Clarification of potential bug in ISRES implementation

[kramawa]

In the referenced paper, the ISRES algorithm contains the following line for differential variation of the best $k < \mu$:

$x_k' \gets x_i + \gamma (x_1 - x_{i+1})$

In the corresponding code this is stated as

xs[rk*n+j] += GAMMA * (x0[j] - xs[(k+1)*n+j])

where int rk = irank[k];

Since xs[rk*n+j] references similarly $x_k'$ and $x_i$, shouldn't for referencing $x_{i+1}$ instead of xs[(k+1)*n+j],
the following be used: xs[irank[k+1]*n+j]?

My current understanding is that xs[(k+1)*n+j] just references the point with index $k+1$ in the population set, but which is - from my understanding of the algorithm at this point - not necessarily the ranked point $x_{i+1}$ that should be actually accessed.

Full affected line can be found here:

nlopt/src/algs/isres/isres.c

Line 260 in 128b04c

xs[rk*n+j] += GAMMA * (x0[j] - xs[(k+1)*n+j]);

Would appreciate any comments or clarifications regarding this matter.

[stevengj]

I haven't looked at this code for years, but it's possible you are right. Can you try the modified version on a test problem?

[kramawa]

I just tried both versions with the test-tool (testopt) on all objective functions with seed equaling to $1$ and with $300000$ evaluations.

There is for some values a slight difference, the biggest one is at Shekel m=5 function, where the modified algorithm seems to have the more precise value.

Here is the output with the current version of ISRES:

