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51
Effective ContinuousTime Formulation for ShortTerm Scheduling: 3. Multiple Intermediate Due Dates
 Industrial and Engineering Chemistry Research
, 1998
"... The problem of shortterm scheduling often involves the satisfaction of variable product demands at specific due dates within the time horizon under consideration. Ierapetritou and Floudas 1;2 presented a new continuous time formulation to effectively address the problem of shortterm scheduling i ..."
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Cited by 48 (18 self)
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The problem of shortterm scheduling often involves the satisfaction of variable product demands at specific due dates within the time horizon under consideration. Ierapetritou and Floudas 1;2 presented a new continuous time formulation to effectively address the problem of shortterm scheduling in batch, continuous and mixed production facilities where product demands are specified at the end of time horizon. The primary objective of this paper is to extend the continuous time formulation so as to deal with intermediate due dates. The mathematical model is developed and the operation mode of the plant (batch or semicontinuous) is further exploited to result in the most efficient solution strategy. Several examples are provided to illustrate the capabilities of the proposed continuoustime formulations, and it is demonstrated that a variety of problems presented in the literature can be addressed efficiently. 1 Current address: Department of Chemical and Biochemical Engineering, R...
Algorithms for discrete and continuous multicommodity flow network interdiction problems
 IIE Transactions
, 2006
"... The authors also thank two anonymous referees and an Associate Editor for their remarks, which improved the presentation of this paper. We consider a network interdiction problem on a multicommodity flow network, in which an attacker disables a set of network arcs in order to minimize the maximum p ..."
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Cited by 22 (5 self)
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The authors also thank two anonymous referees and an Associate Editor for their remarks, which improved the presentation of this paper. We consider a network interdiction problem on a multicommodity flow network, in which an attacker disables a set of network arcs in order to minimize the maximum profit that can be obtained from shipping commodities across the network. The attacker is assumed to have some budget for destroying (or “interdicting”) arcs, and each arc is associated with a positive interdiction expense. In this paper, we examine problems in which interdiction must be discrete (i.e., each arc must either be left alone or completely destroyed), and in which interdiction can be continuous (the capacities of arcs may be partially reduced). For the discrete problem, we describe a linearized model for optimizing network interdiction that is similar to previous studies in the field, and compare it to a penalty model that does not require linearization constraints. For the continuous case, we prescribe an optimal partitioning algorithm along with a heuristic procedure for estimating the optimal objective function value. We demonstrate on a set of randomly generated test data that our penalty model for the discrete interdiction problem significantly reduces computational time when compared to that consumed by the linearization model. 1
Analyzing and modeling the maximum diversity problem by zeroone programming. Decision Sci
, 1993
"... The problem of maximizing diversity deals with selecting a set of elements from some larger collection such that the selected elements exhibit the greatest variety of characteristics. A new model is proposed in which the concept of diversity is quantifiable and measurable. A quadratic zeroone model ..."
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Cited by 20 (2 self)
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The problem of maximizing diversity deals with selecting a set of elements from some larger collection such that the selected elements exhibit the greatest variety of characteristics. A new model is proposed in which the concept of diversity is quantifiable and measurable. A quadratic zeroone model is formulated for diversity maximization. Based upon the formulation, it is shown that the maximum diversity problem is NPhard. 'Tho equivalent linear integer programs are then presented that offer progressively greater computational efficiency. Another formulation is also introduced which involves a different diversity objective. An example is given to illustrate how additional considerations can be incorporated into the maximum diversity model. Subject Areas: Discnk hgmmming, Linear Rvgmmming, and Mathematical hgmmming.
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 16 (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...
Nonconvex mixedinteger nonlinear programming: A survey
 Surveys in Operations Research and Management Science
, 2012
"... A wide range of problems arising in practical applications can be formulated as MixedInteger Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When nonconvexities are present, how ..."
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Cited by 7 (0 self)
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A wide range of problems arising in practical applications can be formulated as MixedInteger Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When nonconvexities are present, however, things become much more difficult, since then even the continuous relaxation is a global optimisation problem. We survey the literature on nonconvex MINLP, discussing applications, algorithms and software. Special attention is paid to the case in which the objective and constraint functions are quadratic. Key Words: mixedinteger nonlinear programming, global optimisation, quadratic programming, polynomial optimisation.
Different formulations for solving the heaviest ksubgraph problem
, 2002
"... Abstract. We consider the heaviest ksubgraph problem, i.e. determine a block of k nodes of a weighted graph (of n nodes) such that the total edge weight within the subgraph induced by the block is maximized. We compare from a theoretical and practical point of view different mixed integer programmi ..."
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Cited by 7 (1 self)
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Abstract. We consider the heaviest ksubgraph problem, i.e. determine a block of k nodes of a weighted graph (of n nodes) such that the total edge weight within the subgraph induced by the block is maximized. We compare from a theoretical and practical point of view different mixed integer programming formulations of this problem. Computational experiments when the weight of each edge is equal to 1 are reported. Key words: Heaviest ksubgraph problem, mixed integer linear programming, upper bounds, experiments. 1.
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...
Integrated MultiEchelon Supply Chain Design with Inventories under Uncertainty
 MINLP Models, Computational Strategies. AIChE Journal
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S.: Control of switched hybrid systems based on disjunctive formulations
 In: Hybrid Systems: Computation and Control. LNCS 2289
, 2002
"... Abstract. This contribution addresses the task of computing optimal control trajectories for hybrid systems with switching dynamics. Starting from a continuoustime formulation of the control task we derive an optimization problem in which the system behavior is modelled by a hybrid automaton with l ..."
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Cited by 4 (2 self)
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Abstract. This contribution addresses the task of computing optimal control trajectories for hybrid systems with switching dynamics. Starting from a continuoustime formulation of the control task we derive an optimization problem in which the system behavior is modelled by a hybrid automaton with linear discretetime dynamics and discrete as well as continuous inputs. In order to transform the discrete dynamics into an equationbased form we present and compare two different approaches: one uses the ‘traditional ’ Mformulation and one is based on disjunctive formulations. The control problem is then solved by mixed integer programming using a moving horizon setting. As illustrated for an example, the disjunctive formulation can lead to a considerable reduction of the computational effort.
Extending the QCR method to general mixedinteger programs
"... Abstract. Let (MQP) be a general mixed integer quadratic program that consists of minimizing a quadratic function subject to linear constraints. In this paper, we present a convex reformulation of (MQP), i.e. we reformulate (MQP) into an equivalent program, with a convex objective function. Such a r ..."
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Cited by 3 (0 self)
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Abstract. Let (MQP) be a general mixed integer quadratic program that consists of minimizing a quadratic function subject to linear constraints. In this paper, we present a convex reformulation of (MQP), i.e. we reformulate (MQP) into an equivalent program, with a convex objective function. Such a reformulation can be solved by a standard solver that uses a branch and bound algorithm. We prove that our reformulation is the best one within a convex reformulation scheme, from the continuous relaxation point of view. This reformulation, that we call MIQCR (Mixed Integer Quadratic Convex Reformulation), is based on the solution of an SDP relaxation of (MQP). Computational experiences are carried out with instances of (MQP) including one equality constraint or one inequality constraint. The results show that most of the considered instances with up to 40 variables can be solved in one hour of CPU time by a standard solver. Key words: General integer programming, mixedinteger programming, quadratic programming, convex reformulation, semidefinite programming, experiments