to suboptimal solutions. In summary, optimization has become a major technology that helps companies to remain competitive.Applications in Process Integration (Process Design and Synthesis) have been dominated by NLP and MINLP models due to the need for the explicit handling of performance equations, although simpler targeting models in process synthesis can give rise to LP and MILP problems. An extensive review of optimization models for process integration can be found in Grossmann et al. (1999). In contrast, Supply Chain Management problems tend to be dominated by linear models, LP and MILP, for planning and scheduling (see Grossmann et al. 2002 for a review). Finally, global optimization has concentrated more on

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Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems

Cited by 342 publications

References 27 publications

Integrating Benders Decomposition Within Constraint Programming

Integrating Benders Decomposition Within Constraint Programming

Planning and scheduling in the process industry

Advances in Logic‐Based Optimization Approaches to Process Integration and Supply Chain Management

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