-----------------------------------------------------------
Optimizing Rosenbrock function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -2 -2]
upper bounds at ub = [ 2 2]
Starting guess x = [ -0.165956 0.440649]
Starting function value = 18.4252
finished after 0.046917 seconds.
return code 5 from nlopt_minimize
Found minimum f = 0 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1]
|f - minf| = 0
vs. global minimum f = 0 at x = [ 1 1]
-----------------------------------------------------------
Optimizing McCormic function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -1.5 -3]
upper bounds at ub = [ 4 4]
Starting guess x = [ 1.02181 1.27114]
Starting function value = 3.45767
finished after 0.051592 seconds.
return code 5 from nlopt_minimize
Found minimum f = -1.91322 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -0.547198 -1.5472]
|f - minf| = 4.98104e-09, |f - minf| / |minf| = 2.603479e-09
vs. global minimum f = -1.91322 at x = [ -0.547198 -1.5472]
-----------------------------------------------------------
Optimizing Box and Betts exponential quadratic sum (3 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0.9 9 0.9]
upper bounds at ub = [ 1.2 11.2 1.2]
Starting guess x = [ 1.03755 10.3424 0.975017]
Starting function value = 0.00122421
finished after 0.098883 seconds.
return code 5 from nlopt_minimize
Found minimum f = 0 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 10 1]
|f - minf| = 0
vs. global minimum f = 0 at x = [ 1 10 1]
-----------------------------------------------------------
Optimizing Paviani function (10 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 2.001 2.001 2.001 2.001 2.001 2.001 2.001 2.001 2.001 2.001]
upper bounds at ub = [ 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999]
Starting guess x = [ 5.66817 6.88108 4.00096 5.20953 4.58738 4.36976 4.74535 5.3824 5.58717 6.15523]
Starting function value = 10.9262
finished after 0.189978 seconds.
return code 5 from nlopt_minimize
Found minimum f = -45.7785 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027]
|f - minf| = 7.44631e-09, |f - minf| / |minf| = 1.626597e-10
vs. global minimum f = -45.7785 at x = [ 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027]
-----------------------------------------------------------
Optimizing Generalized Rosenbrock function (30 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30]
upper bounds at ub = [ 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30]
Starting guess x = [ -2.48934 6.60973 -14.9966 -5.93002 -10.5973 -12.2298 -9.41219 -4.63318 -3.09698 1.1645 -2.42416 5.55659 -8.86643 11.3435 -14.1784 5.11403 -2.48086 1.76069 -10.7884 -9.05696 9.02234 14.0478 -5.59727 5.76968 11.2917 11.8382 -12.4487 -13.8284 -9.90509 11.3443]
Starting function value = 3.55995e+07
finished after 0.473126 seconds.
return code 5 from nlopt_minimize
Found minimum f = 29.0893 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 0.293901 0.083745 0.0292208 -0.0241097 0.0457075 0.00271288 0.0136066 0.0329111 0.00186233 0.0179083 0.0127778 -0.00600684 0.0406652 0.00304871 -0.00947953 0.00840274 0.0211317 0.0478192 0.000118107 -0.00820445 0.0229245 0.0303591 0.0424255 -0.000709953 0.0458232 0.0281055 0.0134992 0.0246513 0.0134011 -0.00294885]
|f - minf| = 29.0893
vs. global minimum f = 0 at x = [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
-----------------------------------------------------------
Optimizing Goldstein and Price function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -2 -2]
upper bounds at ub = [ 2 2]
Starting guess x = [ -0.165956 0.440649]
Starting function value = 4523.99
finished after 0.051598 seconds.
return code 5 from nlopt_minimize
Found minimum f = 3 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1.07396e-09 -1]
|f - minf| = 9.59233e-14, |f - minf| / |minf| = 3.197442e-14
vs. global minimum f = 3 at x = [ 0 -1]
-----------------------------------------------------------
Optimizing Shekel m=5 function (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0 0 0 0]
upper bounds at ub = [ 10 10 10 10]
Starting guess x = [ 4.58511 6.10162 2.50057 4.01166]
Starting function value = -0.308018
finished after 0.080257 seconds.
return code 5 from nlopt_minimize
Found minimum f = -3.84957 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 3.92292 3.79056 4.19722 4.2863]
|f - minf| = 6.30363, |f - minf| / |minf| = 6.208516e-01
