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ASME International Design Engineering Technical Conferences/Computers and Information in Engineering Conference

作者： Mgwatu, M. I. Opiyo, E. Z. Victor, M. A. M. Univ Dar Es Salaam Dept Mech & Ind Engn Dar Es Salaam Tanzania

ISBN: (纸本)9780791849026

In the work presented in this paper, we made an attempt to integrate the decisions for interrelated sub-problems of part design or selection, machine loading and machining optimization in a random flexible manufacturing system (FMS). The main purpose was to come up with an optimization model for achieving more generic and consistent decisions for the FMS and which can be practically implemented on the shop floor to help designers and other engineers in several ways, including, for instance, to optimize the designs of parts for specific FMS. In order to attain the generic decisions, an integer nonlinear programming (INLP) problem was formulated and solved to maximize the FMS throughput. Based on the results, the part design or selection, machine loading and machining optimization decisions can be simultaneously made. To get more insights of the results and also to check the validity of the model, a two-factor full factorial design was implemented for the sensitivity analysis, analysis of variance (ANOVA) and residual analysis. The computational analyses show that the tooling budget and available processing time were both statistically significant to throughput and confirmed that the model is valid with the data normally distributed.

关键词： Optimization part design part selection machine loading machining optimization integer nonlinear programming flexible manufacturing systems

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Differential evolution algorithm for static and multistage transmission expansion planning

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IET GENERATION TRANSMISSION & DISTRIBUTION 2009年第4期3卷 365-384页

作者： Sum-Im, T. Taylor, G. A. Irving, M. R. Song, Y. H. Brunel Univ Brunel Inst Power Syst Sch Engn & Design Uxbridge UB8 3PH Middx England Univ Liverpool Dept Elect Engn & Elect Liverpool L69 3GJ Merseyside England

A novel differential evolution algorithm (DEA) is applied directly to the DC power flow-based model in order to efficiently solve the problems of static and multistage transmission expansion planning (TEP). The purpose of TEP is to minimise the transmission investment cost associated with the technical operation and economical constraints. Mathematically, long-term TEP using the DC model is a mixed integer nonlinear programming problem that is difficult to solve for large-scale real-world transmission networks. In addition, the static TEP problem is considered both with and without the resizing of power generation in this research. The efficiency of the proposed method is initially demonstrated via the analysis of low, medium and high complexity transmission network test cases. The analysis is performed within the mathematical programming environment of MATLAB using both DEA and conventional genetic algorithm and a detailed comparative study is presented.

关键词： DC power flow-based model power transmission planning Power transmission, distribution and supply Power system planning and layout Power system management, operation and economics Optimisation techniques nonlinear programming integer programming large-scale transmission network DEA investment cost power transmission economics integer nonlinear programming evolutionary computation MATLAB environment multistage transmission expansion planning load flow static TEP economical constraint costing differential evolution algorithm

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EFFICIENT REDUCTION OF POLYNOMIAL ZERO-ONE OPTIMIZATION TO THE QUADRATIC CASE

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SIAM JOURNAL ON OPTIMIZATION 2008年第4期18卷 1398-1413页

作者： Buchheim, Christoph Rinaldi, Giovanni Univ Cologne Inst Informat D-50969 Cologne Germany CNR Ist Anal Sistemi Informat Antonio Ruberti I-00185 Rome Italy

We address the problem of optimizing a polynomial with real coefficients over binary variables. We show that a complete polyhedral description of the linearization of such a problem can be derived in a simple way from the polyhedral description of the linearization of some quadratic optimization problem. The number of variables in the latter linearization is only slightly larger than in the former. If polynomial constraints are present in the original problem, then their linearized counterparts carry over to the linearized quadratic problem unchanged. If the original problem formulation does not contain any constraints, we obtain a reduction to unconstrained quadratic zero-one optimization, which is equivalent to the well-studied max-cut problem. The separation problem for general unconstrained polynomial zero-one optimization thus reduces to the separation problem for the cut polytope. This allows us to transfer the entire knowledge gained for the latter polytope by intensive research and, in particular, the sophisticated separation techniques that have been developed. We report preliminary experimental results obtained with a straightforward implementation of this approach.

