Relative Position Indexing Approach - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 113

val1 = Min[val1 , val2] , val1 = Min[val1 , val2] ,

Optimize`NMinimizeDump`vec = vec1];

Optimize`NMinimizeDump`vec = vec1];

Optimize`NMinimizeDump`vec = vec1];
If[val1 < best ,

If[val1 < best ,

If[val1 < best ,
best = val1;

best = val1;

best = val1;
vec1 = bestvec = Optimize`NMinimizeDump`vec;

vec1 = bestvec = Optimize`NMinimizeDump`vec;

vec1 = bestvec = Optimize`NMinimizeDump`vec;
If[printFlag ,

If[printFlag ,

If[printFlag ,
Print[“new low ” , ++indx , “

Print[“new low ” , ++indx , “

Print[“new low ” , ++indx , “

{ { { it erat ion , elapsedtime , newvalue

it erat ion , elapsedtime , newvalue it erat ion , elapsedtime , newvalue

} } } ” ,

” , ” ,

{ { { i , TimeUsed[] − i , TimeUsed[] i , TimeUsed[] − − tt , best tt , best tt , best } } ]];tt = TimeUsed[]; ]; } ]];tt = TimeUsed[]; ]; ]];tt = TimeUsed[]; ];

]]];
val1]; val1];

bestvec = Range[len];

val1];

bestvec = Range[len];
best = To tal[Flatten[mat1

bestvec = Range[len];

best = To tal[Flatten[mat1 best = To tal[Flatten[mat1 ∗ ∗ ∗ mat2]]; mat2]]; mat2]];

{ { { nmin , vals nmin , vals nmin , vals = NMinimize[objfunc[vars] , rnges ,

MaxIterations

} } } = NMinimize[objfunc[vars] , rnges , = NMinimize[objfunc[vars] , rnges ,

MaxIterations MaxIterations → → → it , Compiled it , Compiled it , Compiled → → → False , StepMonitor : False , StepMonitor : False , StepMonitor : → → → i ++ , i ++ , i ++ ,

Method Method Method →{ →{ →{ DifferentialEvolution , SearchPoints DifferentialEvolution , SearchPoints DifferentialEvolution , SearchPoints → → → sp ,, sp ,, sp ,,

CrossProbability CrossProbability CrossProbability → → → cpScalingFactor cpScalingFactor cpScalingFactor → → → sc , PostProcess sc , PostProcess sc , PostProcess → → → False False False } } } ]; ]; ];

Clear[objfunc2]; Clear[objfunc2];

{

{ { To tal[Flatten[mat1 To tal[Flatten[mat1 To tal[Flatten[mat1 permuteMatrix[mat2 ,

Ordering[bestvec]]]] , Ordering[bestvec]

∗ ∗ ∗ permuteMatrix[mat2 , permuteMatrix[mat2 ,

Ordering[bestvec]]]] , Ordering[bestvec] Ordering[bestvec]]]] , Ordering[bestvec] } } } ] ] ]

We now show a run with printout included. The parameter settings are, as usual, based
on shorter tuning runs.

Timing[QAP4[mat1 , mat2 ,. 08 , 400 , 320 ,. 4 , 4 ,. 4 , False , True]]

locally improved { 4838 , 4788 }

new low 1 { iteration, elapsed time, new value }{ 0 , 0 . 280017 , 4788 }

locally improved { 4788 , 4724 }

new low 2 { iteration, elapsed time, new value }{ 0 , 0 . 012001 , 4724 }

locally improved { 4724 , 4696 }

new low 3 { iteration, elapsed time, new value }{ 0 , 0 ., 4696 }

locally improved { 4696 , 4644 }

new low 4 { iteration, elapsed time, new value }{ 0 , 0 ., 4644 }

locally improved { 4644 , 4612 }

{ }{

0 , 0 . 240015 , 4612

}

new low 5 iteration, elapsed time, new value

{

4612 , 4594

}

locally improved

{ }{

0 , 0 . 100006 , 4594

}

new low 6 iteration, elapsed time, new value

locally improved { 4594 , 4566 }

new low 7 { iteration, elapsed time, new value }{ 0 , 0 . 004 , 4566 }

locally improved { 4566 , 4498 }

new low 8 { iteration, elapsed time, new value }{ 0 , 0 ., 4498 }

locally improved { 4498 , 4370 }

new low 9 { iteration, elapsed time, new value }{ 0 , 0 . 972061 , 4370 }

locally improved { 4370 , 4348 }

new low 10 { iteration, elapsed time, new value }{ 0 , 0 . 004 , 4348 }

locally improved { 4348 , 4322 }

new low 11 { iteration, elapsed time, new value }{ 10 , 21 . 3933 , 4322 }