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10th International Conference on Computer Aided Design in Engineering (OPTI 2007)

作者： Kravanja, S. Zula, T. Univ Maribor Fac Civil Engn Maribor Slovenia

ISBN: (纸本)9781845640705

This paper presents the cost optimization of a single-storey industrial steel building structure. The optimization is performed by the mixed-integer non-linear programming approach, MINLP. The structure consists of the main portal frames, which are mutually connected with the purlins. All structural elements are proposed to be built up of standard hot rolled I sections. The MINLP performs the simultaneous cost, topology and discrete sizes optimization of the building structure. Since the discrete/continuous optimization problem is non-convex and highly non-linear, the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm has been used for the optimization. Alongside the optimal structure's costs, the optimal number of main portal frames and purlins as well as all standard cross-section sizes have been obtained.

关键词： structural optimization cost optimization topology optimization discrete sizes optimization mixed-integer non-linear programming MINLP industrial building

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A variable time transformation method for mixed-integer optimal control problems

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OPTIMAL CONTROL APPLICATIONS & METHODS 2006年第3期27卷 169-182页

作者： Gerdts, M Univ Hamburg Dept Math D-20146 Hamburg Germany

The article discusses a variable time transformation method for the approximate solution of mixed-integer non-linear optimal control problems (MIOCP). Such optimal control problems enclose real-valued and discrete-valued controls. The method transforms MIOCP using a discretization into an optimal control problem with only real-valued controls. The latter can be solved efficiently by direct shooting methods. Numerical results are obtained for a problem from automobile test-driving that involves a discrete-valued control for the gear shift of the car. The results are compared to those obtained by Branch&Bound and show a drastic reduction of computation time. This very good performance makes the suggested method applicable even for many discretization points. Copyright (C) 2006 John Wiley & Sons, Ltd.

关键词： optimal control mixed-integer non-linear programming direct discretization method

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A multipurpose parallel genetic hybrid algorithm for non-linear non-convex programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第1期152卷 195-214页

作者： Östermark, R Abo Akad Univ Dept Business Adm FIN-20500 Turku Finland

The genetic hybrid algorithm (GHA) is a general-purpose algorithm, spanning several areas of mathematical problem solving. GHA makes calls to an (empty) accelerator function at key stages of the solution process, providing it with the current population of solution vectors in the argument list of the function. On return from the accelerator, GHA processes the population further. The user has control over the specific stage (generation of a new population, crossover, mutation etc.) and can modify the population of solution vectors, e.g., by making calls to special purpose algorithms through the accelerator channel. If needed, the steps of GHA can be partly or completely superseded by the special purpose mathematical/artificial intelligence based algorithm. The system can be used as a package for classical mathematical programming with the genetic sub-block deactivated. On the other hand, the algorithm can be turned into a machinery for stochastic analysis (e.g. for Monte Carlo simulation, time series modelling or neural networks), where the mathematical programming and genetic computing facilities are deactivated. Finally, pure evolutionary computation can be activated for studying genetic phenomena. As a completely new feature, we design and implement a flexible multicomputer framework for the basic GHA. (C) 2002 Elsevier B.V. All rights reserved.

关键词： discontinuous functions non-convexity mixed-integer non-linear programming evolutionary computation

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Supporting supply chain planning and scheduling decisions in the oil and chemical industry

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COMPUTERS & CHEMICAL ENGINEERING 2004年第6-7期28卷 863-870页

作者： Lasschuit, W Thijssen, N Shell Global Solut Int NL-2501 CM The Hague Netherlands

