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Resource-constrained project scheduling with concave processing rate functions

JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2015年第5期66卷 794-806页

作者： Steeneek, Daniel W. Sarin, Subhash C. Virginia Tech Blacksburg VA 24061 USA

In this paper, we address a resource-constrained project scheduling problem involving a single resource. The resource can be applied at varying consumption rates to the activities of the project. The duration of each activity is defined by a convex, non-increasing time-resource trade-off function. In addition, activities are not preemptable (ie, the resource consumption rate of an activity cannot be altered while the activity is being processed). We explicitly consider variation of the rate at which an activity is performed with variation in resource consumption rate. We designate the number of units (amount of an activity) performed per unit time with variation in resource consumption rate as the processing rate function, and assume this function to be concave. We present a tree-search-based method in concert with the solution of a nonlinear program and the use of dominance properties to determine: (i) the sequence in which to perform the activities of the project, and (ii) the resource consumption rate to allocate to each activity so as to minimize the project duration (makespan). We also present results of an experimental investigation that reveal the efficacy of the proposed methodology Finally, we present an application of this methodology to a practical setting.

关键词： project scheduling project management mixed-integer programming non-linear programming

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An optimization model for a monopolistic firm serving an environmentally conscious market: Use of chemical reaction optimization algorithm

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2015年 164卷 409-420页

作者： Choudhary, Alok Suman, Ravi Dixit, Vijaya Tiwari, M. K. Fernandes, Kiran Jude Chang, Pei-Chann Univ Loughborough Sch Business & Econ Loughborough LE11 3TU Leics England Indian Inst Technol Dept Ind & Syst Engn Kharagpur 721302 W Bengal India Natl Inst Ind Engn Bombay 400087 Maharashtra India Univ Durham Sch Business Durham England Yuan Ze Univ Dept Informat Management Taoyuan Taiwan

This work considers a monopolist firm which faces the following twin challenges of serving an environmentally sensitive market. The first challenge is the demand's elasticity to emissions and price. To entice its emission conscious customers and generate higher demand, the firm incrementally invests in cleaner production technologies. It also adopts a voluntary limit on its emissions from transportation. However, such investments and penalty lead to the second challenge of reduced net profit. To address above trade-off, a non-linear programming (NLP) model with a maximization quadratic profit function has been formulated. Recently developed, Chemical Reaction Optimization algorithm, with superior computational performance, has been adopted to solve the NLP. The output of the model provides near optimal monopolistic price, best attainable reduction in manufacturing emissions through proportional investment and makes a choice of suitable mode of transportation for each type of product offered by the firm. Three types of sensitivity analyses were performed by varying contextual parameters: customers' emission elasticity, penalty charged per unit emission and investment coefficient. The results, underpin the importance of investments in cleaner technologies and the need of financial aids for profit maximizing firms operating in cleaner markets. This work provides a decision making tool to determine the near optimal degree of each of the above dimension in multiple business fronts. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Emission elasticity Chemical reaction optimization non-linear programming Cleaner technologies

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Adaptive firefly algorithm with chaos for mechanical design optimization problems

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APPLIED SOFT COMPUTING 2015年 36卷 152-164页

作者： Baykasoglu, Adil Ozsoydan, Fehmi Burcin Dokuz Eylul Univ Fac Engn Dept Ind Engn TR-35397 Izmir Turkey

Firefly algorithm (FA) is a newer member of bio-inspired meta-heuristics, which was originally proposed to find solutions to continuous optimization problems. Popularity of FA has increased recently due to its effectiveness in handling various optimization problems. To enhance the performance of the FA even further, an adaptive FA is proposed in this paper to solve mechanical design optimization problems, and the adaptivity is focused on the search mechanism and adaptive parameter settings. Moreover, chaotic maps are also embedded into AFA for performance improvement. It is shown through experimental tests that some of the best known results are improved by the proposed algorithm. (C) 2015 Elsevier B.V. All rights reserved.

