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Algorithms for hybrid MILP/CP models for a class of optimization problems
 INFORMS Journal on Computing
, 2001
"... The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered ..."
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Cited by 72 (12 self)
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The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have nonzero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CPbased branchandbound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the leastcost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILPCP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.
Review of nonlinear mixedinteger and disjunctive programming techniques
 Optimization and Engineering
, 2002
"... This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, OuterApproximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are ex ..."
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Cited by 61 (15 self)
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This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, OuterApproximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.
New Algorithms for Nonlinear Generalized Disjunctive Programming
 Computers and Chemical Engineering Journal
, 2000
"... Generalized Disjunctive Programming (GDP) has been introduced recently as an alternative model to MINLP for representing discrete/continuous optimization problems. The basic idea of GDP consists of representing discrete decisions in the continuous space with disjunctions, and constraints in the disc ..."
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Cited by 29 (19 self)
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Generalized Disjunctive Programming (GDP) has been introduced recently as an alternative model to MINLP for representing discrete/continuous optimization problems. The basic idea of GDP consists of representing discrete decisions in the continuous space with disjunctions, and constraints in the discrete space with logic propositions. In this paper, we describe a new convex nonlinear relaxation of the nonlinear GDP problem that relies on the use of the convex hull of each of the disjunctions involving nonlinear inequalities. The proposed nonlinear relaxation is used to reformulate the GDP problem as a tight MINLP problem, and for deriving a branch and bound method. Properties of these methods are given, and the relation of this method with the Logic Based OuterApproximation method is established. Numerical results are presented for problems in jobshop scheduling, synthesis of process networks, optimal positioning of new products and batch process design.
LOGMIP: a disjunctive 0/1 nonlinear optimizer for process system models
 Computers and Chemical Engineering 23
, 1999
"... Discretecontinuous nonlinear optimization models are frequently used to formulate problems in process system engineering. Major modeling alternatives and solution algorithms include generalized disjunctive programming and mixed integer nonlinear programming (MINLP). Both have advantages and drawb ..."
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Cited by 25 (10 self)
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Discretecontinuous nonlinear optimization models are frequently used to formulate problems in process system engineering. Major modeling alternatives and solution algorithms include generalized disjunctive programming and mixed integer nonlinear programming (MINLP). Both have advantages and drawbacks depending on the problem they are dealing with. In this work, we describe the theory behind LOGMIP, a new computer code for disjunctive programming and MINLP. We discuss a hybrid modeling framework that combines both approaches, allowing binary variables and disjunctions for expressing discrete choices. An extension of the logicbased outer approximation (OA) algorithm has been implemented to solve the proposed hybrid model. Computational experience is reported on several examples, which are solved using disjunctive, MINLP and hybrid formulations.
A Global Optimization Algorithm for Nonconvex Generalized Disjunctive Programming and Applications to Process Systems
 Computers and Chemical Engineering
, 2000
"... A global optimization algorithm for nonconvex Generalized Disjunctive Programming (GDP) problems is proposed in this paper. By making use of convex underestimating functions for bilinear, linear fractional and concave separable functions in the continuous variables, the convex hull of each nonlinear ..."
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Cited by 19 (9 self)
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A global optimization algorithm for nonconvex Generalized Disjunctive Programming (GDP) problems is proposed in this paper. By making use of convex underestimating functions for bilinear, linear fractional and concave separable functions in the continuous variables, the convex hull of each nonlinear disjunction is constructed. The relaxed convex GDP problem is then solved in the first level of a twolevel branch and bound algorithm, in which a discrete branch and bound search is performed on the disjunctions to predict lower bounds. In the second level, a spatial branch and bound method is used to solve nonconvex NLP problems for updating the upper bound. The proposed algorithm exploits the convex hull relaxation for the discrete search, and the fact that the spatial branch and bound is restricted to fixed discrete variables in order to predict tight lower bounds. Application of the proposed algorithm to several example problems is shown, as well as comparisons with other algorithms.
