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Optimization Engr Design

by: Chloe Reilly

Optimization Engr Design ME 6103

Chloe Reilly

GPA 3.62

Berdinus Bras

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Berdinus Bras
Class Notes
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This 0 page Class Notes was uploaded by Chloe Reilly on Monday November 2, 2015. The Class Notes belongs to ME 6103 at Georgia Institute of Technology - Main Campus taught by Berdinus Bras in Fall. Since its upload, it has received 24 views. For similar materials see /class/234235/me-6103-georgia-institute-of-technology-main-campus in Mechanical Engineering at Georgia Institute of Technology - Main Campus.

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Date Created: 11/02/15
ME 6103 Optimization in Engineering Design Bras N L 4 UI REVISED MULTIPHASE SIMPLEX MULTIPLEX ALGORITHM Find v so as to lexmin uT clTv CkTV cKTv subject to Av b KN X v20 where VL77JLd J p d Initialization Let VB 11 d39 Thus B I B391 I and B b Set k 1 Initially all variables are unchecked Develop tlie pricing vector Determine 1ckT cBkT B391 Price out all UNCHECKED nonbasic columns Compute rjk 1tkT aj cJ39k for allj S N where N is the set of nonbasic and unchecked variables Selection of entering nonbasic variable Examine those rjk as computed in step 3 If none are positive proceed to step 8 Otherwise select the nonbasic variable with the most positive rjk ties may be broken arbitrarily as the entering variable Designate this variable as vq Update tlie entering column Evaluate aq B391 aq Determine tbe lea vmg basic variable The leaving variable row is designated as lp Using the present representation of 3 B39lb and the values of aq as derived in step 5 determine e e 01 If on qgt 0 Again ties may be broken arbitrarily The basic variable associated with row ip is the leaving variable VBp If none exists the entering variable is unbounded all an S 0 This condition will not occur as long as v 2 0 andck 2 0 for all k In such case no elements of uT can become less than 0 and therefore are always bounded Pivot Replace the column ap in B by aq and compute the neWbasis inverse B39l Return to step 2 Convergence clieck If either one or both of the following conditions holds STOP as the optimal solution has been found a if all rjk as computed in step 3 are negative or b if k K where K the number of priority levels or terms in uT Dr Bert Bras Telephone 4048949667 Fax 4048949342 Email bertbrasmegatechedu


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