جنبه های محاسباتی از روش سیمپلکس برنامه ریزی خطی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|25035||2000||7 صفحه PDF||سفارش دهید||3550 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Advances in Engineering Software, Volume 31, Issues 8–9, August 2000, Pages 539–545
In this paper, the Simplex method is re-examined from the computational view points. Efficient numerical implementation for the Simplex procedure is suggested. Special features of artificial variables, and variables with unrestriction in signs are exploited to reduce the com-putational efforts, and computer memory requirement. The developed Simplex code has been tested on several examples, and its performance has been compared with existing Simplex codes.
Any linear programming (LP) problems can  and  be expressed in the following standard form. Find the design variable vector such that Minimize equation(1) Subject To equation(2) and equation(3) As an example, consider the following simple problem: Find the vector Minimize equation(4) Subject to equation(5) equation(6) equation(7) The inequality constraints shown in and can be put in the standard (equality) form by introducing slack and/or surplus variables x3 and x4 as following: equation(8) equation(9) and represent system of two equations and four unknowns. Therefore, there exists infinite number of possible solutions. One possible set of solution is to set equation(10) and therefore, one can easily find In the Simplex method, and are said to be in the Canonical form (the columns associated with variables x3 and x4 only contain 0's and 1's). Furthermore, the variables with zero values are defined as “Non-Basic” variables, whereas the variables with rhs values are referred to as “Basic” variables. Thus, for the LP problem defined in , , and , x3 and x4 are the basic variables, and x1 and x2 are non-basic variables.
نتیجه گیری انگلیسی
Based upon the result obtained up to this date, the following conclusions can be made: • The developed ODU-NASA Simplex (FORTRAN) code is much more efficient (in terms of speed, accuracy, memory requirements) than the Numerical Recipe code. • The revised Simplex procedures and the computer program developed in this work could be applied to solve nonlinear programming problems where the LP code is required as the basic building block .