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Univariate parameterization for global optimization of mixed-integer polynomial problems

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第3期229卷 613-625页

作者： Teles, Joao P. Castro, Pedro M. Matos, Henrique A. Lab Nacl Energia & Geol Unidade Modelacao & Optimizacao Sistemas Energet P-1649038 Lisbon Portugal Inst Super Tecn DEQ Ctr Proc Quim P-1049001 Lisbon Portugal

This paper presents a new relaxation technique to globally optimize mixed-integer polynomial programming problems that arise in many engineering and management contexts. Using a bilinear term as the basic building block, the underlying idea involves the discretization of one of the variables up to a chosen accuracy level (Teles, J.P., Castro, P.M., Matos, H.A. (2013). Multiparametric disaggregation technique for global optimization of polynomial programming problems. J. Glob. Optim. 55, 227-251), by means of a radix-based numeric representation system, coupled with a residual variable to effectively make its domain continuous. Binary variables are added to the formulation to choose the appropriate digit for each position together with new sets of continuous variables and constraints leading to the transformation of the original mixed-integer non-linear problem into a larger one of the mixed-integer linear programming type. The new underestimation approach can be made as tight as desired and is shown capable of providing considerably better lower bounds than a widely used global optimization solver for a specific class of design problems involving bilinear terms. (c) 2013 Elsevier B.V. All rights reserved.

关键词： Global optimization non-linear programming integer programming mixed-integer non-linear programming

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A logarithmic method for eliminating binary variables and constraints for the product of free-sign discrete functions

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DISCRETE OPTIMIZATION 2013年第1期10卷 11-24页

作者： Lu, Hao-Chun Fu Jen Catholic Univ Coll Management Dept Informat Management Sinjhuang City 242 Taipei County Taiwan

In this paper, a logarithmic method was developed to solve optimization problems containing the product of free-sign discrete functions (PFDF). The current deterministic methods used to handle these problems are based on the concept of continuous variables;therefore, the methods always transform the original model into another programming model (e.g., DC programming, convex programming) and solve them with a commercial solver. As the nature of a discrete variable is quite different from that of a continuous one, developing a novel method to address the above mentioned problems is necessary. This study proposes a concise and efficient method that linearizes PFDF term into a set of linear inequalities directly without redundant transformation. Further, the proposed method only requires the logarithmic numbers of binary variables and constraints. Numerical examples demonstrate that the proposed formulation significantly outperforms current approaches. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Discrete function Free-sign variables mixed-integer non-linear programming

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A COMPREHENSIVE FORMULATION FOR RAILROAD BLOCKING PROBLEM

A COMPREHENSIVE FORMULATION FOR RAILROAD BLOCKING PROBLEM

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27th European Conference on Modelling and Simulation, ECMS 2013

作者： Hasany, Reza Mohammad Shafahi, Yousef Kazemi, Seyed Farzan Sharif Univ Technol Dept Civil Engn Azadi St Tehran 113659313 Iran

ISBN: (纸本)9780956494467

In rail transportation, there have been several attempts to determine the best routes for shipments (a number of cars with the same origin-destination) through the network. Shipments enter into several intermediate yards on their routes to separate and regroup shipments into new trains. Most of time, every entering into a yard includes excessive delay for shipments;therefore it is an ideal plan that each shipment has been transported by an exclusive train service. Mainly because of restriction on a number of running trains,. this plan cannot be adapted in most cases. Finding the optimal route over the rail network with above and other common constraints would be handled by railroad blocking problem. From 1980 to the present, many mathematical programs have been proposed in this issue. In literature, however, there has not been any model with all realistic constraints. In this article, we give a brief literature review on railroad blocking problem. Afterwards, we present a comprehensive mixed integer programming formulation for this problem. Finally, we solve a test instance to show our model is in line with our expectation.

关键词： mixed-integer non-linear programming Railroad Planning Tactical Level of Managment Blocking Problem

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A revised model for compressor design and scheduling in gas-lifted oil fields

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IIE TRANSACTIONS 2012年第5期44卷 342-351页

作者： Camponogara, Eduardo Nazari, Luiz F. Meneses, Claudio N. Univ Fed Santa Catarina Dept Automat & Syst Engn BR-88040900 Florianopolis SC Brazil Fed Univ ABC BR-09210170 Santo Andre SP Brazil

The design and real-time scheduling of lift-gas compressors in oil fields entails solving a mixed-integer non-linear problem that generalizes the facility location problem. This article presents a revised formulation that represents the constraints on compressor discharge pressure as a family of linear inequalities, which is shown to be tighter than a previous formulation. mixed-integer linear approximations for these formulations are obtained by piecewise linearizing the non-linear functions, using binary variables and specially ordered set variables. Valid inequalities for compressor capacity along with separation and lifting procedures are proposed. The article also presents computational experiments comparing the formulations and evaluating the impact of cutting plane generation on solution speed.

