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A Memetic Algorithm for Global optimization in Chemical Process Synthesis Problems

IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2011年第5期15卷 659-683页

作者： Urselmann, Maren Barkmann, Sabine Sand, Guido Engell, Sebastian Tech Univ Dortmund Dept Biochem & Chem Engn D-44227 Dortmund Germany Bayer Technol Serv GmbH D-51368 Leverkusen Germany ABB Corp Res D-68526 Ladenburg Germany

Design optimization problems in chemical engineering and in many other engineering domains are characterized by the presence of a large number of discrete and continuous decision variables, complex nonlinear models that restrict the search space, nonlinear cost functions, and the presence of many local optima. The classical approach to such problems are mixed integer nonlinear program solvers that work on a superstructure formulation which explicitly represents all design alternatives. The structural decisions lead to a large number of discrete variables and an exponential increase in the computational effort. The mathematical programming (MP) methods which are usually employed to solve the continuous subproblems that arise by fixing the discrete variables provide only one local optimum which depends strongly on the initialization. Thus standard methods may not find the global optimum despite long computation times. In this contribution we introduce a memetic algorithm (MA) for the global optimization of a computational demanding real-world design problem from the chemical engineering domain. The MA overcomes the problem of getting stuck in local optima by the use of an evolution strategy (ES) which addresses the global optimization of the design decisions, whereas a robust MP solver is used to handle complex nonlinear constraints as well as to improve the individuals of the ES by performing a local search in continuous sub-spaces in an integrated fashion. The MA is discussed in detail, the novel decomposition of the problem class at hand is analyzed and the MA is tested for the example of the optimal design of a reactive distillation column with several thousand decision variables. The MA is the only algorithm that finds the global solution in reasonable computation times. The introduction of structural decisions and additional constraints and discontinuous penalty terms lead only to a moderate increase in the computational effort which demonstrates the potential o

关键词： Chemical process synthesis global optimization memetic algorithm mixed-integer nonlinear optimization

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A profit-maximization location-capacity model for designing a service system with risk of service interruptions

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2016年 96卷 113-134页

作者： Hoseinpour, Pooya Ahmadi-Javid, Amir Amirkabir Univ Technol Dept Ind Engn Tehran Iran

This paper considers the design of an immobile service system in which each facility's service process is subject to the risk of interruptions. The location-capacity decisions and allocations are simultaneously made to maximize the difference between the service provider's profit and the sum of customers' transportation and waiting costs. An efficient Lagrangian-based solution algorithm is developed, which solves large-sized instances with up to 50 service facilities and 500 customers in a few seconds. Several sensitivity analyses and managerial insights are presented. The model is also applied to a case study on a logistics network design problem in the zinc mining industry. (C) 2016 Published by Elsevier Ltd.

关键词： Location-allocation problem Service system design Congested network Queue systems with service interruptions mixed-integer nonlinear optimization Lagrangian relaxation

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Portfolio selection with divisible and indivisible assets: Mathematical algorithm and economic analysis

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ANNALS OF OPERATIONS RESEARCH 2007年第1期152卷 273-295页

作者： Lazimy, Rafael Univ Wisconsin Grainger Hall975 Univ Ave Madison WI 53706 USA

We extend the classic mean-variance framework to a broad class of investment decisions under risk where investors select optimal portfolios of risky assets that include perfectly divisible as well as perfectly indivisible assets. We develop an algorithm for solving the associated mixed-integer nonlinear program and report on the results of a computational study. We then study the mean-variance structure of the investment frontier facing an individual investor in the presence of investment opportunities in both risky divisible and indivisible assets. Finally, we analyze the economic implications of the presence of investment opportunities in risky indivisible assets on the investor's investment strategy and on his risk evaluation.

