This paper integrates the natural gas and hydrothermal systems in terms of power and gas optimal short-term operations planning and unit commitment. In this paper, the natural gas network model including storages and ...
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ISBN:
(纸本)9781424421893
This paper integrates the natural gas and hydrothermal systems in terms of power and gas optimal short-term operations planning and unit commitment. In this paper, the natural gas network model including storages and pipelines are integrated with hydrothermal systems to optimize short-term operation of both systems simultaneously. The proposed model considers the constraints at the hydrothermal system, natural gas extraction, natural gas storage operation and pipeline. The proposed model results in a large-scale mixed-integer nonlinear programming problem where the objective function is to minimize the integrated gas-electricity system operation costs. To solve the integrated electricity-gas optimal short-term planning problem an approach based on Dual Decomposition, Lagrangian Relaxation and Dynamic programming is employed. A didactic integrated hydrothermal and gas system case study is presented. The proposed model shows the importance of the integration of the two systems in terms of operation, planning, security and reliability.
An improved method for solving the optimal distribution problem of a gas piping system is introduced. Mathematical programming has been used to solve for the optimal distribution and the problem represented by a mathe...
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An improved method for solving the optimal distribution problem of a gas piping system is introduced. Mathematical programming has been used to solve for the optimal distribution and the problem represented by a mathematical model. The optimization problem is a mixed-integer non-linear programming problem, and in general discrete non-linear programming problems are difficult to solve. In this paper, several continuous variables are introduced to replace the discrete decision variables, most importantly the pipe segment length, and in this way the original problem becomes a nonlinearprogramming problem. The original nonlinearprogramming problem is decomposed into two optimization subsystems, phase 1 and phase 2. The interconnection between phase 1 and phase 2 involves the gas flow rate and the segment length. The output variables of phase 1 are the input variables for phase 2, and the output variables of phase 2 are also the input variables for Phase 1.
nonlinearly mixed-integer reliability design problems are investigated in this paper where both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simul...
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nonlinearly mixed-integer reliability design problems are investigated in this paper where both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximize the reliability of system. The reliability design problems have been studied in the literature for decades, usually using mathematical programming or heuristic/metaheuristic optimization approaches. The difficulties confronted for both methodologies are to maintain feasibility with respect to three nonlinear constraints, namely, cost, weight and volume related constraints. A penalty guided artificial immune algorithm is presented for solving such mixed-integer reliability design problems. It can search over promising feasible and infeasible regions to find the feasible optimal/near optimal solution effectively and efficiently. Numerical examples indicate that the proposed approach performs well for the reliability-redundant allocation design problems considered in this paper. As reported, solutions obtained by the proposed approach are as well as or better than the previously best-known solutions. (c) 2006 Elsevier Inc. All rights reserved.
Considering the viewpoint of a retailer, this paper analyzes the problem of setting up contracts on both the supplier and end-user sides to maximize profits while maintaining an acceptable level of settlement risk. Th...
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Considering the viewpoint of a retailer, this paper analyzes the problem of setting up contracts on both the supplier and end-user sides to maximize profits while maintaining an acceptable level of settlement risk. The proposed stochastic optimization model can assist retailers with these efforts and guide them in their contractual arrangements. A realistic example illustrates the capabilities of the methodology proposed.
This paper develops a fuzzy chance constrained mixed-integer nonlinear programming (FCC-MINLP) model and the solution methods for refinery short-term crude oil scheduling problem under demands uncertainty. To reduce t...
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ISBN:
(纸本)9781424403417
This paper develops a fuzzy chance constrained mixed-integer nonlinear programming (FCC-MINLP) model and the solution methods for refinery short-term crude oil scheduling problem under demands uncertainty. To reduce the calculation complexity of the model, it is transformed into its equivalent fuzzy chance constrained mixed-integer linear programming (FCC-MILP) model by using the method of Quesada & Grossmann [5]. After that the FCC-MILP model is solved through its crisp equivalent algorithm and fuzzy simulation algorithm rely on the theory presented by Liu & 1wamura [12][13] for the first time in this area. Finally, a case study which has 265 continuous variables, 68 binary variables and 318 constraints is effectively solved in LINGO 8.0 [8] with the proposed approaches.
This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number...
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This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number of linear constraints far exceeds the number of nonlinear constraints, and with most variables participating in the nonconvex terms. As a result global optimization methods are needed. A branch-and-bound algorithm (BB) is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of linear branching functions, which depend linearly on the search variables. This leads to a significant reduction in the dimensionality of the search space. The construction of linear underestimators for a class of functions is also presented. The CAMD problem that is considered is the design of optimal solvents to be used as cleaning agents in lithographic printing. (C) 2002 Elsevier Science Ltd. All rights reserved.
