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| − | |'''Time'''
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| − | |'''Narration'''
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| − | |નમસ્તે મિત્રો,
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| − | | '''Scilab''' ઉપયોગ કરીને '''Optimization of Linear Functions with Linear Constraints ''' પરના સ્પોકન ટ્યુટોરીયલમાં તમારું સ્વાગત છે.
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| − | | આ ટ્યુટોરીયલમ્ક આપને શીખ્યા :
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| − | | '''Optimization''' નો અર્થ શું છે ?
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| − | | અને ઓપ્ટિમાઇઝેશન માં '''Scilab function karmarkar''' ને કેવી રીતે ઉપયોગ કરે છે.
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| − | |'''Optimization''' નો અર્થ
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| − | | આપેલ '''objective function''' ને મીનીમાઇઝ અથવા મેક્સીમાઈઝ કરવાનું છે.
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| − | |ડીસીજ્ન વેરીએબલને જુદું કરીને ક્યારે ક્યારે આને '''Cost function''' પણ કરે છે.
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| − | | પૂર્વવ્યાખ્યાયિત '''constraints '''ના અનુસાર ડીસીજ્ન વેરીએબલને બદલવાય છે.
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| − | | આ '''constraints ''' વેરીએબલના અમુક ફંકશન ના ફોર્મમાં પણ હોય છે.
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| − | | '''Optimization''' વ્યાપક રૂપથી આપેલ એન્જીનિયરિંગ અને નોન-એન્જીનિયરિંગ ક્ષેત્રો માં વધુ ઉપયોગ થાય છે.
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| − | | ઇકોનોમિક્સ
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| − | | કન્ટ્રોલ થીયરી અને
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| − | | ઓપરેશન્સ અને રિસર્ચ.
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| − | | '''Scilab function karmarkar''' આપેલમાં ઉપયોગ થાય છે:
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| − | |લીન્યર ઓબ્જેક્ટીવ ફંકશન ને ઓપ્ટીમાઈઝ કરવા માટે,
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| − | | લીનીયર '''constraints ''' પર
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| − | || ડીસીજ્ન વેરીએબલસ પર.
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| − | || આપણે '''karmarkar''' ફંકશન ઉપયોગ કરીને આપેલ ઉદાહરણોને હલ કરીશું:
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| − | | આપેલ ઇક્વેશન ના માટે મીનીમાઇઝ '''minus three 'x' one minus 'x' two minus three 'x' three''' મીનીમાઇઝ કરો.
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| − | | '''two 'x' one plus 'x' two plus 'x' three less than or equal to two.''' ના માટે:
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| − | |''' 'x' one plus two 'x' two plus three 'x' three less than or equal to five.'''
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| − | ||'''two 'x' one plus two 'x' two plus 'x' three less than or equal to six.'''
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| − | |જ્યાં ''' 'x' one 'x' two 'x' three''' are all '''greater than''' or '''equal to zero'''
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| − | | નોંધ લો કે બધા ફંકશન જો તે સમાન્ય હોય અથવા પ્રતિબંધીત લીનીયર હોય છે .
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| − | |01:49
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| − | ||આપેલ પ્રોબ્લમ ને હલ કરવા પહેલા '''scilab console''' પર જાવ અને ટાઈપ કરો:
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| − | |01:54
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| − | | '''help karmarkar'''
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| − | | અને '''Enter.''' દબાવો.
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| − | | 01:59
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| − | ||તમે આર્ગ્યુંમેંટસ ની કોલિંગ સિક્વેંસ જોઈ શકો છો.
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| − | | હેલ્પ બ્રાઉઝરમાં આર્ગ્યુમેન્ટનું સ્પષ્ટિકરણ, વિવરણ અને અમુક ઉદાહરણ.
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| − | | '''Help Browser ''' ને બંદ કરો.
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| − | |02:14
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| − | | અહી આપણે ઈનપુટ અને આઉટપુટ આર્ગ્યુમેન્ટસનું સારાંશ લેશું.
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| − | |આઉટપુટ અર્ગ્યુંમેંટ છે ''' 'x' opt, 'f' opt, exitflag, iter, 'y' opt '''.
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| − | |''' 'x' opt:''' એ '''optimum ''' એટલેકે સર્વોત્તમ સોલ્યુશન છે .
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| − | | 02:28
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| − | | ઓપ્ટીમમ સોલ્યુશન પર ઓબ્જેક્ટીવ ફંકશન વેલ્યુ છે
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| − | | 02:33
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| − | | એક્ઝીક્યુશ્નનું સ્ટેટસ છે, આ ઓળખવા માં મદદ કરે છે કે એલ્ગોરીધમ ભેગું થાય છે કે નહી.
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| − | |''' 'iter' ''': ''' 'x' opt.''' સુધી પહોચવા માટે જરૂરી ઈટરેશન ની સંખ્યા છે
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| − | |''' 'y' opt''' : એ '''dual solution.''' ધરાવનાર સંરચના છે.
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| − | | આ ''' Lagrange multipliers.''' આપે છે.
