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Sensitivity analysis in optimization and reliability problems

RELIABILITY ENGINEERING & SYSTEM SAFETY 2008年第12期93卷 1788-1800页

作者： Castillo, Enrique Minguez, Roberto Castillo, Carmen Univ Cantabria Dept Appl Math & Computat Sci E-39005 Santander Spain Univ Castilla La Mancha Dept Appl Math E-13071 Ciudad Real Spain Univ Castilla La Mancha Dept Civil Engn E-13071 Ciudad Real Spain

The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Failure modes non-linear programming Optimization, Probabilistic models Reliability analysis Safety factors Sensitivity analysis Bridge crane design Retaining wall Composite breakwaters Calculus of variations Slope stability

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A spreadsheet modeling approach to the Holt-Winters optimal forecasting

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第2期131卷 375-388页

作者： Segura, JV Vercher, E Univ Valencia Dept Estadist & Invest Operat E-46100 Valencia Spain Univ Miguel Hernandez Elche Dept Estadist & Matemat Aplicada Alicante 03202 Spain

The objective of this paper is to determine the optimal forecasting for the Holt-Winters exponential smoothing model using spreadsheet modeling. This forecasting procedure is especially useful for short-term forecasts for series of sales data or levels of demand for goods. The non-linear programming problem associated with this forecasting model is formulated and a spreadsheet model is used to solve the problem of optimization efficiently. Also, a spreadsheet makes it possible to work in parallel with various objective functions (measures of forecast errors) and different procedures for calculating the initial values of the components of the model. Using a scenario analysis, the set of local minima obtained may be visualized. We have solved some examples in order to illustrate this approach. (C) 2001 Elsevier Science B,V. All rights reserved.

关键词： forecasting exponential smoothing non-linear programming spreadsheet modelling

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Design optimization with chaos embedded great deluge algorithm

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APPLIED SOFT COMPUTING 2012年第3期12卷 1055-1067页

作者： Baykasoglu, Adil Dokuz Eylul Univ Fac Engn Dept Ind Engn TR-35160 Izmir Turkey

In this paper, the great deluge algorithm (GDA), which has not been previously used in constrained mechanical design optimization problems is employed to solve several design optimization problems selected from the literature. The GDA algorithm needs only one basic parameter to setup, which makes it very attractive for solving optimization problems. First time in this paper, an attempt is made to see whether it is possible to enhance the performance of a very simple algorithm like GDA to solve complex constrained non-linear design optimization problems by embedding chaotic maps in its neighborhood generation mechanism. Eight different chaotic maps are tested and compared in this paper. It is observed that chaotic maps can considerably improve the performance of GDA and enables it to find the best possible solutions for the studied problems. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Great deluge algorithm Chaotic maps Design optimization non-linear programming

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Thermodynamic simulation of transesterification reaction by Gibbs energy minimization

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FLUID PHASE EQUILIBRIA 2013年 341卷 12-22页

作者： Yancy-Caballero, Daison M. Guirardello, Reginaldo Univ Estadual Campinas UNICAMP Sch Chem Engn BR-13083852 Campinas SP Brazil

In this study, simultaneous chemical and phase equilibrium calculations were carried out by the method of direct Gibbs energy minimization to perform a thermodynamic analysis of transesterification reaction of soybean oil with both ethanol and methanol in order to improve the processes for producing biodiesel. The CONOPT solver was used to solve the problem as a nonlinear programming model in the GAMS (R) 23.2.1 software. In addition, the UNIFAC model was employed to describe the liquid phase non-idealities. A strategy of balance of radicals is proposed to satisfy the requirement of conservation of number of moles in the specific case of transesterification reaction, in order to take into account the degrees of freedom of reacting system without explicitly writing all individual reactions. The results showed that the use of optimization techniques associated with the GAMS software are useful and efficient tools to calculate the chemical and phase equilibrium by minimizing of the Gibbs energy, provided that different initial guesses are used. Furthermore, the computational times spent in the calculations were quite small. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Biodiesel Gibbs energy minimization Chemical and phase equilibrium non-linear programming GAMS