关键词： polynomial zero-one optimization integer nonlinear programming pseudo-boolean functions max-cut problem multilinear function optimization

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integer polynomial optimization in fixed dimension

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MATHEMATICS OF OPERATIONS RESEARCH 2006年第1期31卷 147-153页

作者： De Loera, JA Hemmecke, R Köppe, M Weismantel, R Univ Calif Davis Dept Math Davis CA 95616 USA Univ Magdeburg FMA IMO D-39106 Magdeburg Germany

We classify according to their computational complexity, integer optimization problems whose constraints and objective functions e polynomials with integer coefficients, and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials that are nonnegative over the polytope, these sequences of bounds lead to a fully polynomial-time approximation scheme for the optimization problem.

关键词： integer nonlinear programming integer programming in fixed dimension computational complexity rational functions approximation algorithms FPTAS

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A weapon-target assignment approach to media allocation

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APPLIED MATHEMATICS AND COMPUTATION 2006年第2期175卷 1266-1275页

作者： Cetin, Eyup Esen, Seda Tolun Istanbul Univ Fac Business Adm Quantitat Methods Dept TR-34320 Istanbul Turkey

An important problem which media planners face with is media allocation including budget allocation for an advertising campaign in an optimal frame. This study developed a near optimization model, originated from the weapon-target assignment problem of military operations research, that allocates both media and budget. The proposed model, which is independent of the duration of an advertising campaign, also schedules advertisements during the day. The presented model is an integer nonlinear programming problem. A hypothetical example is given and solved by MS Excel as a powerful spreadsheet tool. MS Excel's Solver is also proposed to solve NP-complete type problems. This study is a good example of military operations research models that can be adapted to contemporary business world applications. (c) 2005 Elsevier Inc. All rights reserved.

关键词： media modeling advertising campaign budget allocation integer nonlinear programming spreadsheet modeling military operations research

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Solving a nonlinear non-convex trim loss problem with a genetic hybrid algorithm

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COMPUTERS & OPERATIONS RESEARCH 1999年第6期26卷 623-635页

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

In the present paper, we invoke a newly developed genetic hybrid algorithm (GHA) to solve the trim loss problem of a paper-converting mill. The genetic algorithm was specifically designed for nonconvex mixed integer nonlinear programming problems. The current problem is an integer non-convex nonlinear programming (INLP) problem involving bilinear constraints. As shown elsewhere, the problem can be written in expanded linear form and solved either as an integer linear programming (ILP) or as a mixed integer linear programming (MILP) problem. In each case, the formulation is a special case of MINLP and, therefore, directly solvable by the genetic hybrid algorithm. The example considered is taken from the family of real daily trim optimization problems encountered at a Finnish paper-converting mill with a yearly capacity of 100 000 t. In this paper, we present the genetic hybrid algorithm, the INLP-problem to be solved and compare the results with those obtained by a classical optimization method. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： optimization integer nonlinear programming trim loss problems evolutionary programming

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Crew pairing at Air France

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1997年第2期97卷 245-259页

作者： Desaulniers, G Desrosiers, J Dumas, Y Marc, S Rioux, B Solomon, MM Soumis, F ECOLE POLYTECH DEPT MATH & GENIE IND MONTREAL PQ H3C 3A7 CANADA ECOLE HAUTES ETUD COMMERCIALES MONTREAL PQ CANADA AD OPT TECHNOL INC MONTREAL PQ CANADA AIR FRANCE PARIS FRANCE NORTHEASTERN UNIV COLL BUSINESS ADM MANAGEMENT SCI GRP BOSTON MA 02115 USA