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

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A comparison of fuzzy regression methods for the estimation of the implied volatility smile function

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FUZZY SETS AND SYSTEMS 2015年 266卷 131-143页

作者： Muzzioli, S. Ruggieri, A. De Baets, B. Univ Modena & Reggio Emilia Dept Econ I-41121 Modena Italy Univ Modena & Reggio Emilia CEFIN I-41121 Modena Italy Univ Roma La Sapienza Dept Econ & Social Sci Rome Italy Univ Ghent Dept Math Modelling Stat & Bioinformat KERMIT B-9000 Ghent Belgium

The information content of option prices on the underlying asset has a special importance in finance. In particular, with the use of option implied trees, market participants may price other derivatives, estimate and forecast volatility (see e.g. the volatility index VIX), or higher moments of the underlying asset distribution. A crucial input of option implied trees is the estimation of the smile (implied volatility as a function of the strike price), which boils down to fitting a function to a limited number of existing knots. However, standard techniques require a one-to-one mapping between volatility and strike price, which is not met in the reality of financial markets, where, to a given strike price, two different implied volatilities are usually associated (coming from different types of options: call and put). In this paper we compare the widely used methodology of discarding some implied volatilities and interpolating the remaining knots with cubic splines, to a fuzzy regression approach which does not require an a-priori choice of implied volatilities. To this end, we first extend some linear fuzzy regression methods to a polynomial form and we apply them to the financial problem. The fuzzy regression methods used range from the possibilistic regression method of Tanaka et al. [28], to the least squares fuzzy regression method of Savic and Pedrycz [27] and to the hybrid method of Ishibuchi and Nii [11].

关键词： Fuzzy statistics and data analysis Finance Fuzzy regression methods non-linear programming Implied volatility

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Sensitivity analysis, economic optimization, and configuration design of mixed refrigerant cycles by NLP techniques

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JOURNAL OF NATURAL GAS SCIENCE AND ENGINEERING 2015年 24卷 144-155页

作者： Amidpour, Majid Hamedi, M. H. Mafi, M. Ghorbani, B. Shirmohammadi, R. Salimi, M. KNToosi Univ Technol Dept Energy Syst Fac Mech Engn Tehran Iran KNToosi Univ Technol Dept Energy Convers Fac Mech Engn Tehran Iran Imam Khomeini Int Univ Dept Energy Convers Fac Mech Engn Qazvin Iran Islamic Azad Univ South Tehran Branch Young Researchers & Elite Club Tehran Iran

Over the past decades, increasing attention has been paid to optimal design and operation of energy intensive industries. The purpose of this paper is to present a systematic method based on a combination of mathematical methods and thermodynamic viewpoints to acquire optimized design configuration by non-linear programming techniques. Economic optimization was developed through a combination of multi-stream exchanger design and optimized operation parameters. Next, perturbations method was applied for the sensitivity analysis in the discussed refrigeration cycles in the paper. Ultimately, the results showed the one-stage cascade of mixed refrigerant refrigeration cycle (MRRC) as the best option to replace pure ethylene cycle in the olefin plant of Tabriz Petrochemical Complex. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Refrigeration system Thermal integration Economic optimization Sensitivity analysis non-linear programming

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Optimisation of mine ventilation networks using the Lagrangian algorithm for equality constraints

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INTERNATIONAL JOURNAL OF MINING RECLAMATION AND ENVIRONMENT 2015年第3期29卷 201-212页

作者： Nyaaba, W. Frimpong, S. El-Nagdy, K. A. Missouri Univ Sci & Technol Min & Nucl Engn Dept Rolla MO 65409 USA Suez Univ Min Dept Fac Engn Suez Egypt

This work presents a new method of mine ventilation network optimisation as standard non-linear programming problem and discusses the use of a novel first-order Lagrangian (FOL) algorithm for equality constraints as a solution tool for these problems. Slack variables have been defined to transform such inequality constraints into their corresponding equality forms. The problem is then converted to non-linear problem with equality constrains. The methodology adopted in this paper is capable of dealing with the non-linear convex model with significant savings on computational efforts due to its use of only first derivatives. A MATLAB programme has been developed based on the FOL method to solve a generalised mine ventilation network optimisation problem. To study the validity and the viability of the FOL programme, the programme has been applied to already published network problems and both results are identical.