vs. global minimum f = -10.1532 at x = [ 4.00004 4.00013 4.00004 4.00013]
-----------------------------------------------------------
Optimizing Shekel m=7 function (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0 0 0 0]
upper bounds at ub = [ 10 10 10 10]
Starting guess x = [ 4.58511 6.10162 2.50057 4.01166]
Starting function value = -0.670516
finished after 0.084586 seconds.
return code 5 from nlopt_minimize
Found minimum f = -10.4029 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 4.00057 4.00069 3.99949 3.99961]
|f - minf| = 3.18133e-09, |f - minf| / |minf| = 3.058111e-10
vs. global minimum f = -10.4029 at x = [ 4.00057 4.00069 3.99949 3.99961]
-----------------------------------------------------------
Optimizing Shekel m=10 function (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0 0 0 0]
upper bounds at ub = [ 10 10 10 10]
Starting guess x = [ 4.58511 6.10162 2.50057 4.01166]
Starting function value = -0.741761
finished after 0.079244 seconds.
return code 5 from nlopt_minimize
Found minimum f = -10.5364 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 4.00075 4.00059 3.99966 3.99951]
|f - minf| = 3.30795e-09, |f - minf| / |minf| = 3.139541e-10
vs. global minimum f = -10.5364 at x = [ 4.00075 4.00059 3.99966 3.99951]
-----------------------------------------------------------
Optimizing Levy n=4 function (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -10 -10 -10 -10]
upper bounds at ub = [ 10 10 10 10]
Starting guess x = [ -0.82978 2.20324 -4.99886 -1.97667]
Starting function value = 43.4181
finished after 0.089601 seconds.
return code 5 from nlopt_minimize
Found minimum f = -21.5024 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1 1 -9.75236]
|f - minf| = 2.38633e-09, |f - minf| / |minf| = 1.109797e-10
vs. global minimum f = -21.5024 at x = [ 1 1 1 -9.75236]
-----------------------------------------------------------
Optimizing Levy n=5 function (5 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5 -5 -5 -5 -5]
upper bounds at ub = [ 5 5 5 5 5]
Starting guess x = [ -0.41489 1.10162 -2.49943 -0.988337 -1.76622]
Starting function value = 17.2599
finished after 0.096389 seconds.
return code 5 from nlopt_minimize
Found minimum f = -11.5044 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1 1 1 -4.7544]
|f - minf| = 1.37622e-09, |f - minf| / |minf| = 1.196257e-10
vs. global minimum f = -11.5044 at x = [ 1 1 1 1 -4.7544]
-----------------------------------------------------------
Optimizing Levy n=6 function (6 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5 -5 -5 -5 -5 -5]
upper bounds at ub = [ 5 5 5 5 5 5]
Starting guess x = [ -0.41489 1.10162 -2.49943 -0.988337 -1.76622 -2.03831]
Starting function value = 28.1595
finished after 0.117763 seconds.
return code 5 from nlopt_minimize
Found minimum f = -11.5044 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1 1 1 1 -4.7544]
|f - minf| = 1.37622e-09, |f - minf| / |minf| = 1.196257e-10
vs. global minimum f = -11.5044 at x = [ 1 1 1 1 1 -4.7544]
-----------------------------------------------------------
Optimizing Levy n=7 function (7 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5 -5 -5 -5 -5 -5 -5]
upper bounds at ub = [ 5 5 5 5 5 5 5]
Starting guess x = [ -0.41489 1.10162 -2.49943 -0.988337 -1.76622 -2.03831 -1.5687]
Starting function value = 43.4563
finished after 0.133465 seconds.
return code 5 from nlopt_minimize
Found minimum f = -11.5044 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1 1 1 1 1 -4.7544]
|f - minf| = 1.37622e-09, |f - minf| / |minf| = 1.196257e-10
vs. global minimum f = -11.5044 at x = [ 1 1 1 1 1 1 -4.7544]
-----------------------------------------------------------
Optimizing Griewank function (10 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -500 -500 -500 -500 -500 -500 -500 -500 -500 -500]
upper bounds at ub = [ 600 600 600 600 600 600 600 600 600 600]
Starting guess x = [ 4.3621 171.178 -224.937 -58.7171 -144.284 -174.214 -122.557 -34.9416 -6.77789 71.3492]
Starting function value = 39.978
finished after 0.182145 seconds.
return code 5 from nlopt_minimize
Found minimum f = 0.027037 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -2.52187e-09 4.43844 6.06611e-09 6.65291e-10 1.2603e-08 -5.43648e-09 1.16176e-09 9.84502e-10 9.38255 1.26715e-09]
|f - minf| = 0.027037
vs. global minimum f = 0 at x = [ 0 0 0 0 0 0 0 0 0 0]
-----------------------------------------------------------
