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Note on Solving Probabilistic programming Problems Involving Multi-choice Parameters

JOURNAL OF INTERDISCIPLINARY MATHEMATICS 2015年第5期18卷 617-627页

作者： Hung, Kuo-Chen Lin, Scott Shu-Cheng Chu, Chun-Hsiao Hungkuang Univ Dept Comp Sci & Informat Management Taichung Taiwan Chungyu Inst Technol Dept Tourism & Travel Management Keelung Taiwan Aletheia Univ Dept Tourism New Taipei Taiwan

We study the probabilistic programming problems with multi-choice parameters proposed by Acharya and Biswal (2011) that was published in Opsearch. We point out that the multi-choice parameters can be simplified to avoid the complicated solution procedure proposed by Acharya and Biswal (2011). We use the same numerical example of Acharya and Biswal (2011) to demonstrate that our simplification is effective to derive better minimum.

关键词： Probabilistic programming multi-choice programming non-linear programming deterministic programming

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Funções penalidade para o tratamento das variáveis discretas do problema de fluxo de potência ótimo reativo

Funções penalidade para o tratamento das variáveis discre...

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作者： Silva, Daisy Paes Universidade Estadual Paulista

O problema de Fluxo de Potência Ótimo (FPO) é considerado um importante problema da Engenharia Elétrica desde a década de 1960. A partir de então, muitos trabalhos foram publicados com diferentes formulações e abordagens para a resolução deste problema. Muitas destas abordagens desconsiderava a natureza discreta das variáveis de controle e consideram todas as variáveis do problema como contínuas. Estas formulações são aproximações do problema de FPO, pois, algumas variáveis podem somente ser ajustadas por passos discretos, conforme a realidade do sistema. No problema de Fluxo de Potência Ótimo Reativo (FPOR), caso particular do problema de FPO, as variáveis relacionadas à potência ativa são fixadas e a otimização somente considera as variáveis relacionadas à potência reativa. O problema de FPOR pode ser modelado matematicamente como um problema de programação não-linear com variáveis discretas e contínuas. Neste trabalho, propõem-se das abordagens para resolução do problema FPOR que consideram a natureza discreta das variáveis do problema. Nas abordagens propostas são utilizadas funções penalidade associadas a um método de pontos interiores, combinando as vantagens de ambos para a resolução do problema de FPOR. Desenvolvem-se funções penalidade polinomiais para tratar as variáveis de controle discretas do problema, taps dos transformadores e bancos de capacitores e de reatores shunt, obtendo-se uma sequência de problemas contínuos, diferenciáveis e penalizados, que são resolvidos pelo método de pontos interiores implementado no solver gratuito IPOPT. As soluções de tais problemas convergem para a solução do problema original. Os testes numéricos foram realizados com os sistemas elétricos IEEE 14, 30, 118 e 300 barras para verificar a eficiência das abordagens *** Optimal Power Flow Problem (OPF) is considered an important problem of the electrical engineering since the 1960s. From that moment, many papers were published with different formulations and appr

关键词： Fluxo de potência ótimo reativo Programação não-linear Variáveis discretas Funções penalidade polinomiais Reactive optimal power flow non-linear programming Discrete Variables Polynomial penalty functions Dissertação de mestrado

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Optimising the extraction rate of a non-durable non-renewable resource in a monopolistic market: a mathematical programming approach

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SPRINGERPLUS 2015年第1期4卷 1页

作者： Corominas, Albert Fossas, Enric Univ Politecn Cataluna Inst Ind & Control Engn E-08028 Barcelona Spain

We assume a monopolistic market for a non-durable non-renewable resource such as crude oil, phosphates or fossil water. Stating the problem of obtaining optimal policies on extraction and pricing of the resource as a non-linear program allows general conclusions to be drawn under diverse assumptions about the demand curve, discount rates and length of the planning horizon. We compare the results with some common beliefs about the pace of exhaustion of this kind of resources.

