The problem of short-term 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 short-term 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 semi-continuous) is further exploited to result in the most efficient solution strategy. Several examples are provided to illustrate the capabilities of the proposed continuous-time 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...

: Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear ffBB, SMIN--ffBB, and the General structure Mixed Integer Nonlinear ffBB, GMIN--ffBB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of MINLPs involving twice--differentiable 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 SMIN--ffBB; mixed nonlinear terms whose continuous relaxation is twice--differentiable are handled by the GMIN--ffBB. While both algorithms use the concept of a branch & bound tree, they rely on fundamentally different bounding and branching strategies. In the GMIN--ffBB 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...

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 maxi-mum 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 exam-ine 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 ca-pacities 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 con-straints. 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

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 mixed-integer optimization model. Due to the nonlinearity of chemical models, these problems are generally classified as Mixed-Integer Nonlinear Programming (MINLP) problems. A number of local optimization algorithms, developed for the solution of this class of problems, are presented in this pap...

Abstract. We consider the heaviest k-subgraph 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 k-subgraph problem, mixed integer linear programming, upper bounds, experiments. 1.

Abstract. This contribution addresses the task of computing optimal control trajectories for hybrid systems with switching dynamics. Starting from a continuous-time formulation of the control task we derive an optimization problem in which the system behavior is modelled by a hybrid automaton with linear discrete-time dynamics and discrete as well as continuous inputs. In order to transform the discrete dynamics into an equation-based form we present and compare two different approaches: one uses the ‘traditional ’ M-formulation 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.

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Abstract — Wireless sensor networks (WSNs) have recently received increasing attention from research and development communities. In a WSN, the field information (e.g., temperature, humidity, airflow) is acquired via several battery-equipped wireless devices and is relayed towards a sink node. As the size of the WSNs increases, it becomes inefficient to gather all information in one sink. To tackle this problem, the number of sinks can be increased. The data information flow towards each of the sinks is called a commodity. In this paper, we formulate a lexicographically optimal commodity lifetime (LOCL) routing problem. A stepwise algorithm is proposed to obtain the optimal routing solution which can lead to lexicographical fairness among commodity lifetimes. Simulation results show that our proposed algorithm increases the normalized commodity lifetime compared to MLMS [1] and LMM [2] routing algorithms. I.

We consider the Module Allocation Problem with Non-Uniform communication costs (MAPNU), where a set of program modules must be assigned to a set of processors. The optimal assignment minimizes the sum of execution costs and communication costs between modules. This problem is naturally formulated as a quadratic 0-1 problem with linear constraints. In this paper, we compare two exact solution methods for this problem. The first method is based on linear programming and Mixed Integer Linear Programming. The second one uses semidefinite programming and Mixed Integer Quadratic Programming. Both of these methods are easy to implement by use of available optimization software. We describe each of these methods and carry out a comparative computational work for instances of MAPNU.

We address in this paper the mid-term planning of chemical complexes with integration of stochastic inventory management under supply and demand uncertainty. By using the guaranteed service approach to model the time delays in the chemical flows inside the chemical process network, we capture the stochastic nature of the supply and demand variations, and develop an equivalent deterministic optimization model to minimize the total cost including production cost, feedstock purchase cost, cycle inventory and safety stock costs. The model simultaneously determines the optimal purchases of the feedstocks, production levels of the processes, sales of final products and safety stock levels of all the chemicals, as well as the internal demand of the production processes. The model also captures “risk-pooling ” effects to allow centralization of inventory management for chemicals that are consumed/produced by multiple processes. We formulate the model as a mixed-integer nonlinear program (MINLP) with a nonconvex objective function and nonconvex constraints. To solve the global optimization problem with modest computational times, we exploit some model