Optimizing Six-hump camel back function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5 -5]
upper bounds at ub = [ 5 5]
Starting guess x = [ -0.41489 1.10162]
Starting function value = 1.2077
finished after 0.10642 seconds.
return code 5 from nlopt_minimize
Found minimum f = -1.03163 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 0.089842 -0.712656]
|f - minf| = 4.89878e-10, |f - minf| / |minf| = 4.748589e-10
vs. global minimum f = -1.03163 at x = [ 0.089842 -0.712656]
-----------------------------------------------------------
Optimizing Convex product of cosh functions (10 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -1 0 0 0 0 0 0 0 0 0]
upper bounds at ub = [ 2 3 6 7 8 10 11 13 14 16]
Starting guess x = [ 0.375533 1.83049 1.50034 2.80816 2.58702 2.96169 3.77443 5.49614 6.27737 8.31053]
Starting function value = 1.75958e+29
finished after 0.184133 seconds.
return code 5 from nlopt_minimize
Found minimum f = 1 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -1.87084e-09 1 2 3 4 5 6 7 8 9]
|f - minf| = 0, |f - minf| / |minf| = 0.000000e+00
vs. global minimum f = 1 at x = [ 0 1 2 3 4 5 6 7 8 9]
-----------------------------------------------------------
Optimizing Branin function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -10 -10]
upper bounds at ub = [ 10 10]
Starting guess x = [ -0.82978 2.20324]
Starting function value = 9.61175
finished after 0.048849 seconds.
return code 5 from nlopt_minimize
Found minimum f = 3.08149e-33 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 0.148696 0.402086]
|f - minf| = 3.08149e-33
vs. global minimum f = -0 at x = [ 1 0]
-----------------------------------------------------------
Optimizing Shubert function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -10 -10]
upper bounds at ub = [ 10 10]
Starting guess x = [ -0.82978 2.20324]
Starting function value = 4.74089
finished after 0.07388 seconds.
return code 5 from nlopt_minimize
Found minimum f = -24.0625 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -6.77458 -6.77458]
|f - minf| = 4.33429e-09, |f - minf| / |minf| = 1.801265e-10
vs. global minimum f = -24.0625 at x = [ -6.77458 -6.77458]
-----------------------------------------------------------
Optimizing Hansen function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -10 -10]
upper bounds at ub = [ 10 10]
Starting guess x = [ -0.82978 2.20324]
Starting function value = 4.09728
finished after 0.062086 seconds.
return code 5 from nlopt_minimize
Found minimum f = -176.542 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -1.30671 -7.70831]
|f - minf| = 4.57305e-11, |f - minf| / |minf| = 2.590352e-13
vs. global minimum f = -176.542 at x = [ -1.30671 -1.42513]
-----------------------------------------------------------
Optimizing 1d oscillating function with a single minimum (1 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5]
upper bounds at ub = [ 5]
Starting guess x = [ -0.41489]
Starting function value = 0.926593
finished after 0.032019 seconds.
return code 5 from nlopt_minimize
Found minimum f = -1 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1.23457]
|f - minf| = 0, |f - minf| / |minf| = 0.000000e+00
vs. global minimum f = -1 at x = [ 1.23457]
-----------------------------------------------------------
Optimizing 4d function with minimum at corner (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0 0 0 0]
upper bounds at ub = [ 1 1 1 1]
Starting guess x = [ 0.458511 0.610162 0.250057 0.401166]
Starting function value = 3.48162
finished after 0.087994 seconds.
return code 5 from nlopt_minimize
Found minimum f = 1 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 2.61998e-09 3.00523e-17 8.03991e-16 2.42016e-16]
|f - minf| = 0, |f - minf| / |minf| = 0.000000e+00
vs. global minimum f = 1 at x = [ 0 0 0 0]
-----------------------------------------------------------
Optimizing 4d function with minimum at side (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0.1 -1 -1 -1]
upper bounds at ub = [ 1 1 1 1]
Starting guess x = [ 0.51266 0.220324 -0.499886 -0.197667]
Starting function value = -23.7322
finished after 0.080519 seconds.
return code 5 from nlopt_minimize
Found minimum f = -141.285 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 0.1 0.102971 0.0760521 -0.0497099]
|f - minf| = 4.78678e-10, |f - minf| / |minf| = 3.388034e-12
vs. global minimum f = -141.285 at x = [ 0.1 0.102971 0.0760521 -0.0497099]

