8323

7721

كارشناسي ارشد

صنايع

اصفهان: دانشگاه صنعتي اصفهان، دانشكده صنايع و سيستم ها

1392

دوازده،68ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

ناصر ملاوردي

1/10/92

نادر شتاب بوشهري، محمد سعيد صباغ

مهندسي صنايع و سيستم ها

ID7721

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Solving Large Scale Linear Programming Problems Using a Limited Memory BFGS Method Hiwa Esmaeil Zadeh h esmailzadeh@in iut ac ir Date of Submission Department of Industrial Engineering IsfahanUniversity of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Naser Mollaverdi naserm@cc iut ac ir Abstract In general the application of the general algorithm for solving linear programming problems on a large scale is not desirable Many researches develop specific algorithms for these groups of problems are ongoing Researchers by using various methods have introduced variety of algorithms that each of which have their own features In this thesis a quasi Newton limited memory BFGS method is proposed for solving linear programs with a very large number of constraints and a very large number of variables In this method referring to the previous researches an exterior penalty function an unconstraint optimization problem is developed This function is a piecewise quadratic convex function which is equivalent to our primal problem and solving this optimization problem leads to solving primal problem In previous research a fast newton algorithm is utilized to solve this function This method acquires solution of least 2 norm of linear programming For improving the efficiency of newton method we used the quasi Newton limited memory BFGS method with the fixed step length to solve super large scale linear programming problems Direction of this new ction For comparing our proposed algorithm with other algorithms over 250 random linear programming problems with their optimal point and objective function are generated By comparing numerical results we find that our proposed new algorithm efficiency is higher than other methods Computational results for small scale problems are almost the same with the dual simplex algorithm and Newton method And for large scale the proposed quasi Newton algorithm will solve the problem faster than other methods Moreover the CPLEX Dual software and the Newton algorithm for the problems that they are unable to resolve due to lack of memory error can be solved with great efficiency Keywords Linear Programming Super Large scale Limited memory BFGS method Exterior penalty function PDF created with pdfFactory trial version www pdffactory com

ناصر ملاوردي

نادر شتاب بوشهري، محمد سعيد صباغ