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IAs based approach for reliability redundancy allocation problems

APPLIED MATHEMATICS AND COMPUTATION 2006年第2期182卷 1556-1567页

作者： Chen, Ta-Cheng Natl Formosa Univ Dept Informat Management Yuanlin 632 Taiwan

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.

关键词： reliability design immune algorithm mixed-integer nonlinear programming

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Optimal price and quantity determination for retail electric power contracts

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IEEE TRANSACTIONS ON POWER SYSTEMS 2006年第1期21卷 180-187页

作者： Gabriel, SA Conejo, AJ Plazas, MA Balakrishnan, S Univ Maryland Dept Civil & Environm Engn College Pk MD 20742 USA Univ Castilla La Mancha Dept Elect Engn E-13071 Ciudad Real Spain ANB Enterprises Inc Sugar Land TX 77479 USA

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.

关键词： contract design electricity market mixed-integer nonlinear programming retailer viewpoint stochastic optimization

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Fuzzy chance constrained programming model for refinery short-term scheduling problem

Fuzzy chance constrained programming model for refinery shor...

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9th International Conference on Control, Automation, Robotics and Vision

作者： Cuiwen, C. Bin, J. Xingsheng, G. E China Univ Sci & Technol Res Inst Automat Shanghai Peoples R China Shanghai Dianji Univ Dept Elect Engn Shanghai Peoples R China

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.

关键词： crude oil short-term scheduling fuzzy chance constrained mixed-integer nonlinear programming

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On the solution of mixed-integer nonlinear programming models for computer aided molecular design

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COMPUTERS & CHEMISTRY 2002年第6期26卷 645-660页

作者： Ostrovsky, GM Achenie, LEK Sinha, M Univ Connecticut Dept Chem Engn Storrs CT 06269 USA

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.

关键词： global optimization linear underestimators computer aided molecular design branch-and-bound procedure mixed-integer nonlinear programming

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Simultaneous synthesis of mass exchange networks for waste minimization

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COMPUTERS & CHEMICAL ENGINEERING 2005年第7期29卷 1561-1576页

作者： Chen, CL Hung, PS Natl Taiwan Univ Dept Chem Engn Taipei 10617 Taiwan

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.

关键词： mass exchange network synthesis superstructure mixed-integer nonlinear programming

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A polyhedral branch-and-cut approach to global optimization

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MATHEMATICAL programming 2005年第2期103卷 225-249页

作者： Tawarmalani, M Sahinidis, NV Purdue Univ Krannert Sch Management W Lafayette IN 47907 USA Univ Illinois Dept Chem & Biomol Engn Urbana IL 61801 USA

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 nonlinear programming 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.

关键词： mixed-integer nonlinear programming outer approximation convexification factorable programming convexity identification

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An exact solution method for reliability optimization in complex systems

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ANNALS OF OPERATIONS RESEARCH 2005年第1-4期133卷 129-148页

作者： Li, D Sun, XL McKinnon, K Chinese Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China Shanghai Univ Dept Math Shanghai 200436 Peoples R China Univ Edinburgh Sch Math Edinburgh EH9 3JZ Midlothian Scotland

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.

关键词： reliability optimization complex system global optimization convexification method mixed-integer nonlinear programming branch-and-bound

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Optimization of multi-echelon supply chain networks with uncertain sales prices

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JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 2004年第7期37卷 822-834页

作者： Chen, CL Lee, WC Natl Taiwan Univ Dept Chem Engn Taipei 10617 Taiwan

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.

关键词： process systems engineering supply chain management uncertainty mixed-integer nonlinear programming fuzzy optimization

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A single-stage supply chain system controlled by kanban under just-in-time philosophy

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2004年第5期55卷 485-494页

作者： Wang, S Sarker, BR Louisiana State Univ Dept Ind & Mfg Syst Engn Baton Rouge LA 70803 USA SE Missouri State Univ Cape Girardeau MO 63701 USA

The production system using kanban was pioneered by Toyota Motor Company in Japan and subsequently it was adopted by numerous other Japanese and US companies for applying the just-in-time manufacturing principles. This research studies a single-stage supply chain system that is controlled by kanban mechanism. The supply chain system is modelled as a mixed-integer nonlinear programming (MINLP) problem. It is solved optimally by branch-and-bound method to determine the number of kanbans, batch size, number of batches, and the total quantity over one period. Meanwhile. the kanban operation between two adjacent plants is worked out considering the factors of loading and unloading time. and transport time. Coupled with plant-wide efforts for cost control and management commitment to enhance other measures of performance, a logistics system for controlling the production as well,is the supply chain system is developed. which results in minimizing the total cost of the supply chain system. The results show that the improvements in reduction of inventory, wasted labour, and customer service in a supply chain are accomplished through the kanban mechanism.

关键词： kanban supply chain inventory control mixed-integer nonlinear programming

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Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices

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COMPUTERS & CHEMICAL ENGINEERING 2004年第6-7期28卷 1131-1144页

作者： Chen, CL Lee, WC Natl Taiwan Univ Dept Chem Engn Taipei 10617 Taiwan

A multi-product, multi-stage, and multi-period scheduling model is proposed in this paper to deal with multiple incommensurable goals for a multi-echelon supply chain network with uncertain market demands and product prices. The uncertain market demands are modeled as a number of discrete scenarios with known probabilities, and the fuzzy sets are used for describing the sellers' and buyers' incompatible preference on product prices. The supply chain scheduling model is constructed as a mixed-integer nonlinear programming problem to satisfy several conflict objectives, such as fair profit distribution among all participants, safe inventory levels, maximum customer service levels, and robustness of decision to uncertain product demands, therein the compromised preference levels on product prices from the sellers and buyers point of view are simultaneously taken into account. The inclusion of robustness measures as part of objectives can significantly reduce the variability of objective values to product demand uncertainties. For purpose that a compensatory solution among all participants of the supply chain can be achieved, a two-phase fuzzy decision-making method is presented and, by means of application of it to a numerical example, proved effective in providing a compromised solution in an uncertain multi-echelon supply chain network. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： supply chain management uncertainty robustness multiple objectives mixed-integer nonlinear programming fuzzy optimization

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