In the downstream oil and chemical industry, planning and scheduling are resource-intensive, complex, rolling processes. Decisions are taken at different stages within the supply chain (supply, manufacturing and distribution) and at different levels in the management hierarchy (planning, scheduling and operations). They differ in business scope, time horizon & resolution, data certainty & accuracy, process detail and optimizing mechanism. Aligning each step of this complex process is critical to competitive advantage. Decision support tools must therefore be provided within a coherent framework, including mechanisms which allow consistent economic and operational steering, taking due account of available (real-time) information on actual operations and market economics. At the strategic and global planning level for a network of manufacturing plants, decisions have to be taken on feedstock procurement & distribution, utilization of production capacities, utilization of modes of transport and demand allocation. Not only existing capabilities have to be considered, but also new opportunities in all areas have to be evaluated. The resulting mathematical programming model is a mixed-integer non-linear programming (MINLP) model: integer aspects arise because of e.g. fixed costs/investment costs, tiered pricing and cargo costs. non-linear relations are mainly caused by multiplication of quantity and economic variables. In the presentation, the various strategic planning problem areas, the contents of the MINLP aspects and the implemented solution approach will be further elaborated. The use of such models during the aforementioned (strategic) decision-taking process yields substantial benefits not only in economic terms but also in an improved understanding of the interactions between the various components of the business. (C) 2003 Published by Elsevier Ltd.

关键词： strategic business planning mixed-integer non-linear programming

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Supporting supply chain planning and scheduling decisions in the oil and chemical industry

Supporting supply chain planning and scheduling decisions in...

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International Conference on Foundations of Computer-Aided Process Operations

作者： Lasschuit, W Thijssen, N Shell Global Solut Int NL-2501 CM The Hague Netherlands

关键词： strategic business planning mixed-integer non-linear programming

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Solving Pseudo-Convex mixed integer Optimization Problems by Cutting Plane Techniques

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OPTIMIZATION AND ENGINEERING 2002年第3期3卷 253-280页

作者： Westerlund, Tapio Porn, Ray Abo Akad Univ Proc Design Lab FIN-20500 Turku Finland Swedish Polytech Technol & Commun FIN-65200 Vaasa Finland

In the present paper a cutting plane approach to solve mixed-integer non-linear programming (MINLP) problems, containing pseudo-convex functions, is given. It is shown how valid cutting planes for pseudo convex functions can be obtained and, furthermore, it is shown how a class of non-convex MINLP problems with a pseudo-convex objective function and pseudo-convex constraints, can be solved to global optimality with the considered cutting plane technique. Finally the numerical efficiency of the procedure, when solving some example problems, is illustrated.

关键词： optimization mixed-integer non-linear programming integer non-linear programming quasi-convex functions pseudo-convex functions non-convex MINLP problems extended cutting plane method

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Comparison of certain MINLP algorithms when applied to a model structure determination and parameter estimation problem

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COMPUTERS & CHEMICAL ENGINEERING 1998年第12期22卷 1829-1835页

作者： Skrifvars, H Leyffer, S Westerlund, T Abo Akad Univ Dept Chem Engn FIN-20500 Turku Finland Univ Dundee Dept Math & Comp Sci Dundee DD1 4HN Scotland

The maximum likelihood method is frequently used in parameter estimation. If the structure of the model is unknown, the maximization of the likelihood function can be replaced by minimizing an information criterion. One criterion that allows this to be done is Akaike's information criterion (AIC). Minimizing the AIC is a mixed integer non-linear programming (MINLP) problem. In this paper, three different MINLP algorithms are compared in the solution of a simultaneous model structure determination and parameter estimation problem by minimizing the AIC criterion. The problem considered appears in quantitative Fourier transformed infra red (FTIR) spectroscopy where concentration estimates of certain gas components are to be obtained from measured absorbances at different wave numbers. The resulting problem is a large MINLP problem containing several hundreds, or even thousands, of variables including a huge number of possible model structures. It is, however, found that the studied algorithms solve the considered problem in quite a small number of iterations and a reasonable CPU-time. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： identification estimation maximum likelihood optimization mixed-integer non-linear programming

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An extended cutting plane method for a class of non-convex MINLP problems

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COMPUTERS & CHEMICAL ENGINEERING 1998年第3期22卷 357-365页

作者： Westerlund, T Skrifvars, H Harjunkoski, I Porn, R Abo Akad Univ Proc Design Lab FIN-20500 Turku Finland Abo Akad Univ Dept Math FIN-20500 Turku Finland