Decomposition Techniques for Multistage Scheduling Problems Using MixedInteger and Constraint Programming Methods
 Comp. Chem. Engng
, 2002
"... In this paper two strategies are presented to reduce the combinatorial complexity when solving single stage and multistage optimization scheduling problems that involve cost minimization and due dates. These problems can naturally be decomposed into assignment and sequencing subproblems. The propose ..."
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Cited by 16 (10 self)
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In this paper two strategies are presented to reduce the combinatorial complexity when solving single stage and multistage optimization scheduling problems that involve cost minimization and due dates. These problems can naturally be decomposed into assignment and sequencing subproblems. The proposed strategies rely on either combining mixedinteger programming (MILP) to model the assignment part and constraint programming (CP) for modeling the sequencing part, or else combining MILP models for both parts. The subproblems are solved sequentially by adding integer cuts to the first MILP to generate new assignments. Results are presented for both single and multistage systems.
Global optimization for the synthesis of integrated water systems in chemical processes
 Comp. Chem. Eng
"... In this paper, we address the problem of optimal synthesis of an integrated water system, where water using processes and water treatment operations are combined into a single network such that the total cost of obtaining freshwater for use in the water using operations, and treating wastewater is m ..."
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Cited by 14 (5 self)
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In this paper, we address the problem of optimal synthesis of an integrated water system, where water using processes and water treatment operations are combined into a single network such that the total cost of obtaining freshwater for use in the water using operations, and treating wastewater is minimized. A superstructure, which incorporates all feasible design alternatives for water treatment, reuse and recycle, is proposed. We formulate this structure as a nonconvex NonLinear Programming (NLP) problem, which is solved to global optimality. The problem takes the form of a nonconvex Generalized Disjunctive Program (GDP) if there is a flexibility of choosing different treatment technologies for the removal of the various contaminants in the wastewater streams. A new deterministic spatial branch and contract algorithm is proposed for optimizing such systems, in which piecewise under and overestimators are used to approximate the nonconvex terms in the original model to obtain a convex relaxation whose solution gives a lower bound on the global optimum. These lower bounds are made to converge to the solution within a branch and bound procedure. Several examples are presented to illustrate the optimization of these integrated networks using the proposed algorithm.
An Iterative Aggregation/Disaggregation Approach for the Solution of a Mixed Integer Nonlinear Oilfield Infrastructure Planning Model
, 1999
"... A multiperiod MINLP model for offshore oilfield infrastructure planning is presented where nonlinear reservoir behavior is incorporated directly into the formulation. Discrete decisions include the selection of production platforms, well platforms and wells to be installed/drilled, as well as the dr ..."
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Cited by 14 (8 self)
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A multiperiod MINLP model for offshore oilfield infrastructure planning is presented where nonlinear reservoir behavior is incorporated directly into the formulation. Discrete decisions include the selection of production platforms, well platforms and wells to be installed/drilled, as well as the drilling schedule for the wells over the planning horizon. Continuous decisions include the capacities of the platforms, as well as the production profile for each well in each time period. For the solution of this model, an iterative aggregation/disaggregation algorithm is proposed in which logicbased methods, a bilevel decomposition technique, the use of convex envelopes and aggregation of time periods are integrated. Furthermore, a novel dynamic programming subproblem is proposed to improve the aggregation scheme at each iteration in order to obtain an aggregate problem that resembles the disaggregate problem more closely. A number of examples are presented to illustrate the performance of the proposed method. Keywords Oilfield planning, MINLP, aggregation, decomposition
Logic, Optimization, and Constraint Programming
 INFORMS Journal on Computing
, 2000
"... Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use ..."
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Cited by 13 (2 self)
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Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use logical inference in di#erent ways, and how these ways can be combined. It sketches the intellectual background for recent e#orts at integration. In particular, it traces the history of logicbased methods in optimization and the development of constraint programming in artificial intelligence. It concludes with a review of recent research, with emphasis on schemes for integration, relaxation methods, and practical applications. Optimization and constraint programming are beginning to converge, despite their very di#erent origins. Optimization is primarily associated with mathematics and engineering, while constraint programming developed much more recently in the computer science an...