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Strengthening of lower bounds in the global optimization of Bilinear and Concave Generalized Disjunctive Programs

COMPUTERS & CHEMICAL ENGINEERING 2010年第6期34卷 914-930页

作者： Ruiz, Juan P. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

This paper is concerned with global optimization of Bilinear and Concave Generalized Disjunctive Programs. A major objective is to propose a procedure to find relaxations that yield strong lower bounds. We first present a general framework for obtaining a hierarchy of linear relaxations for nonconvex Generalized Disjunctive Programs (GDP). This framework combines linear relaxation strategies proposed in the literature for nonconvex MINLPs with the results of the work by Sawaya and Grossmann (2009) for Linear GDPs. We further exploit the theory behind Disjunctive programming by proposing several rules to guide more efficiently the generation of relaxations by considering the particular structure of the problems. Finally, we show through a set of numerical examples that these new relaxations can substantially strengthen the lower bounds for the global optimum, often leading to a significant reduction of the number of nodes when used within a spatial branch and bound framework. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Disjunctive programming mixed-integer nonlinear programming Global optimization Relaxations

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A Multi-Objective Optimization Approach to Polygeneration Energy Systems Design

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AICHE JOURNAL 2010年第5期56卷 1218-1234页

作者： Liu, Pei Pistikopoulos, Efstratios N. Li, Zheng Univ London Imperial Coll Sci Technol & Med CPSE Dept Chem Engn London SW7 2AZ England Tsinghua Univ Dept Thermal Engn Beijing 100084 Peoples R China

Polygeneration, typically involving co-production of methanol and electricity, is a promising energy conversion technology which provides opportunities for high energy utilization efficiency and low/zero emissions. The optimal design of such a complex, large-scale and highly nonlinear process system poses significant challenges. In this article, we present a multiobjective optimization model for the optimal design of a methanol/electricity poly generation plant. Economic and environmental criteria are simultaneously optimized over a superstructure capturing a number of possible combinations of technologies and types of equipment. Aggregated models are considered, including a detailed methanol synthesis step with chemical kinetics and phase equilibrium considerations. The resulting model is formulated as a non-convex mixed-integer nonlinear programming problem. Global optimization and parallel computation techniques are employed to generate an optimal Pareto frontier. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 1218-1234, 2010

关键词： polygeneration process design mixed-integer nonlinear programming global multiobjective optimization parallel computation

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Sensitivity-Based Approaches for Handling Discrete Variables in Optimal Power Flow Computationse

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IEEE TRANSACTIONS ON POWER SYSTEMS 2010年第4期25卷 1780-1789页

作者： Capitanescu, Florin Wehenkel, Louis Univ Liege Dept Elect Engn & Comp Sci B-4000 Liege Belgium

This paper proposes and compares three iterative approaches for handling discrete variables in optimal power flow (OPF) computations. The first two approaches rely on the sensitivities of the objective and inequality constraints with respect to discrete variables. They set the discrete variables values either by solving a mixed-integer linear programming (MILP) problem or by using a simple procedure based on a merit function. The third approach relies on the use of Lagrange multipliers corresponding to the discrete variables bound constraints at the OPF solution. The classical round-off technique and a progressive round-off approach have been also used as a basis of comparison. We provide extensive numerical results with these approaches on four test systems with up to 1203 buses, and for two OPF problems: loss minimization and generation cost minimization, respectively. These results show that the sensitivity-based approach combined with the merit function clearly outperforms the other approaches in terms of: objective function quality, reliability, and computational times. Furthermore, the objective value obtained with this approach has been very close to that provided by the continuous relaxation OPF. This approach constitutes therefore a viable alternative to other methods dealing with discrete variables in an OPF.

关键词： Discrete variables mixed-integer linear programming mixed-integer nonlinear programming nonlinear programming optimal power flow

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Optimizing the design of complex energy conversion systems by Branch and Cut

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COMPUTERS & CHEMICAL ENGINEERING 2010年第8期34卷 1226-1236页

作者： Ahadi-Oskui, Turang Vigerske, Stefan Nowak, Ivo Tsatsaronis, George Humboldt Univ Dept Math D-10099 Berlin Germany Tech Univ Berlin Inst Energy Engn D-10587 Berlin Germany

The paper examines the applicability of mathematical programming methods to the simultaneous optimization of the structure and the operational parameters of a combined-cycle-based cogeneration plant. The optimization problem is formulated as a nonconvex mixed-integer nonlinear problem (MINLP) and solved by the MINLP solver LaGO. The algorithm generates a convex relaxation of the MINLP and applies a Branch and Cut algorithm to the relaxation. Numerical results for different demands for electric power and process steam are discussed and a sensitivity analysis is performed. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Cogeneration plant Energy conversion system Design optimization Global optimization mixed-integer nonlinear programming Convex relaxation

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A Hybrid Tabu Search Heuristic for a Bilevel Competitive Facility Location Model

A Hybrid Tabu Search Heuristic for a Bilevel Competitive Fac...