关键词： Facility location mixed-integer non-linear programming piecewise linearization scheduling oil fields

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Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing

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COMPUTERS & OPERATIONS RESEARCH 2012年第11期39卷 2642-2658页

作者： Kia, R. Baboli, A. Javadian, N. Tavakkoli-Moghaddam, R. Kazemi, M. Khorrami, J. Univ Lyon DISP Lab INSA Lyon F-69621 Villeurbanne France Islamic Azad Univ Firoozkooh Branch Dept Ind Engn Firoozkooh Iran Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Univ Tehran Dept Ind Engn Coll Engn Tehran Iran Birjand Univ Technol Dept Ind Engn Birjand Iran

This paper presents a novel mixed-integer non-linear programming model for the layout design of a dynamic cellular manufacturing system (DCMS). In a dynamic environment, the product mix and part demands are varying during a multi-period planning horizon. As a result, the best cell configuration for one period may not be efficient for successive periods, and thus it necessitates reconfigurations. Three major and interrelated decisions are involved in the design of a CMS;namely cell formation (CF), group layout (GL) and group scheduling (GS). A novel aspect of this model is concurrently making the CF and GL decisions in a dynamic environment. The proposed model integrating the CF and GL decisions can be used by researchers and practitioners to design GL in practical and dynamic cell formation problems. Another compromising aspect of this model is the utilization of multi-rows layout to locate machines in the cells configured with flexible shapes. Such a DCMS model with an extensive coverage of important manufacturing features has not been proposed before and incorporates several design features including alternate process routings, operation sequence, processing time, production volume of parts, purchasing machine, duplicate machines, machine capacity, lot splitting, intra-cell layout, inter-cell layout, multi-rows layout of equal area facilities and flexible reconfiguration. The objective of the integrated model is to minimize the total costs of intra and inter-cell material handling, machine relocation, purchasing new machines, machine overhead and machine processing. linearization procedures are used to transform the presented non-linear programming model into a linearized formulation. Two numerical examples taken from the literature are solved by the Lingo software using a branch-and-bound method to illustrate the performance of this model. An efficient simulated annealing (SA) algorithm with elaborately designed solution representation and neighborhood generation

关键词： Dynamic cellular manufacturing systems mixed-integer non-linear programming Group layout Multi-rows layout Flexible reconfiguration Simulated annealing

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Designing an intra-cell layout model in dynamic cellular manufacturing systems with unequal-area facilities

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INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE AND ENGINEERING MANAGEMENT 2012年第1期7卷 10-19页

作者： Kia, Reza Khorrami, Javad Mahdavi, Iraj Javadian, Nikbakhash Kazemi, Mohammad Islamic Azad Univ Dept Ind Engn Firoozkooh Branch Firoozkooh Iran Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Birjand Univ Technol Dept Ind Engn Birjand Iran

This paper presents a novel mixed-integer non-linear programming model for an intra-cell layout (ICL) design for a dynamic cellular manufacturing system (DCMS). In a dynamic environment, the product mix and part demands vary during a multi-period planning horizon. As a result, the best cell configuration and part routings for one period may not be efficient for successive periods, and necessitating reconfiguration. A novel aspect of this model is the concurrent making of the cell formations and ICL decisions in a dynamic environment. Another aspect of this model is the utilization of a multi-row machine layout for machines of unequal-area. The DCMS model presented incorporates several design features including alternative process routings, operation sequencing, processing time, parts production volume, duplicate machines, machine capacity, ICL, multi-row layout of unequal-area facilities, continuous-area cells and machine relocation. The objective of the integrated model is to minimize the total costs of intra and inter-cell material handling, machine relocation, machine overheads and machine processing. The main constraints are part processing requirements, machine availability, maximal and minimal cell size, machine time-capacity and the non-overlapping of facilities. A comprehensive example is solved using Lingo software to verify the performance of the proposed model. Also, the computational results show that to some extent the proposed model overcomes common disadvantages in the existing dynamic cell formation models that have not yet considered layout problems of unequal-area facilities.

关键词： dynamic cellular manufacturing systems mixed-integer non-linear programming intra-cell layout unequal-area facilities cell reconfiguration

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Transmission Expansion Planning Including Reactive Power Procurement in Deregulated Environment

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2011年第13期39卷 1403-1423页

作者： Singh, Kanwardeep Padhy, Narayana Prasad Sharma, Jaydev GNDEC Dept Elect Engn Ludhiana 141006 Punjab India Indian Inst Technol Dept Elect Engn Roorkee Uttar Pradesh India