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| − | ||ઈનપુટ આર્ગ્યુમેન્ટસ છે ''' 'Aeq' 'beq' 'c' 'x zero' 'rtolf 'gam' 'maxiter' 'outfun' 'A' 'b' 'lb' અને 'ub' '''
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| − | || ''' 'Aeq' ''' : is the Matrix in the linear equality constraints. | + | || ''' 'Aeq' ''' : લીન્યર ''' linear equality constraints.''' મેટ્રીક્સ છે. |
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| − | | ''' 'beq' ''' :is the right hand side of the linear '''equality''' constraint. | + | | ''' 'beq' ''' : ''' linear equality constraint.''' નું જમણું ભાગ છે. |
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| − | |''' 'c' ''' : is the '''Linear objective function''' coefficients of ''' 'x'. ''' | + | |''' 'c' ''' : ''' 'x'. ''' નું '''Linear objective function''' એ ''' coefficients ''' છે. |
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| − | | ''' 'x' zero''' : is the '''Initial guess .''' | + | | ''' 'x' zero''' : '''Initial guess .''' છે. |
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| − | ||''' rtolf ''': is Relative tolerance on ''' 'f' of 'x' is equals to 'c' transpose multiplied by 'x'. ''' | + | ||''' rtolf ''': ''' 'f' of 'x' is equals to 'c' transpose multiplied by 'x'. ''' પર રીલેટીવ ટોલેરેન્સ છે. |
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| − | |''' 'gam' ''' : is the Scaling factor. | + | |''' 'gam' ''' : સ્કેલીંગ ફેક્ટર છે . |
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| − | |''' 'maxiter' ''' : is the ''' maximum''' number of iterations after which the output is returned. | + | |''' 'maxiter' ''' : આઉટપુટ રીટર્ન થવા પછી ઈટરેશન ની અધિકતમ સંખ્યા છે. |
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| − | |''' 'outfun' ''' : is the additional user-defined output function. | + | |''' 'outfun' ''' : અતિરિક્ત યુજર ડિફાઇંડ આઉટપુટ ફંકશન છે. |
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| − | | ''' 'A' ''': is the Matrix of linear inequality constraints
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| − | | ''' 'b' ''': is the right hand side of the linear ''' inequality''' constraints.
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| − | ||''' 'lb' ''': is the ''' lowerbound''' of ''' 'x'.'''
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| − | ||''' 'ub'''' are the '''upper bound''' of ''' 'x'. '''
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| − | ||Now, we can solve the given example in Scilab using '''karmarkar''' function.
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| − | |Go to the ''' scilab console''' and type:
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| − | |'A' is equals to open square bracket, two <space> one <space> one <semicolon> one <space> two <space> three <semicolon> two <space> two <space> one, close the square bracket
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| − | |and press Enter.
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| − | |similarly type: small 'b' equals to open square bracket, two <semicolon> five <semicolon> six, close the square bracket.
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| − | | and press '''Enter'''.
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| − | | Type: 'c' equals to open square bracket, minus three <semicolon> minus one <semicolon> minus three, close the square bracket.
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| − | |and press ''' Enter'''.
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| − | | Type: 'lb' equals to open square bracket, zero <semicolon> zero <semicolon> zero, close the square bracket.
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| − | |and press '''Enter'''.
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| − | |Now clear the console using '''clc''' command.
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| − | | Type: '''open square bracket, 'x' opt <comma> 'f' opt <comma> 'exitflag' <comma> iter, close the square bracket equals to karmarkar open parenthesis, open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> 'c' <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> capital 'A' <comma> 'small b' <comma> 'lb', close the round bracket.'''
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| − | | and Press '''Enter'''.
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| − | | Press Enter to continue the display.
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| − | | This will give the output as shown on the screen
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| − | | where '''xopt''' is the ''' optimum solution''' to the problem,
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| − | |'''fopt''' is the value of the objective function, calculated at optimum solution x is equal to '''xopt'''
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| − | |and number of iteration required to reach the optimum solution '''xopt''' is '''70'''.
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| − | |Please note that: it is mandatory to specify the input arguments in the same order
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| − | |in which they have been listed above, while calling the function.
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| − | |In this tutorial, we learned:
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| − | |What is ''' optimization?'''
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| − | |Use of '''Scilab function karmarkar''' in optimization to solve linear problems.
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| − | | 07:01
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| − | |To contact the scilab team, please write to '''contact@scilab.in'''
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| − | |07:08
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| − | | Watch the video available at the following link.
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| − | | It summarizes the Spoken Tutorial project.
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| − | |07:14
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| − | ||If you do not have good bandwidth, you can download and watch it.
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| − | |07:18
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| − | ||The spoken tutorial project Team:
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| − | |07:20
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| − | ||Conducts workshops using spoken tutorials.
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| − | |07:23
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| − | ||Gives certificates to those who pass an online test.
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| − | |07:27
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| − | ||For more details, please write to contact@spoken-tutorial.org.
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| − | |07:34
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| − | |Spoken Tutorial Project is a part of the Talk to a Teacher project.
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| − | | 07:37
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| − | | It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
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| − | | 07:44
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| − | |More information on this mission is available at spoken-tutorial.org/NMEICT-Intro.
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| − | | 07:53
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| − | |This is Anuradha Amrutkar from IIT Bombay, signing off.
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| − | |07:57
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| − | | Thank you for joining. Good Bye.
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