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7th International Workshop on Hybrid Metaheuristics

作者： Kucukaydin, Hande Aras, Necati Altinel, I. Kuban Bogazici Univ Dept Ind Eng Istanbul Turkey

ISBN: (纸本)9783642160530

We consider a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor. The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit. The competitor, on the other hand, can react by adjusting the attractiveness of its existing facilities, opening new facilities and/or closing existing ones with the objective of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at prespecified candidate sites. We employ Huff's gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. In order to find a feasible solution of this model, we develop a hybrid tabu search heuristic which makes use of two exact methods as subroutines: a gradient ascent method and a branch-and-bound algorithm with nonlinear programming relaxation.

关键词： Tabu search competitive facility location bilevel programming mixed-integer nonlinear programming

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Multi-objective mixed integer strategy for the optimisation of biological networks

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IET SYSTEMS BIOLOGY 2010年第3期4卷 236-248页

作者： Sendin, J. O. H. Exler, O. Banga, J. R. IIM CSIC Spanish Natl Res Council Proc Engn Grp Vigo 36208 Spain Univ Bayreuth Dept Comp Sci D-95440 Bayreuth Germany

In this contribution, the authors consider multi-criteria optimisation problems arising from the field of systems biology when both continuous and integer decision variables are involved. Mathematically, they are formulated as mixed-integer non-linear programming problems. The authors present a novel solution strategy based on a global optimisation approach for dealing with this class of problems. Its usefulness and capabilities are illustrated with two metabolic engineering case studies. For these problems, the authors show how the set of optimal solutions (the so-called Pareto front) is successfully and efficiently obtained, providing further insight into the systems under consideration regarding their optimal manipulation.

关键词： complex networks biology computing integer decision variables Pareto front global optimisation approach mixed-integer nonlinear programming Pareto optimisation Systems theory applications in biology and medicine multiobjective mixed integer strategy General, theoretical, and mathematical biophysics multicriteria optimisation problems continuous decision variables Optimisation techniques systems biology nonlinear programming metabolic engineering biological network optimisation

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Optimal Plug-In Hybrid Electric Vehicle Design and Allocation for Minimum Life Cycle Cost, Petroleum Consumption, and Greenhouse Gas Emissions

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JOURNAL OF MECHANICAL DESIGN 2010年第9期132卷 091013-091013页

作者： Shiau, Ching-Shin Norman Kaushal, Nikhil Hendrickson, Chris T. Peterson, Scott B. Whitacre, Jay F. Michalek, Jeremy J. Carnegie Mellon Univ Pittsburgh PA 15213 USA

Plug-in hybrid electric vehicle (PHEV) technology has the potential to reduce operating cost, greenhouse gas (GHG) emissions, and petroleum consumption in the transportation sector. However, the net effects of PHEVs depend critically on vehicle design, battery technology, and charging frequency. To examine these implications, we develop an optimization model integrating vehicle physics simulation, battery degradation data, and U. S. driving data. The model identifies optimal vehicle designs and allocation of vehicles to drivers for minimum net life cycle cost, GHG emissions, and petroleum consumption under a range of scenarios. We compare conventional and hybrid electric vehicles (HEVs) to PHEVs with equivalent size and performance (similar to a Toyota Prius) under urban driving conditions. We find that while PHEVs with large battery packs minimize petroleum consumption, a mix of PHEVs with packs sized for similar to 25-50 miles of electric travel under the average U. S. grid mix (or similar to 35-60 miles under decarbonized grid scenarios) produces the greatest reduction in life cycle GHG emissions. Life cycle cost and GHG emissions are minimized using high battery swing and replacing batteries as needed, rather than designing underutilized capacity into the vehicle with corresponding production, weight, and cost implications. At 2008 average U. S. energy prices, Li-ion battery pack costs must fall below $590/kW h at a 5% discount rate or below $410/kW h at a 10% rate for PHEVs to be cost competitive with HEVs. Carbon allowance prices offer little leverage for improving cost competitiveness of PHEVs. PHEV life cycle costs must fall to within a few percent of HEVs in order to offer a cost-effective approach to GHG reduction. [DOI: 10.1115/1.4002194]