This article proposes a novel approach for transmission expansion planning in pool-based deregulated electricity markets. The transmission expansion planning problem is formulated as an optimization problem consisting of minimization of annualized investment cost of prospective transmission lines and maximization of social welfare as an objective function, subject to operational and security constraints. Reactive power procurement cost to be paid to the generator companies, in addition to commonly used real power generation cost of generator companies and benefits of distribution companies/bulk consumers, have also been considered in the social welfare function. The reactive power procurement cost needs to be included in the social welfare function in order to pay compensation to generator companies for their reactive power supply in a deregulated environment. The proposed method for transmission expansion planning takes into account a number of potential scenarios on the basis of an annum and is solved by a mixed-integer non-linear programming method as well as by a proposed iterative two-stage approach. The effectiveness of proposed approach is tested on Garver's 6-bus, the IEEE 24-bus reliability test, the IEEE 57-bus, and the IEEE 118-bus systems. The comparisons of the proposed approach are presented (a) without including reactive power procurement cost in the present formulation and (b) with an existing DC formulation based transmission expansion planning approach.

关键词： locational marginal pricing reactive power procurement social welfare transmission expansion planning mixed-integer non-linear programming

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Medium-term Rail Planning at Rio Tinto Iron Ore

Medium-term Rail Planning at Rio Tinto Iron Ore

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MSSANZ 19th Biennial Congress on Modelling and Simulation (MODSIM)

作者： Garcia-Flores, R. Singh, G. Ernst, A. Welgama, P. CSIRO Math Informat & Stat Private Bag 33 Clayton Vic 3169 Australia Rio Tinto Tech Serv Perth WA 6837 Australia

ISBN: (纸本)9780987214317

In minerals supply chains, medium term plans over time horizons from two weeks to two years are used not only to maximise throughput and identify bottlenecks, but also for scheduling crews, production and maintenance. These plans need to observe constraints like maintenance and production requirements, fleet capacities, and dumping, loading and stockyard management at every site. Additionally, the iron ore supply chains considered in this paper also needs to deal with grade quality constraints. This introduces extra complexities in terms of non-linear constraints as the quality depends on the mixing ratio of ore from different sources. We present an optimisation tool that was developed for Rio Tinto Iron Ore for such planning. The tool provides optimal number of trains while taking into account all the system constraints and has already reduced total planning time significantly.

关键词： Scheduling Rail planning Medium-term planning Blending mixed-integer non-linear programming

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A Simulated Annealing for Solving a Group Layout Design Model of a Dynamic Cellular Manufacturing System

A Simulated Annealing for Solving a Group Layout Design Mode...

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IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

作者： Kia, Reza Tavakkoli-Moghaddam, Reza Javadian, Nikbakhsh Kazemi, Mohammad Khorrami, Javad Islamic Azad Univ Firoozkooh Branch Dept Ind Engn Firoozkooh Iran Univ Tehran Coll Engn Dept Ind Engn Tehran Iran Mazandaran Univ Sci & Technol Dept Ind Engn Babol Iran

ISBN: (纸本)9781457707391

This paper presents a novel mixed-integer non-linear programming model for the layout design of a dynamic cellular manufacturing system (DCMS). A novel aspect of this model is concurrently making the cell formation (CF) and group layout (GL) decisions in a dynamic environment. The proposed model incorporates several design features including alternate process routings, operation sequence, processing time, production volume of parts, purchasing machine, duplicate machines, machine capacity, lot splitting, intra-cell layout, inter-cell layout, multi-rows layout of equal area facilities, and flexible reconfiguration. An efficient simulated annealing (SA) algorithm is extended to solve the proposed model because of its NP-hardness. It is then tested using several problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison with the Lingo software. The obtained results show that the proposed SA is able to find the near-optimal solutions in a reasonable computational time.

关键词： Dynamic cellular manufacturing systems group layout mixed-integer non-linear programming simulated annealing

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Cost optimization of industrial steel building structures

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ADVANCES IN ENGINEERING SOFTWARE 2010年第3期41卷 442-450页

作者： Kravanja, S. Zula, T. Univ Maribor Fac Civil Engn SLO-2000 Maribor Slovenia

The paper presents the simultaneous cost, topology and standard cross-section optimization of single-storey industrial steel building structures. The considered structures are consisted from main portal frames, which are mutually connected with purlins. The optimization is performed by the mixed-integer non-linear programming approach, MINLP. The MINLP superstructure of different structure/topology and standard cross-section alternatives has been generated and the MINLP optimization model of the structure has been developed. The defined cost objective function is subjected to the set of (in)equality constraints known from the structural analysis. Internal forces and deflections are calculated by the elastic first-order analysis constraints. The dimensioning constraints of steel members are defined in accordance with Eurocode 3. The modified outer-approximation/equality-relaxation (OA/ER) algorithm, a two-phase MINLP strategy and a special prescreening procedure of discrete alternatives are used for the optimization. A numerical example of the cost optimization of a single-storey industrial steel building is presented at the end of the paper. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Cost optimization Structural optimization Topology optimization Cross-section optimization mixed-integer non-linear programming MINLP Industrial building Steel structures

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