The information related to the optimization methods (ALM, FR, and LS)
appears in a listing file that is dedicated to the optimization, rather
than the standard listing file. The base name of this listing file is the same as
that of the output sensitivities file (that is, the .sen
file), and is followed by the extension .optslv (for
example, MyExample.optslv). The names of the design
variables, objective functions and constraints are unknowns in this file; only their
assigned index numbers are known.
The listing file for optimization contains the optimizer parameters and the bounds of the design variables, as shown in the example that follows.
********************** * * * POLYFLOW * * OPTIMIZER * * * ********************** PARAMETERS: - Maximum number of solutions to reach optimum: 100 - Max iteration to find bracketed minimum: 3 - Max iteration before reseting search direction: 4 - Initial penalty coefficient: +1.000000000e+000 - Penalty factor multiplier: +2.000000000e+000 - Max penalty: +5.000000000e+005 INITIAL VARIABLES AND BOUNDS: Design Variables data: ====================== 1)End_Parallel_Dis 2)J_F_Displ. Lower bounds 1) +0.000000000e+000 +0.000000000e+000 Current values 1) +0.000000000e+000 +0.000000000e+000 Upper bounds 1) +4.990000000e+000 +1.000000000e+000
Next, an iteration of the ALM method begins, and the initial function values, the
penalty coefficient, and the Lagrange Multiplier associate with the violated
constraints is printed. The values, the limit value, and the augmented Lagrange
limit (
) are printed for the constraints:
BEGIN AUGMENTED LAGRANGE SEQUENCE: 2 Initial Design variable values ------------------------------ Design variables: 1) +4.528190109e+000 +1.000000000e+000 Initial Function values ----------------------- Objective function = +8.457564090e-001 Normalized objective = +1.008457564e+002 Normalized cost (A) = +1.008532804e+002 Constraints: - Constraint on inlet pressure is violated (limit + aug. Lagrange limit) value = -4.645558861e+004 > +0.000000000e+000 + 3.047173562e+010 Penalty and Lagrange Multipliers for constraints ------------------------------------------------ Penalty = +2.000000000e+000 lambda = +7.082372134e-002 for constraint number 0
At the beginning of the FR method algorithm, the gradient of the cost function
(
), the search direction, and the scaled search direction are
printed:
BEGIN FLETCHER-REEVES STEP 1
Gradient of objective function df/dDV (Number of gradient evaluation 5)
1) -4.322516811e-002 -2.005566734e-001
Search direction:
1) -3.220570555e-001 +0.000000000e+000
Search direction (Scaled) :
1) -1.000000000e+000 +0.000000000e+000
At the beginning of the LS method algorithm, the initial and the maximum values of
are printed:
Proposed alfa = +2.331935609e-002 alfaMax = +9.074529275e-001 BEGIN ONE-DIMENSIONAL SEARCH Find brackets on minimum
Next, the current value of the design variables, the value of the objective
function (
), the normalized objective (
), the normalized cost (
), and the status and value of constraints are printed for each
function evaluation:
1) Alfa = +2.331935609e-002 (Number of function evaluations : 21)
Design variables
1) +4.411826522e+000 +1.000000000e+000
Objective function = +8.515483763e-001
Normalized objective = +1.008515484e+002
Normalized cost (A) = +1.008515505e+002
Constraints:
- Constraint on inlet pressure is violated (limit + aug. Lagrange limit)
value = -3.965115075e+001 > +0.000000000e+000 + 2.322779430e+004
The same information as noted previously is printed for a subiteration, except with an appropriate subiteration index number. When the minimum is bracketed, a message is printed with the bracketed bounds:
Brackets, alfaLower = +0.000000000e+000 alfaUpper = +6.105086684e-002
At the end of the LS method algorithm, the information that was printed during the LS iteration is printed. Since the end of the LS method is also the end of one iteration of the FR method, the convergence information related to the FR method is printed as well:
Result of line search :
Alfa = +1.507287472e-002 (Number of function evaluations : 24)
Design variables
1) +4.452976464e+000 +1.000000000e+000
Objective function = +8.493531370e-001
Normalized objective = +1.008493531e+002
Normalized cost (A) = +1.008508696e+002
Constraints:
- Constraint on inlet pressure is violated (limit + aug. Lagrange limit)
value = -1.644541087e+004 > +0.000000000e+000 + 2.322779430e+004
END FLETCHER-REEVES STEP 1
CONVERGENCE TEST.
Step check:
step = +1.507287472e-002 | precDV*.5 = +4.999999850e-006
step+stepDirPrev = +1.015072875e+000 | precDV = +9.999999700e-006
Cost check:
fCost-fCostprev = +2.410837052e-003 | CADOE_EPSILON = +1.000000000e-014
(fCost-fCostprev)/SDelta = +2.390497123e-005 | precLag = +9.999999700e-006
SDelta = +1.008508661e+002
Non Convergence for design variables and cost.
Slope = +2.173368091e-006
When convergence is reached for the FR method algorithm, the information related to the convergence of the ALM method is printed:
END OF AUGMENTED LAGRANGE SEQUENCE 2
Design variables
1) +4.452616373e+000 +1.000000000e+000
Objective and constraint values
Objective function = +8.493717665e-001
Normalized objective = +1.008493718e+002
Normalized cost (A) = +1.008508695e+002
Constraints:
- Constraint on inlet pressure is violated (limit + aug. Lagrange limit)
value = -1.630181300e+004 > +0.000000000e+000 + 2.322779430e+004
Gradient of objective function df/dDV (Number of gradient evaluation : 7)
1) -5.175122201e-002 -1.985748837e-001
CHECK CONVERGENCE OF NON_LINEAR CONSTRAINT
const[ 0] = +1.242643884e-002 | precision : +9.999999700e-006
Convergence not assumed for non-linear constraints.
CHECK CONVERGENCE OF BOUND CONSTRAINT
Bound constraints are converged.
CHECK CONVERGENCE OF OBJECTIVE FUNCTION
Final cost = +8.493717665e-001
Previous cost = +8.457564090e-001
Cost variation = +3.615357495e-003 | precision = +9.999999700e-004
Convergence not assumed for function cost.
GLOBAL CONVERGENCE NOT YET SATISFIED
At the end of the optimization, the total number of function evaluations (including those that failed and succeeded) and the sensitivities (gradient) evaluations are printed:
GLOBAL CONVERGENCE: End of Optimization _____________________ Number of function evaluation : 45 Number of gradient evaluation : 13