And here is the output with my proposed modification. For convenience I added an additional printf-statement to the ISRES implementation.

-----------------------------------------------------------
Optimizing Rosenbrock function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -2 -2]
upper bounds at ub = [ 2 2]
Starting guess x = [ -0.165956 0.440649]
Starting function value = 18.4252
ISRES: Using updated version of indeces.
finished after 0.049579 seconds.
return code 5 from nlopt_minimize
Found minimum f = 0 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1]
|f - minf| = 0
vs. global minimum f = 0 at x = [ 1 1]
-----------------------------------------------------------
Optimizing McCormic function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -1.5 -3]
upper bounds at ub = [ 4 4]
Starting guess x = [ 1.02181 1.27114]
Starting function value = 3.45767
ISRES: Using updated version of indeces.
finished after 0.048238 seconds.
return code 5 from nlopt_minimize
Found minimum f = -1.91322 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -0.547198 -1.5472]
|f - minf| = 4.98104e-09, |f - minf| / |minf| = 2.603479e-09
vs. global minimum f = -1.91322 at x = [ -0.547198 -1.5472]
-----------------------------------------------------------
Optimizing Box and Betts exponential quadratic sum (3 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0.9 9 0.9]
upper bounds at ub = [ 1.2 11.2 1.2]
Starting guess x = [ 1.03755 10.3424 0.975017]
Starting function value = 0.00122421
ISRES: Using updated version of indeces.
finished after 0.097927 seconds.
return code 5 from nlopt_minimize
Found minimum f = 0 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 10 1]
|f - minf| = 0
vs. global minimum f = 0 at x = [ 1 10 1]
-----------------------------------------------------------
Optimizing Paviani function (10 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 2.001 2.001 2.001 2.001 2.001 2.001 2.001 2.001 2.001 2.001]
upper bounds at ub = [ 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999 9.999]
Starting guess x = [ 5.66817 6.88108 4.00096 5.20953 4.58738 4.36976 4.74535 5.3824 5.58717 6.15523]
Starting function value = 10.9262
ISRES: Using updated version of indeces.
finished after 0.193015 seconds.
return code 5 from nlopt_minimize
Found minimum f = -45.7785 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027]
|f - minf| = 7.44631e-09, |f - minf| / |minf| = 1.626597e-10
vs. global minimum f = -45.7785 at x = [ 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027 9.35027]
-----------------------------------------------------------
Optimizing Generalized Rosenbrock function (30 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30]
upper bounds at ub = [ 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30]
Starting guess x = [ -2.48934 6.60973 -14.9966 -5.93002 -10.5973 -12.2298 -9.41219 -4.63318 -3.09698 1.1645 -2.42416 5.55659 -8.86643 11.3435 -14.1784 5.11403 -2.48086 1.76069 -10.7884 -9.05696 9.02234 14.0478 -5.59727 5.76968 11.2917 11.8382 -12.4487 -13.8284 -9.90509 11.3443]
Starting function value = 3.55995e+07
ISRES: Using updated version of indeces.
finished after 0.481741 seconds.
return code 5 from nlopt_minimize
Found minimum f = 29.3491 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 0.297308 0.0717253 -0.00478655 0.0281387 0.00109478 -0.0375167 -0.0151316 -0.0149271 0.0078109 0.0164012 0.0069337 0.0192961 -0.00895776 -0.00961966 0.0601332 0.0494229 0.023024 0.00305588 -0.00634535 0.000961425 0.0109218 0.00334781 -0.00145413 0.00868089 0.000194466 -0.00382627 0.0255585 -0.00421487 0.0108357 -0.0447896]
|f - minf| = 29.3491
vs. global minimum f = 0 at x = [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
-----------------------------------------------------------
Optimizing Goldstein and Price function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -2 -2]
upper bounds at ub = [ 2 2]
Starting guess x = [ -0.165956 0.440649]
Starting function value = 4523.99
ISRES: Using updated version of indeces.
finished after 0.050635 seconds.
return code 5 from nlopt_minimize