In the airline industry, crew schedules consist of a number of pairings, These are round trips originating and terminating at the same crew home base composed of legal work days, called duties, separated by rest periods, The purpose of the airline crew pairing problem is to generate a set of minimal cost crew pairings covering all flight legs, The set of pairings must satisfy all the rules in the work convention and all the appropriate air traffic regulations, The resulting constraints can affect duty construction, may restrict each pairing, or be imposed on the overall crew schedule. The pairing problem is formulated as an integer, nonlinear multi-commodity network flow problem with additional resource variables. nonlinearities occur in the objective function as well as in a large subset of constraints. A branch-and-bound algorithm based on an extension of the Dantzig-Wolfe decomposition principle is used to solve this model. The master problem becomes a Set Partitioning type model, as in the classical formulation, while pairings are generated using resource constrained shortest path subproblems, This primal approach implicitly considers all feasible pairings and also provides the optimality gap value on a feasible solution. A nice feature of this decomposition process is that it isolates all nonlinear aspects of the proposed multi-commodity model in the subproblems which are solved by means of a specialized dynamic programming algorithm. We present the application and implementation of this approach at Air France. It is one of the first implementations of an optimal approach for a large airline carrier We have chosen a subproblem network representation where the duties rather than the legs are on the arcs, This ensures feasibility relative to duty restrictions by definition, As opposed to Lavoie, Minoux and Odier (1988), the nonlinear cost function is modeled without approximations. The computational experiments were conducted using actual Air France medium haul d

关键词： crew pairing integer nonlinear programming multi-commodity flow model Dantzig-Wolfe decomposition set partitioning

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AN EXTENDED CUTTING PLANE METHOD FOR SOLVING CONVEX MINLP PROBLEMS

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COMPUTERS & CHEMICAL ENGINEERING 1995年第0期19卷 S131-S136页

作者： WESTERLUND, T PETTERSSON, F Process Design Laboratory at &Aring bo Akademi University Biskopsgatan 8 FIN-20500 &Aring bo Finland

An extended version of Kelley's cutting plane method is introduced in the present paper. The extended method can be applied for the solution of convex MINLP (mixed-integer non-linear programming) problems, while Kelley's cutting plane method was originally introduced for the solution of convex NLP (non-linear programming) problems only. The method is suitable for solving large convex MINLP problems with a moderate degree of nonlinearity. The convergence properties of the method are given in the present paper and an example is provided to illustrate the numerical procedure.

关键词： OPTIMIZATION MIXED-integer nonlinear programming integer nonlinear programming EXTENDED CUTTING PLANE

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LAGRANGEAN DECOMPOSITION FOR integer nonlinear-programming WITH LINEAR CONSTRAINTS

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MATHEMATICAL programming 1991年第2期52卷 303-313页

作者： MICHELON, P MACULAN, N FED UNIV RIO DE JANEIRO COPPEBR-21945 RIO DE JANEIROBRAZIL FED UNIV RIO DE JANEIRO INST MATEMATBR-21945 RIO DE JANEIROBRAZIL

We present a Lagrangean decomposition to study integer nonlinear programming problems. Solving the dual Lagrangean relaxation we have to obtain at each iteration the solution of a nonlinear programming with continuous variables and an integer linear programming. Decreasing iteratively the primal-dual gap we propose two algorithms to treat the integer nonlinear programming.

关键词： integer nonlinear programming LAGRANGEAN DECOMPOSITION LAGRANGEAN RELAXATION

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On the Maximization of a Pseudo-Boolean Function

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Journal of the ACM (JACM) 1972年第2期19卷 265-282页

作者： Hammer, Peter L. Peled, Uri N. University of Montreal Montreal Canada Israel Defense Forces Doar Zvai 2770 Israel Faculty of Industrial and Management Engineering Technion-Israel Insitutue of Technology Haifa Israel

A branch-and-bound method is proposed for the maximization of real valued functions with variables assuming only the values 0 and 1. The importance of the problem consists-as has been shown by Hammer and Rudeanu-in the fact that numerous problems in operations research, graph theory, combinatorial mathematics, etc., can be brought to this form. The method has been successfully tested on an IBM 360/50 computer. © 1972, ACM. All rights reserved.

关键词： 0-1 programming Boolean equations branch-and-bound computational results implicit enumeration integer nonlinear programming pseudo-Boolean functions

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