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Efficient heuristic algorithm used for optimal capacitor placement in distribution systems

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2010年第1期32卷 71-78页

作者： Segura, Silvio Romero, Ruben Rider, Marcos J. Univ Estadual Campinas Dept Elect Energy Syst Sao Paulo Brazil Univ Estadual Paulista Fac Engn Ilha Solteira Sao Paulo Brazil

An efficient heuristic algorithm is presented in this work in order to solve the optimal capacitor placement problem in radial distribution systems. The proposal uses the solution from the mathematical model after relaxing the integrality of the discrete variables as a strategy to identify the most attractive bus to add capacitors to each step of the heuristic algorithm. The relaxed mathematical model is a nonlinear programming problem and is solved using a specialized interior point method, The algorithm still incorporates an additional strategy of local search that enables the finding of a group of quality solutions after small alterations in the optimization strategy. Proposed solution methodology has been implemented and tested in known electric systems getting a satisfactory outcome compared with metaheuristic methods. The tests carried out in electric systems known in specialized literature reveal the satisfactory outcome of the proposed algorithm compared with metaheuristic methods. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Optimal capacitor placement Distribution systems Heuristic algorithms non-linear programming Radial power flow

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A class of globally convergent three-term Dai-Liao conjugate gradient methods

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APPLIED NUMERICAL MATHEMATICS 2020年 151卷 354-366页

作者： Yao, Shengwei Feng, Qinliang Li, Lue Xu, Jieqiong Guangxi Univ Finance & Econ Guangxi ASEAN Res Ctr Finance & Econ Nanning 530003 Peoples R China Guangxi Univ Finance & Econ Guangxi Key Lab Cultivat Base Cross Border Ecomme Nanning 530003 Peoples R China Guangxi Univ Finance & Econ Sch Informat & Stat Nanning 530003 Peoples R China Guangxi Univ Coll Math & Informat Sci Nanning 530009 Peoples R China

Due to their simple structure and low memory requirements, conjugate gradient methods are widely used for solving large-scale optimization problems. In this paper, combining Dai-Liao conjugacy condition with a modified symmetric Perry matrix, a class of three-term Dai-Liao conjugate gradient algorithms are proposed. The given methods possess both Dai-Liao conjugacy condition and sufficient descent condition. Meanwhile, the global convergence of the presented algorithms are established under Wolfe line search for general objective functions. Numerical experiments show that the proposed methods are promising. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： non-linear programming Unconstrained optimization Conjugate gradient method Conjugacy condition Global convergence

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Two-Level Parallel Augmented Schur Complement Interior-Point Algorithms for the Solution of Security Constrained Optimal Power Flow Problems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2020年第2期35卷 1340-1350页

作者： Kardos, Juraj Kourounis, Drosos Schenk, Olaf Univ Svizzera Italiana Inst Computat Sci Adv Comp Lab CH-6904 Lugano Switzerland NEPLAN AG CH-8700 Kusnacht Switzerland

Modern power grids incorporate renewable energy at an increased pace, placing greater stress on the power grid equipment and shifting their operational conditions towards their limits. As a result, failures of any network component, such as a transmission line or power generator, can be critical to the overall grid operation. The security constrained optimal power flow (SCOPF) aims for the long term precontingency operating state, such that in the event of any contingency, the power grid will remain secure. For a realistic power network, however, with numerous contingencies considered, the overall problem size becomes intractable for single-core optimization tools in short time frames established by real-time industrial operations. We propose a parallel distributed memory structure exploiting framework, BELTISTOS-SC, which accelerates the solution of SCOPF problems over state of the art techniques. The acceleration on single-core execution is achieved by a structure-exploiting interior point method, employing successive Schur complement evaluations to further reduce the size of the systems solved at each iteration while maintaining sparsity, resulting in lower computational resources for the linear system solution. Additionally the parallel, distributed memory implementation of the proposed framework is also presented in detail and validated through several large-scale examples, demonstrating its efficiency for large-scale SCOPF problems.