关键词： portfolio selection mean-variance analysis asset pricing divisible and indivisible assets mixed-integer nonlinear optimization outer-approximation relaxation

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Global optimization in the 21st century: Advances and challenges

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COMPUTERS & CHEMICAL ENGINEERING 2005年第6期29卷 1185-1202页

作者： Floudas, CA Akrotirianakis, IG Caratzoulas, S Meyer, CA Kallrath, J Princeton Univ Dept Chem Engn Princeton NJ 08544 USA BASF G Sci Comp D-67056 Ludwigshafen Germany Univ Florida Dept Astron Gainesville FL 32611 USA

This paper presents an overview of the research progress in global optimization during the last 5 years (1998-2003), and a brief account of our recent research contributions. The review part covers the areas of (a) twice continuously differentiable nonlinear optimization, (b) mixed-integer nonlinear optimization, (c) optimization with differential-algebraic models, (d) optimization with grey-box/black-box/nonfactorable models, and (e) bilevel nonlinear optimization. Our research contributions part focuses on (i) improved convex underestimation approaches that include convex envelope results for multilinear functions, convex relaxation results for trigonometric functions, and a piecewise quadratic convex underestimator for twice continuously differentiable functions, and (ii) the recently proposed novel generalized alpha BB framework. Computational studies will illustrate the potential of these advances. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： global optimization nonlinear optimization mixed-integer nonlinear optimization differential-algebraic optimization optimization with nonfactorable/grey-box models bilevel nonlinear optimization nonconvexities convex envelopes convex underestimators trilinear monomials trigonometric functions twice continuously differentiable functions

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A mixed-integer simulation-based optimization approach with surrogate functions in water resources management

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optimization AND ENGINEERING 2008年第4期9卷 341-360页

作者： Hemker, Thomas Fowler, Kathleen R. Farthing, Matthew W. von Stryk, Oskar Tech Univ Darmstadt Dept Comp Sci Simulat Syst Optimizat & Robot Grp D-64289 Darmstadt Germany Clarkson Univ Dept Math Clarkson Ctr Environm Potsdam NY 13676 USA Univ N Carolina Dept Environm Sci & Engn Ctr Integrated Study Environm Chapel Hill NC 27599 USA

Efficient and powerful methods are needed to overcome the inherent difficulties in the numerical solution of many simulation-based engineering design problems. Typically, expensive simulation codes are included as black-box function generators;therefore, gradient information that is required by mathematical optimization methods is entirely unavailable. Furthermore, the simulation code may contain iterative or heuristic methods, low-order approximations of tabular data, or other numerical methods which contribute noise to the objective function. This further rules out the application of Newton-type or other gradient-based methods that use traditional finite difference approximations. In addition, if the optimization formulation includes integer variables the complexity grows even further. In this paper we consider three different modeling approaches for a mixed-integer nonlinear optimization problem taken from a set of water resources benchmarking problems. Within this context, we compare the performance of a genetic algorithm, the implicit filtering algorithm, and a branch-and-bound approach that uses sequential surrogate functions. We show that the surrogate approach can greatly improve computational efficiency while locating a comparable, sometimes better, design point than the other approaches.

关键词： mixed-integer nonlinear optimization computational engineering simulation-based optimization groundwater management surrogate optimization

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Expansion Planning of Medium Voltage Distribution Networks 50

Expansion Planning of Medium Voltage Distribution Networks

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50th International Universities Power Engineering Conference (UPEC)

作者： Mansor, Nurulafiqah Nadzirah Binti Levi, Victor Univ Manchester Manchester M13 9PL Lancs England

ISBN: (纸本)9781467396820

The paper proposes a new methodology for optimal planning of medium voltage distribution networks. The overall model is presented as a two-stage optimization model, where the first stage deals with the investment part and the second stage focuses on the operation part. The novelty of the proposed model is demonstrated through the explicit incorporation of network security constraints in the mathematical model, in line with the UK planning standards, while taking into consideration different operating regimes with changing load and generation profiles, integration of new distributed generation units, construction of circuits on new corridors and optimal network reconfiguration. The highly complex mixed-integer nonlinear optimization model is applied to a few practical medium-voltage test systems of up to 120 nodes using a dedicated commercial software package. Some of the characteristics results are examined and highlighted in this paper. Additionally, sensitivity analyses are done to determine critical parameters affecting the development and performance of medium voltage distribution networks.

