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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 30 (14 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.
Global Optimization of MixedInteger Nonlinear Problems
 AIChE J
"... Two novel deterministic global optimization algorithms for nonconvex mixedinteger problems (MINLPs) are proposed, using the advances of the ffBB algorithm for nonconvex NLPs Adjiman et al. (1998a). The Special Structure MixedInteger ffBB algorithm (SMINffBB addresses problems with nonconvexities ..."
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Cited by 27 (4 self)
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Two novel deterministic global optimization algorithms for nonconvex mixedinteger problems (MINLPs) are proposed, using the advances of the ffBB algorithm for nonconvex NLPs Adjiman et al. (1998a). The Special Structure MixedInteger ffBB algorithm (SMINffBB addresses problems with nonconvexities in the continuous variables and linear and mixedbilinear participation of the binary variables. The General Structure MixedInteger ffBB algorithm (GMINffBB), is applicable to a very general class of problems for which the continuous relaxation is twice continuously differentiable. Both algorithms are developed using the concepts of branchandbound, but they differ in their approach to each of the required steps. The SMINffBB algorithm is based on the convex underestimation of the continuous functions while the GMINffBB algorithm is centered around the convex relaxation of the entire problem. Both algorithms rely on optimization or interval based variable bound updates to enhance effici...
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 20 (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.
Global Optimization of MINLP Problems in Process Synthesis and Design
 Computers & Chemical Engineering
, 1997
"... : Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear ffBB, SMINffBB, and the General structure Mixed Integer Nonlinear ffBB, GMINffBB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of ..."
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Cited by 18 (7 self)
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: Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear ffBB, SMINffBB, and the General structure Mixed Integer Nonlinear ffBB, GMINffBB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of MINLPs involving twicedifferentiable nonconvex functions in the continuous variables can be identified. The conditions imposed on the functionality of the binary variables differ for each method : linear and mixed bilinear terms can be treated with the SMINffBB; mixed nonlinear terms whose continuous relaxation is twicedifferentiable are handled by the GMINffBB. While both algorithms use the concept of a branch & bound tree, they rely on fundamentally different bounding and branching strategies. In the GMINffBB algorithm, lower (upper) bounds at each node result from the solution of convex (nonconvex) MINLPs derived from the original problem. The construction of convex lower bound...
A Differential Evolution Approach for Global Optimization of MINLP
 Problems, Proceedings of 4 th Asia Pacific Conference on Simulated Evolution and Learning (SEAL2002
"... The global optimization of mixed integer nonlinear programming (MINLP) problems is an active research area in many engineering fields. In this work, Differential Evolution (DE), a hybrid Evolutionary Computation method, is used for the optimization of nonconvex MINLP problems and a comparison is ma ..."
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Cited by 15 (7 self)
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The global optimization of mixed integer nonlinear programming (MINLP) problems is an active research area in many engineering fields. In this work, Differential Evolution (DE), a hybrid Evolutionary Computation method, is used for the optimization of nonconvex MINLP problems and a comparison is made among the algorithms based on hybrid of Simplex & Simulated Annealing (MSIMPSA), Genetic Algorithms (GA), and DE. It is found that DE, an exceptionally simple evolutionary computation method, is significantly faster and yields the global optimum for a wide range of the key parameters. Results indicate that DE is more reliable, efficient and hence a better approach to the optimization of nonconvex nonlinear problems. DE found to be the best evolutionary computation method in all the problems studied.
Disjuntive multiperiod optimization methods for design and planning of chemical process systems
 Computers and Chemical Engineering
, 1999
"... In this paper, we present a general disjunctive multiperiod nonlinear optimization model, which incorporates design, as well as operation and expansion planning, and takes into account the corresponding costs incurred in each time period. This model is formulated with the use of logic and disjunctiv ..."
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Cited by 13 (3 self)
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In this paper, we present a general disjunctive multiperiod nonlinear optimization model, which incorporates design, as well as operation and expansion planning, and takes into account the corresponding costs incurred in each time period. This model is formulated with the use of logic and disjunctive programming, and includes Boolean variables for design, operation planning and expansion planning. We propose two algorithms for the solution of these problems. The first is a logicbased Outer Approximation (OA) algorithm for multiperiod problems. The second is a bilevel decomposition algorithm, that exploits the problem structure by decomposing it into an upper level design problem and a lower level operation and expansion planning problem, each of which is solved with the logicbased OA algorithm. Applications are considered in the areas of design and planning of process networks, as well as retrofit design for multiproduct batch plants. The results show that the disjunctive logicbased OA algorithm performs best for small problems, while the disjunctive bilevel decomposition algorithm is superior for larger problems. In both cases, a significant decrease in MILP solution time and total solution time is achieved compared to DICOPT++. Results also show that problems with a significant number of time periods can be solved in
Logicbased Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems
"... This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations ha ..."
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Cited by 9 (6 self)
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This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logicbased modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a twolevel branch and bound procedure.
Advances in Mathematical Programming for Automated Design Integration
 KOREAN J. CHEM. ENG
, 1999
"... This paper presents a review of advances that have taken place in the mathematical programming approach to process design and synthesis. A review is first presented on the algorithms that are available for solving MINLP problems, and its most recent variant, Generalized Disjunctive Programming model ..."
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Cited by 8 (3 self)
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This paper presents a review of advances that have taken place in the mathematical programming approach to process design and synthesis. A review is first presented on the algorithms that are available for solving MINLP problems, and its most recent variant, Generalized Disjunctive Programming models. The formulation of superstructures, models and solution strategies is also discussed for the effective solution of the corresponding optimization problems. The rest of the paper is devoted to reviewing recent mathematical programming models for the synthesis of reactor networks, distillation sequences, heat exchanger networks, mass exchanger networks, utility plants, and total flowsheets. As will be seen from this review, the progress that has been achieved in this area over the last decade is very significant.
MixedInteger Nonlinear Optimization in Process Synthesis
, 1998
"... The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the process synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process flowsheets that convert raw ma ..."
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Cited by 7 (0 self)
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The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the process synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process flowsheets that convert raw materials into desired products. In recent years, the optimization approach to process synthesis has shown promise in tackling this challenge. It requires the development of a network of interconnected units, the process superstructure, that represents the alternative process flowsheets. The mathematical modeling of the superstructure has a mixed set of binary and continuous variables and results in a mixedinteger optimization model. Due to the nonlinearity of chemical models, these problems are generally classified as MixedInteger Nonlinear Programming (MINLP) problems. A number of local optimization algorithms, developed for the solution of this class of problems, are presented in this pap...
Part II: Future Perspective on Optimization
 25TH YEAR ISSUE ON COMPUTERS AND CHEMICAL ENGINEERING
"... Following from Part I, which presents a retrospective on optimization, we focus here on areas that are recent active research topics and are likely to strongly influence the future of optimization algorithms and formulations. First, we discuss recent developments in deterministic global optimization ..."
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Cited by 7 (0 self)
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Following from Part I, which presents a retrospective on optimization, we focus here on areas that are recent active research topics and are likely to strongly influence the future of optimization algorithms and formulations. First, we discuss recent developments in deterministic global optimization algorithms, applied to both nonlinear programs and mixed integer programs. Second, we discuss logicbased optimization and its influence in both modeling and solving mixedinteger optimization problems. Third, we discuss issues and approaches related to largescale optimization algorithms and applications. Finally, we summarize recent progress in scientific computing and software engineering as applied to optimization applications.