关键词： ventilation network optimization first-order Langrangian algorithm non-linear programming mine gases MSHA regulations

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Soil compaction optimization with soft constrain

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2015年第2期29卷 955-962页

作者： Jelusic, Primoz Univ Maribor Fac Civil Engn SLO-2000 Maribor Slovenia

The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In soil mechanics relationship between the causes and effects can be observed with laboratory tests but is difficult to develop analytical functions or numerical relations between input and output. In geotechnical optimization the most usual constraints represent state variables of structural response for each loading case. The aim of this paper is to define the soft constrain with adaptive network-based fuzzy inference system (ANFIS) in the soil mechanics. The developed soft constrain is than applied in non-linear programming (NLP) to obtain optimal solution. In the case of soil compaction the performance of the proposed optimization algorithm is evaluated. The main aim of soil compaction is to define optimal water content at which soil can be compacted to a densest state that improve their mechanical and physical properties.

关键词： Soil compaction fuzzy relation equations adaptive network-based fuzzy inference system non-linear programming

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On second-order directional derivatives of value functions

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OPTIMIZATION 2015年第2期64卷 389-407页

作者： Minchenko, L. Tarakanov, A. Belarus State Univ Informat & Radioelect Dept Informat Minsk BELARUS

Directional derivatives of value functions play an essential role in the sensitivity and stability analysis of parametric optimization problems, in studying bi-level and min-max problems, in quasi-differentiable calculus. Their calculation is studied in numerous works by A.V. Fiacco, V.F. Demyanov and A.M. Rubinov, R.T. Rockafellar, A. Shapiro, J.F. Bonnans, A.D. Ioffe, A. Auslender and R. Cominetti, and many other authors. This article is devoted to the existence of the second order directional derivatives of value functions in parametric problems with non-single-valued solutions. The main idea of the investigation approach is based on the development of the method of the first-order approximations by V.F. Demyanov and A.M. Rubinov.

关键词： 90C31 41A50 49K40 regularity conditions calmness non-linear programming Optimal value function Multi-valued mappings directional derivatives

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A new fractional Chebyshev FDM: an application for solving the fractional differential equations generated by optimisation problem

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2015年第14期46卷 2598-2606页

作者： Khader, M. M. Al Imam Mohammad Ibn Saud Islamic Univ IMSIU Dept Math & Stat Coll Sci Riyadh Saudi Arabia Benha Univ Fac Sci Dept Math Banha Egypt

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method. The algorithm is based on a combination of the useful properties of Chebyshev polynomial approximation and finite difference method. We implement this technique to solve numerically the non-linear programming problem which are governed by fractional differential equations (FDEs). The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the Caputo fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The application of the method to the generated FDEs leads to algebraic systems which can be solved by an appropriate method. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method. A comparison with the fourth-order Runge-Kutta method is given.

关键词： finite difference method dynamic system non-linear programming Chebyshev approximations penalty function Caputo fractional derivatives

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Combined scheduling and capacity planning of electricity-based ammonia production to integrate renewable energies

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第3期241卷 851-862页

作者： Beerbuehl, S. Schulte Froehling, M. Schultmann, F. Karlsruhe Inst Technol Inst Ind Prod D-76187 Karlsruhe Germany

Economic assessment of energy-related processes needs to adapt to the development of large-scale integration of renewable energies into the energy system. Flexible electrochemical processes, such as the electrolysis of water to produce hydrogen, are foreseen as cornerstones to renewable energy systems. These types of technologies require the current methods of energy storage scheduling and capacity planning to incorporate their distinct non-linear characteristics in order to be able to fully assess their economic impact. A combined scheduling and capacity planning model for an innovative, flexible electricity-to-hydrogen-to-ammonia plant is derived in this paper. A heuristic is presented, which is able to translate the depicted, non-convex and mixed-integer problem into a set of convex and continuous non-linear problems. These can be solved with commercially available solvers. The global optimum of the original problem is encircled by the heuristic, and, as the numerical illustration with German electricity market data of 2013 shows, can be narrowed down and approximated very well. The results show, that it is not only meaningfulness, but also feasible to solve a combined scheduling and capacity problem on a convex non-linear basis for this and similar new process concepts. Application to other hydrogen based concepts is straightforward and to other, non-linear chemical processes generally possible. (C) 2014 Elsevier B.V. All rights reserved.

关键词： OR in energy non-linear programming Heuristics Hydrogen storage Ammonia

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