关键词： non-renewable resources Optimal extraction rate non-linear programming

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A single machine EPQ inventory model for a multi-product imperfect production system with rework process and auction

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International Journal of Advanced Logistics 2016年第3-4期5卷 141-152页

In this paper, a multi-product Economic Production Quantity (EPQ) inventory model for a defective production system by a single machine is considered. The faulty produced products are reworked or are put on auction as they are. The aim of this research is to determine the optimal cycle length and the percentage of reworking every fault product such that the total inventory cost, including setup, production, holding, reworking, and lost profit, is minimized. We have proved that this problem is a convex non-linear programming method. Therefore, we came up with the exact algorithm based on differentiation to solve it. Finally, a sensitivity analysis is performed to evaluate the effect of changes in different parameters of the problem.

关键词： EPQ model imperfect production system non-linear programming lost profit

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Numerical solution of the time-delayed optimal control problems with hybrid functions

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2015年第3期32卷 623-638页

作者： Nazemi, Alireza Shabani, Mohammad Mehdi Shahrood Univ Sch Math Sci Dept Math Shahrood Iran

We consider an approximation scheme using hybrid functions for solving time-delayed optimal control problems with terminal inequality constraints. Using a Pade approximation, the problem is first transformed into one without a time-delayed argument. A computational method based on hybrid functions in time-domain is then proposed for solving the obtained non-delay optimal control problem. Hybrid functions integral operational matrix and direct collocation method are utilized to find the approximated optimal trajectory and the optimal control law of the original problem. Numerical results are also given to demonstrate the efficiency of the method.

关键词： time-delayed optimal control problems approximation terminal condition hybrid functions non-linear programming Bernoulli polynomials block-pulse

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An adaptively managed dynamic portfolio selection model using a time-varying investment target according to the market forecast

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2015年第7期66卷 1115-1131页

作者： Jung, Jongbin Kim, Seongmoon Yonsei Univ Sch Business Seoul 120749 South Korea

In this paper, we propose an adaptive investment strategy (AIS) based on a dynamic portfolio selection model (DPSM) that uses a time-varying investment target according to the market forecast. The DPSM allows for flexible investments, setting relatively aggressive investment targets when market growth is expected and relatively conservative targets when the market is expected to be less attractive. The model further allows investments to be liquidated into risk-free assets when the market forecast is pessimistic. By dynamically determining the investment target, the DPSM allows construction of portfolios that are more responsive to market changes, while eliminating the possibility of the model becoming infeasible under certain market conditions. When the proposed DPSM is implemented in real-life investment scenarios using the AIS, the portfolio is rebalanced according to a predefined rebalancing cycle and the model's input parameters are estimated on each rebalancing date using an exponentially weighted moving average (EWMA) estimator. To evaluate the performance of the proposed approach, a 7-year investment experiment was conducted using historical stock returns data from 10 different stock markets around the world. Performance was assessed and compared using diverse measures. Superior performance was achieved using the AIS proposed herein compared with various benchmark approaches for all performance measures. In addition, we identified a converse relationship between the average trading volume of a market and the value of the weighting parameter prescribed to the EWMA estimator, which maximizes cumulative returns in each market.

关键词： adaptive investment strategy dynamic portfolio selection model portfolio rebalancing mean-variance portfolio selection non-linear programming

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Local convergence of filter methods for equality constrained non-linear programming

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OPTIMIZATION 2010年第8期59卷 1153-1171页

作者： Karas, Elizabeth W. Gonzaga, Clovis C. Ribeiro, Ademir A. Univ Fed Parana Dept Math BR-81531980 Curitiba Parana Brazil Univ Fed Santa Catarina Dept Math BR-88040970 Florianopolis SC Brazil

In Gonzaga et al. [A globally convergent filter method for nonlinear programming, SIAM J. Optimiz. 14 (2003), pp. 646-669] we discuss general conditions to ensure global convergence of inexact restoration filter algorithms for non-linear programming. In this article we show how to avoid the Maratos effect by means of a second-order correction. The algorithms are based on feasibility and optimality phases, which can be either independent or not. The optimality phase differs from the original one only when a full Newton step for the tangential minimization of the Lagrangian is efficient but not acceptable by the filter method. In this case a second-order corrector step tries to produce an acceptable point keeping the efficiency of the rejected step. The resulting point is tested by trust region criteria. Under the usual hypotheses, the algorithm inherits the quadratic convergence properties of the feasibility and optimality phases. This article includes a comparison between classical Sequential Quadratic programming (SQP) and Inexact Restoration (IR) iterations, showing that both methods share the same asymptotic convergence properties.