Found minimum f = 3 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -1.07475e-09 -1]
|f - minf| = 9.59233e-14, |f - minf| / |minf| = 3.197442e-14
vs. global minimum f = 3 at x = [ 0 -1]
-----------------------------------------------------------
Optimizing Shekel m=5 function (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0 0 0 0]
upper bounds at ub = [ 10 10 10 10]
Starting guess x = [ 4.58511 6.10162 2.50057 4.01166]
Starting function value = -0.308018
ISRES: Using updated version of indeces.
finished after 0.081207 seconds.
return code 5 from nlopt_minimize
Found minimum f = -10.1532 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 4.00004 4.00013 4.00004 4.00013]
|f - minf| = 9.41769e-10, |f - minf| / |minf| = 9.275592e-11
vs. global minimum f = -10.1532 at x = [ 4.00004 4.00013 4.00004 4.00013]
-----------------------------------------------------------
Optimizing Shekel m=7 function (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0 0 0 0]
upper bounds at ub = [ 10 10 10 10]
Starting guess x = [ 4.58511 6.10162 2.50057 4.01166]
Starting function value = -0.670516
ISRES: Using updated version of indeces.
finished after 0.083889 seconds.
return code 5 from nlopt_minimize
Found minimum f = -10.4029 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 4.00057 4.00069 3.99949 3.99961]
|f - minf| = 3.18133e-09, |f - minf| / |minf| = 3.058111e-10
vs. global minimum f = -10.4029 at x = [ 4.00057 4.00069 3.99949 3.99961]
-----------------------------------------------------------
Optimizing Shekel m=10 function (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0 0 0 0]
upper bounds at ub = [ 10 10 10 10]
Starting guess x = [ 4.58511 6.10162 2.50057 4.01166]
Starting function value = -0.741761
ISRES: Using updated version of indeces.
finished after 0.082556 seconds.
return code 5 from nlopt_minimize
Found minimum f = -10.5364 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 4.00075 4.00059 3.99966 3.99951]
|f - minf| = 3.30795e-09, |f - minf| / |minf| = 3.139541e-10
vs. global minimum f = -10.5364 at x = [ 4.00075 4.00059 3.99966 3.99951]
-----------------------------------------------------------
Optimizing Levy n=4 function (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -10 -10 -10 -10]
upper bounds at ub = [ 10 10 10 10]
Starting guess x = [ -0.82978 2.20324 -4.99886 -1.97667]
Starting function value = 43.4181
ISRES: Using updated version of indeces.
finished after 0.093282 seconds.
return code 5 from nlopt_minimize
Found minimum f = -21.5024 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1 1 -9.75236]
|f - minf| = 2.38633e-09, |f - minf| / |minf| = 1.109797e-10
vs. global minimum f = -21.5024 at x = [ 1 1 1 -9.75236]
-----------------------------------------------------------
Optimizing Levy n=5 function (5 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5 -5 -5 -5 -5]
upper bounds at ub = [ 5 5 5 5 5]
Starting guess x = [ -0.41489 1.10162 -2.49943 -0.988337 -1.76622]
Starting function value = 17.2599
ISRES: Using updated version of indeces.
finished after 0.097082 seconds.
return code 5 from nlopt_minimize
Found minimum f = -11.5044 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1 1 1 -4.7544]
|f - minf| = 1.37622e-09, |f - minf| / |minf| = 1.196257e-10
vs. global minimum f = -11.5044 at x = [ 1 1 1 1 -4.7544]
-----------------------------------------------------------
Optimizing Levy n=6 function (6 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5 -5 -5 -5 -5 -5]
upper bounds at ub = [ 5 5 5 5 5 5]
Starting guess x = [ -0.41489 1.10162 -2.49943 -0.988337 -1.76622 -2.03831]
Starting function value = 28.1595
ISRES: Using updated version of indeces.
finished after 0.120365 seconds.
return code 5 from nlopt_minimize
Found minimum f = -11.5044 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1 1 1 1 -4.7544]
|f - minf| = 1.37622e-09, |f - minf| / |minf| = 1.196257e-10
vs. global minimum f = -11.5044 at x = [ 1 1 1 1 1 -4.7544]
-----------------------------------------------------------
Optimizing Levy n=7 function (7 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5 -5 -5 -5 -5 -5 -5]