关键词： Security constraints optimal power flow non-linear programming interior point method parallel algorithms

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On a multi-product lot scheduling problem subject to an imperfect process with standby modules

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2014年第8期52卷 2243-2257页

作者： Lin, Gary C. Wu, Andy Gong, Dah-Chuang Huang, Boray Ma, Wen-Na Bradley Univ Dept Ind & Mfg Engn & Technol Peoria IL 61625 USA Natl Chung Hsing Univ Dept Mkt Taichung Taiwan Natl Univ Singapore Dept Ind & Syst Engn Singapore 117548 Singapore Chung Yuan Christian Univ Dept Ind Engn Zhongli Taiwan Shih Chien Univ Dept Int Business Taipei Taiwan

An Economic Lot Scheduling Problem is considered under the condition that the production process may shift from an in-control state to an out-of-control state due to the deterioration of the facility's key module. We adopt the Common Cycle policy in two mathematical models depending on whether the key module is repairable or not. Several standby modules are available during a production run. For the model with non-repairable key modules, the active key module, once deteriorated, is disposed of and replaced by a new standby. For the model with repairable key modules, the active one is replaced by a standby as soon as it is deteriorated. The failing module will be restored in a repair shop and rejoin the standbys. The objective is to determine an optimal production cycle time and the economic number of standby modules in order to minimise the long-term average cost including set-up, inventory carrying, standby and defective costs. The convexity of the cost functions is revealed so that efficient algorithms can be developed accordingly to achieve optimal production-inventory policies. It is shown that these policies can be used to significantly improve the system performance.

关键词： imperfect process inventory management non-linear programming standby modules

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A breakpoint search approach for convex resource allocation problems with bounded variables

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OPTIMIZATION LETTERS 2012年第4期6卷 629-640页

作者： De Waegenaere, Anja Wielhouwer, Jacco L. Tilburg Univ Ctr Econ Res NL-5000 LE Tilburg Netherlands Tilburg Univ Dept Econometr & Operat Res NL-5000 LE Tilburg Netherlands Vrije Univ Amsterdam Dept Accounting Fac Econ NL-1081 HV Amsterdam Netherlands

We present an efficient approach to solve resource allocation problems with a single resource, a convex separable objective function, a convex separable resource-usage constraint, and variables that are bounded below and above. Through a combination of function evaluations and median searches, information on whether or not the upper- and lowerbounds are binding is obtained. Once this information is available for all upper and lower bounds, it remains to determine the optimum of a smaller problem with unbounded variables. This can be done through a multiplier search procedure. The information gathered allows for alternative approaches for the multiplier search which can reduce the complexity of this procedure.

关键词： Resource allocation Multiplier search non-linear programming Pegging

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Allocation of long-term financial transmission rights for transmission expansion

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第3期184卷 1122-1139页

作者： Kristiansen, Tarjei Statkraft Energi AS N-0216 Oslo Norway

Long-term financial transmission rights (FTRs) could be used to create incentives for small-scale transmission investments. However, these new investments may cause negative externalities on existing FTRs. Therefore the system operator needs a protocol for awarding incremental FTRs for new transmission capacity that maximize investors' preferences while simultaneously accounting for under-allocation of the existing network capacity by existing FTRs. To preserve revenue adequacy, the system operator calculates a minimum amount of currently unallocated FTRs (or proxy FTRs) that satisfies the power flow constraints in the existing network. The challenge is to define the proxy awards. Hogan proposes to define them as the best use of the current network along the same direction as the incremental FTR awards. This includes allowing positive or negative incremental FTR awards. In this paper we present an implementation through bi-level programming of Hogan's proposal for allocation of long-term FTRs and apply it to a radial line and one of Hogan's examples. Our results show that the simultaneous feasibility of the transmission investment depends on factors such as investor and preset proxy preferences, existing FTRs, and transmission capacity in both the existing network and all proposed expansions of it. (C) 2006 Elsevier B.V. All rights reserved.

关键词： risk management energy non-linear programming finance

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