关键词： plug-in hybrid electric vehicle greenhouse gas emissions environmental policy design optimization mixed-integer nonlinear programming battery degradation vehicle design

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Recursive genetic algorithm-finite element method technique for the solution of transformer manufacturing cost minimisation problem

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IET ELECTRIC POWER APPLICATIONS 2009年第6期3卷 514-519页

作者： Georgilakis, P. S. Tech Univ Crete Dept Prod Engn & Management GR-73100 Khania Greece

The transformer manufacturing cost minimisation (TMCM), also known as transformer design optimisation, is a complex constrained mixed-integer non-linear programming problem with discontinuous objective function. This paper proposes an innovative method combining genetic algorithm (GA) and finite element method (FEM) for the solution of TMCM problem. The main contributions of the proposed method are: (a) introduction of an innovative recursive GA with a novel external elitism strategy associated with variable crossover and mutation rates resulting in an improved GA, (b) adoption of two particular finite element models of increased accuracy and high computational speed for the validation of the optimal design by computing the no-load loss and impedance and (c) combination of the innovative recursive GA with the two particular finite element models resulting in a proposed GA-FEM model that finds the global optimum, as concluded after several tests on actual transformer designs, while other existing methods provided suboptimal solutions that are 3.1-5.8% more expensive than the optimal solution.

关键词： genetic algorithms Optimisation techniques recursive genetic algorithm-finite element method technique transformer design optimisation transformer manufacturing cost minimisation discontinuous objective function nonlinear programming Transformers and reactors transformers finite element analysis mixed-integer nonlinear programming integer programming Finite element analysis

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Reactive Power and Voltage Control in Distribution Systems With Limited Switching Operations

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IEEE TRANSACTIONS ON POWER SYSTEMS 2009年第2期24卷 889-899页

作者： Liu, M. B. Canizares, Claudio A. Huang, W. S China Univ Technol Elect Power Coll Guangzhou Guangdong Peoples R China Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada Guangdong Power Grid Inc Foshan Power Supply Bur Foshan Guangdong Peoples R China

An algorithm based on a nonlinear interior-point method and discretization penalties is proposed in this paper for the solution of the mixed-integer nonlinear programming (MINLP) problem associated with reactive power and voltage control in distribution systems to minimize daily energy losses, with time-related constraints being considered. Some of these constraints represent limits on the number of switching operations of transformer load tap changers (LTCs) and capacitors, which are modeled as discrete control variables. The discrete variables are treated here as continuous variables during the solution process, thus transforming the MINLP problem into an NLP problem that can be more efficiently solved exploiting its highly sparse matrix structure;a strategy is developed to round these variables off to their nearest discrete values, so that daily switching operation limits are properly met. The proposed method is compared with respect to other well-known MINLP solution methods, namely, a genetic algorithm and the popular GAMS MINLP solvers BARON and DICOPT. The effectiveness of the proposed method is demonstrated in the well-known PG&E 69-bus distribution network and a real distribution system in the city of Guangzhou, China, where the proposed technique has been in operation since 2003.

关键词： Distribution systems genetic algorithms interior-point methods mixed-integer nonlinear programming nonlinear programming optimal switching operations optimization solvers reactive power control voltage control

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Optimal acquisition policy with quantity discounts and uncertain demands

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2009年第9期47卷 2409-2425页

作者： Zhang, Guoqing Ma, Liping Univ Windsor Dept Ind & Mfg Syst Engn Windsor ON N9B 3P4 Canada Aspen Technol Canada Ltd Calgary AB Canada

We study the acquisition policy decision problem for a supply network involving one manufacturer and multiple suppliers. The manufacturer produces multiple products under uncertain demands and each supplier provides price discounts. The problem is to determine the manufacturer's acquisition policy and production levels so as to maximise the manufacturer's expected profit, subject to both the manufacturer's and suppliers' capacities. We present a mixed integer nonlinear programming (MINLP) formulation of the problem, for both single- and multiple-sourcing procurement policies. General algebraic modeling system (GAMS) and its solvers, combining external integration functions, are employed to solve the complex MINLP problem. The preliminary computation results and managerial analysis are reported.

关键词： supplier selection uncertainty quantity discount mixed-integer nonlinear programming

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