关键词： filter methods non-linear programming local convergence

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Planning and managing intermodal transportation of hazardous materials with capacity selection and congestion

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2015年 76卷 45-57页

作者： Assadipour, Ghazal Ke, Ginger Y. Verma, Manish Mem Univ Fac Business Adm St John NF Canada McMaster Univ DeGroote Sch Business Hamilton ON L8S 4L8 Canada

The current literature in the rail truck intermodal transportation of hazardous materials (hazmat) domain ignores congestion at intermodal yards. We attempt to close that gap by proposing a bi-objective optimization framework for managing hazmat freight that not only considers congestion at intermodal yards, but also determines the appropriate equipment capacity. The proposed framework, i.e., a non-linear MIP and a multi-objective genetic algorithm based solution methodology, is applied to a realistic size problem instance from existing literature. Our analysis indicates that terminal congestion risk is a significant portion of the network risk;and, that policies and tools involving number of cranes, shorter maximum waiting times, and tighter delivery times could have a positive bearing on risk. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Rail-truck transportation Congestion Hazardous materials Capacity planning non-linear programming Metaheuristics

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Modeling and parameters fitting of chemical and phase equilibria in reactive systems for biodiesel production

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BIOMASS & BIOENERGY 2015年 81卷 544-555页

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

Biodiesel, a non-toxic biodegradable fuel from renewable sources such as vegetable oils, has been developed in order to reduce dependence on crude oil and enable sustainable development. The knowledge of phase equilibrium in systems containing compounds for biodiesel production is valuable, especially in the purification stage of the biodiesel. nonetheless, the refining process of biodiesel and byproducts can be difficult and can elevate the production costs considerably unless it has an appropriate knowledge about the phase separation behavior. In addition, the transesterification reaction yield for producing biodiesel depends upon several operation parameters e.g. the feed molar ratio oil-to-alcohol and the temperature. These parameters were analyzed through a thermodynamic analysis by direct Gibbs energy minimization method in this paper, with the purpose of calculating the chemical and phase equilibrium of some mixtures containing compounds found in biodiesel production. For this, optimization techniques associated with the GAMS 2.5 software were utilized and the UNIQUAC and NRTL models were applied to represent the non-idealities of the liquid phases. Also, binary interaction parameters of studied compounds were correlated for NRTL and UNIQUAC models by using the least squares principle. 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 the Gibbs energy. Moreover, a good agreement was observed in cases in which calculated data were compared with experimental data. (C) 2015 Elsevier Ltd. All rights reserved.

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

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Random derivative-free algorithm for solving unconstrained or bound constrained continuously differentiable non-linear problems

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OPTIMIZATION METHODS & SOFTWARE 2015年第5期30卷 911-933页

作者： Jaberipour, Majid Khorram, Esmaile Karimi, Behrooz Amirkabir Univ Technol Dept Appl Math Fac Math & Comp Sci Tehran 15914 Iran Amirkabir Univ Technol Dept Ind Engn Tehran 15914 Iran

Derivative-free optimization is an area of long history which has so many applications in different fields. It has lately received considerable attention within the engineering community. This paper describes a random derivative-free algorithm for solving unconstrained or bound constrained continuously differentiable non-linear problems. This method is a combination of particle swarm and directional direct search algorithms. The key difference in direct search methods is in the way of generating positive bases. At first glance, a simple way of generating positive bases has been introduced for solving continuously differentiable problems. Then, it has been shown that using the particle swarm algorithm with a direct search algorithm can solve non-linear optimization problems efficiently. Some standard examples have been presented to demonstrate the ability and effectiveness of this approach.

关键词： particle swarm derivative-free unconstrained problems bound constrained problems non-linear programming

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