The paper deals with the synthesis problem of mass exchange networks (MEN's) for waste minimization by adopting a mathematical programming approach based on the stage-wise superstructure representation of the MEN&...
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The paper deals with the synthesis problem of mass exchange networks (MEN's) for waste minimization by adopting a mathematical programming approach based on the stage-wise superstructure representation of the MEN's, analogous to the one introduced by [Yee, T. F., & Grossmann, I. E. (1990a). Simultaneous optimization models for heat integration. I. Area and energy targeting and modeling of multi-stream exchangers. Computers and Chemical Engineering 14, 1151;Yee, T. R, & Grossmann, I. E. (1990b). Simultaneous optimization models for heat integration. II. Heat exchanger network synthesis. Computers and Chemical Engineering 14, 1165] for synthesis of heat exchange networks (HEN's). This stage-wise superstructure-based representation cannot only handle multiple transferable components and reactive separating agents directly, but also be extended to include regeneration networks straightforwardly. Not using any heuristics that are based on the concept of pinch points, the proposed superstructure-based representation for MEN's is formulated as a mixed-integer nonlinear programming (MINLP) optimization model, and therefore the operating cost for the external lean mass separating agents as well as the regenerating agents and the annualized equipment cost for exchange units can be minimized simultaneously. Four benchmark examples from literatures-including those with single recovery component, multiple waste components, reactive mass separating agent, and regenerating streams-are examined to illustrate the applicability of proposed approach for synthesis of various MEN's. (c) 2004 Elsevier Ltd. All fights reserved.
A variety of nonlinear, including semidefinite, relaxations have been developed in recent years for nonconvex optimization problems. Their potential can be realized only if they can be solved with sufficient speed and...
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A variety of nonlinear, including semidefinite, relaxations have been developed in recent years for nonconvex optimization problems. Their potential can be realized only if they can be solved with sufficient speed and reliability. Unfortunately, state-of-the-art nonlinearprogramming codes are significantly slower and numerically unstable compared to linear programming software. In this paper, we facilitate the reliable use of nonlinear convex relaxations in global optimization via a polyhedral branch-and-cut approach. Our algorithm exploits convexity, either identified automatically or supplied through a suitable modeling language construct, in order to generate polyhedral cutting planes and relaxations for multivariate nonconvex problems. We prove that, if the convexity of a univariate or multivariate function is apparent by decomposing it into convex subexpressions, our relaxation constructor automatically exploits this convexity in a manner that is much superior to developing polyhedral outer approximators for the original function. The convexity of functional expressions that are composed to form nonconvex expressions is also automatically exploited. Root-node relaxations are computed for 87 problems from globallib and minlplib, and detailed computational results are presented for globally solving 26 of these problems with BARON 7.2, which implements the proposed techniques. The use of cutting planes for these problems reduces root-node relaxation gaps by up to 100% and expedites the solution process, often by several orders of magnitude.
Systems reliability plays an important role in systems design, operation and management. Systems reliability can be improved by adding redundant components or increasing the reliability levels of subsystems. Determina...
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Systems reliability plays an important role in systems design, operation and management. Systems reliability can be improved by adding redundant components or increasing the reliability levels of subsystems. Determination of the optimal amount of redundancy and reliability levels among various subsystems under limited resource constraints leads to a mixed-integer nonlinear programming problem. The continuous relaxation of this problem in a complex system is a nonconvex nonseparable optimization problem with certain monotone properties. In this paper, we propose a convexification method to solve this class of continuous relaxation problems. Combined with a branch-and-bound method, our solution scheme provides an efficient way to find an exact optimal solution to integer reliability optimization in complex systems.
A multi-product, multi-stage, and multi-period production and distribution planning model is proposed in this paper to tackle the compromised sales prices and the total profit problem of a multi-echelon supply chain n...
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A multi-product, multi-stage, and multi-period production and distribution planning model is proposed in this paper to tackle the compromised sales prices and the total profit problem of a multi-echelon supply chain network with uncertain sales prices. This model is constructed as a mixed-integer nonlinear programming problem to achieve a maximum total profit of the whole network and to guarantee the maximum satisfactory levels of sellers' and buyers' preference on sales prices. For the purpose that a compensatory solution among all participants of the supply chain can be achieved, a fuzzy decision-making method is proposed and, by means of applying it to a numerical example, proved effective in providing a compromised solution in a multi-echelon supply chain network.
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