An extended cutting plane method is introduced. The extended method can be applied in the solution of a class of non-convex MINLP (mixed-integer non-linear programming) problems, although the method was originally introduced for the solution of convex problems only. Global convergence properties of the method are given for pseudo-convex MINLP problems in the present paper and a numerical example from the paper-converting industry is finally provided to illustrate the numerical procedure. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： optimization mixed-integer non-linear programming integer non-linear programming quasi-convex functions pseudo-convex functions extended cutting plane method

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The MINLP optimization approach to structural synthesis - Part II: Simultaneous topology, parameter and standard dimension optimization by the use of the linked two-phase MINLP strategy

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 1998年第2期43卷 293-328页

作者： Kravanja, S Kravanja, Z Bedenik, BS Univ Maribor Fac Civil Engn SI-2000 Maribor Slovenia Univ Maribor Fac Chem & Chem Engn SI-2000 Maribor Slovenia

Part II describes the mixed-integer non-linear programming (MINLP) approach to structural synthesis where standard dimensions are added to simultaneous topology and parameter optimization. For this purpose, the mechanical superstructure has been enhanced and a special MINLP-MS model formulation for mechanical superstructures from Part I adapted to standard dimension alternatives, which give rise to complex MINLP problems that are difficult to solve. A Linked Two-Phase MINLP Strategy has been developed to efficiently accelerate the Solutions of highly combinatorial MINLP problems, performed by the Modified OA/ER algorithm. In the first phase, the strategy uses only continuous dimensions making it easier to find an optimal topology. Based on the obtained global linear approximation of the superstructure, the proposed strategy in the second phase continues to perform an overall simultaneous optimization, where standard dimensions are added as additional discrete optimization alternatives. Thus, simultaneous topology, parameter and standard dimension optimization is now performed in the second phase. The synthesis of a multiple cantilever beam, introduced in Part I, was performed in accordance with the steps proposed by the MINLP optimization approach. This approach enables the obtaining of additional savings when compared to the one in Part I. (C) 1998 John Wiley & Sons, Ltd.

关键词： structural synthesis optimization topology optimization discrete variable optimization mixed-integer non-linear programming MINLP the Modified OA/ER algorithm MINLP strategy

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The MINLP optimization approach to structural synthesis - Part III: Synthesis of roller and sliding hydraulic steel gate structures

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 1998年第2期43卷 329-364页

作者： Kravanja, S Kravanja, Z Bedenik, BS Univ Maribor Fac Civil Engn SI-2000 Maribor Slovenia Univ Maribor Fac Chem & Chem Engn SI-2000 Maribor Slovenia

Part III of this three-part series of papers describes the synthesis of roller and sliding hydraulic steel gate structures performed by the mixed-integer non-linear programming (MINLP) approach. The MINLP approach enables the determination of the optimal number of gate structural elements (girders, plates), optimal gate geometry, optimal intermediate distances between structural elements and all continuous and standard crossectional sizes. For this purpose, special logical constraints for topology alterations and interconnection relations between the alternative and fixed structural elements are formulated. They have been embedded into a mathematical optimization model for roller and sliding steel gate structures GATOP. GATOP has been developed according to a special MINLP model formulation for mechanical superstructures (MINLP-MS), introduced in Parts I and II. The model contains an economic objective function of self-manufacturing and transportation costs of the gate. As the GATOP model is non-convex and highly non-linear, it is solved by means of the Modified OA/ER algorithm accompanied by the Linked Two-Phase MINLP Strategy, both implemented in the TOP computer code. An example of the synthesis is presented as a comparative design research work of the already erected roller gate, the so-called Intake Gate in Aswan II in Egypt. The optimal result yields 29.4 per cent of net savings when compared to the actual costs of the erected gate;(C) 1998 John Wiley & Sons, Ltd.

关键词： structural synthesis optimization topology optimization discrete variable optimization mixed-integer non-linear programming MINLP the Modified OA/ER algorithm MINLP strategy hydraulic gate sliding gate roller gate Aswan

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