关键词： mixed-integer nonlinear optimization planning of distribution networks sensitivity studies UK security criteria

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Development of Distribution Networks with Low Carbon Technologies

Development of Distribution Networks with Low Carbon Technol...

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IEEE Innovative Smart Grid Technologies - Asia (ISGT ASIA 2015)

作者： Mansor, Nurulafiqah Nadzirah Levi, Victor Univ Manchester Dept Elect & Elect Engn Manchester Lancs England

ISBN: (纸本)9781509012374

A new methodology for optimal development of distribution networks with low carbon technologies is proposed in this paper. The complete planning model is developed as a two-stage optimization process, where the first stage deals with the investment problem and the second stage focuses on the operational aspects. The novelty of the proposed investment model is explicit incorporation of network security constraints in the optimization formulation in line with the UK planning standards, while taking into consideration different operating regimes with changing load and generation profiles. Connection of new distributed generation units and new types of demands, construction of circuits on new corridors and optimal network reconfiguration, as well as real-life restoration rules are also included in the model. The investment problem is defined as the complex mixed-integer nonlinear optimization model and solved using a dedicated commercial software package. It is applied to a few practical medium-voltage test systems. Additionally, sensitivity analyses are done to determine critical parameters affecting the development and performance of medium voltage distribution networks.

关键词： Planning of distribution networks mixed-integer nonlinear optimization UK security criteria sensitivity studies

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Analytical Solution to the Radiotherapy Fractionation Problem Including Dose Bound Constraints

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Operations Research Forum 2022年第3期3卷 40页

作者： Fernández, Luis A. Fernández, Lucía Dep. Mathematics Statistics and Computation Universidad de Cantabria (SPAIN) Santander Cantabria Spain

This paper deals with the classic radiotherapy dose fractionation problem for cancer tumors concerning the following goals: (a)To maximize the effect of radiation on the tumor, restricting the effect produced to an organ at risk (healing approach).(b)To minimize the effect of radiation on one organ at risk, while maintaining enough effect of radiation on the tumor (palliative approach). We will assume the linear-quadratic model to characterize the radiation effect without considering the tumor repopulation between doses. The main novelty with respect to previous works concerns the presence of minimum and maximum dose fractions, to achieve the minimum effect and to avoid undesirable side effects, respectively. We have characterized in which situations is more convenient the hypofractionated protocol (deliver few fractions with high dose per fraction) and in which ones the hyperfractionated regimen (deliver a large number of lower doses of radiation) is the optimal strategy. In all cases, analytical solutions to the problem are obtained in terms of the data. © 2022, The Author(s).

关键词： Fractionation Linear quadratic model mixed-integer nonlinear optimization Radiotherapy

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An Outer-Approximation Algorithm for Maximum-Entropy Sampling 7th

An Outer-Approximation Algorithm for Maximum-Entropy Samplin...

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7th International Symposium on Combinatorial optimization (ISCO)

作者： Fampa, Marcia Lee, Jon Univ Fed Rio de Janeiro Rio De Janeiro Brazil Univ Michigan Ann Arbor MI USA

We apply the well-known MINLO outer-approximation algorithm (OA) to the maximum-entropy sampling problem (MESP), using the linx and NLP convex relaxations for MESP. We enhance our approach using disjunctive cuts.

ISBN: (纸本)9783031185298;9783031185304

关键词： Maximum-entropy sampling mixed-integer nonlinear optimization Outer approximation Disjunctive cuts No-good

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Global optimization in the 21st century: Advances and challenges

Global optimization in the 21st century: Advances and challe...

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14th European Symposium on Computer Aided Process Engineering (ESCAPE-14)

ISBN: (纸本)0444516948

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