upper bounds at ub = [ 5 5 5 5 5 5 5]
Starting guess x = [ -0.41489 1.10162 -2.49943 -0.988337 -1.76622 -2.03831 -1.5687]
Starting function value = 43.4563
ISRES: Using updated version of indeces.
finished after 0.186066 seconds.
return code 5 from nlopt_minimize
Found minimum f = -11.5044 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1 1 1 1 1 1 -4.7544]
|f - minf| = 1.37622e-09, |f - minf| / |minf| = 1.196257e-10
vs. global minimum f = -11.5044 at x = [ 1 1 1 1 1 1 -4.7544]
-----------------------------------------------------------
Optimizing Griewank function (10 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -500 -500 -500 -500 -500 -500 -500 -500 -500 -500]
upper bounds at ub = [ 600 600 600 600 600 600 600 600 600 600]
Starting guess x = [ 4.3621 171.178 -224.937 -58.7171 -144.284 -174.214 -122.557 -34.9416 -6.77789 71.3492]
Starting function value = 39.978
ISRES: Using updated version of indeces.
finished after 0.197683 seconds.
return code 5 from nlopt_minimize
Found minimum f = 0.0664047 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -3.14002 4.43844 -5.43325 6.27064 -2.49705e-09 -3.20354e-09 1.33174e-08 8.85036 -9.38255 -1.56563e-08]
|f - minf| = 0.0664047
vs. global minimum f = 0 at x = [ 0 0 0 0 0 0 0 0 0 0]
-----------------------------------------------------------
Optimizing Six-hump camel back function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5 -5]
upper bounds at ub = [ 5 5]
Starting guess x = [ -0.41489 1.10162]
Starting function value = 1.2077
ISRES: Using updated version of indeces.
finished after 0.052905 seconds.
return code 5 from nlopt_minimize
Found minimum f = -1.03163 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -0.089842 0.712656]
|f - minf| = 4.89878e-10, |f - minf| / |minf| = 4.748589e-10
vs. global minimum f = -1.03163 at x = [ 0.089842 -0.712656]
-----------------------------------------------------------
Optimizing Convex product of cosh functions (10 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -1 0 0 0 0 0 0 0 0 0]
upper bounds at ub = [ 2 3 6 7 8 10 11 13 14 16]
Starting guess x = [ 0.375533 1.83049 1.50034 2.80816 2.58702 2.96169 3.77443 5.49614 6.27737 8.31053]
Starting function value = 1.75958e+29
ISRES: Using updated version of indeces.
finished after 0.213436 seconds.
return code 5 from nlopt_minimize
Found minimum f = 1 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -5.96653e-09 1 2 3 4 5 6 7 8 9]
|f - minf| = 0, |f - minf| / |minf| = 0.000000e+00
vs. global minimum f = 1 at x = [ 0 1 2 3 4 5 6 7 8 9]
-----------------------------------------------------------
Optimizing Branin function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -10 -10]
upper bounds at ub = [ 10 10]
Starting guess x = [ -0.82978 2.20324]
Starting function value = 9.61175
ISRES: Using updated version of indeces.
finished after 0.051607 seconds.
return code 5 from nlopt_minimize
Found minimum f = 3.08149e-33 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 0.148696 0.402086]
|f - minf| = 3.08149e-33
vs. global minimum f = -0 at x = [ 1 0]
-----------------------------------------------------------
Optimizing Shubert function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -10 -10]
upper bounds at ub = [ 10 10]
Starting guess x = [ -0.82978 2.20324]
Starting function value = 4.74089
ISRES: Using updated version of indeces.
finished after 0.067208 seconds.
return code 5 from nlopt_minimize
Found minimum f = -24.0625 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -0.491391 -6.77458]
|f - minf| = 4.33429e-09, |f - minf| / |minf| = 1.801263e-10
vs. global minimum f = -24.0625 at x = [ -6.77458 -6.77458]
-----------------------------------------------------------
Optimizing Hansen function (2 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -10 -10]
upper bounds at ub = [ 10 10]
Starting guess x = [ -0.82978 2.20324]
Starting function value = 4.09728
ISRES: Using updated version of indeces.
finished after 0.067565 seconds.
return code 5 from nlopt_minimize
Found minimum f = -176.542 after 300000 evaluations (numevals = 300000).
Minimum at x = [ -7.58989 -1.42513]
|f - minf| = 4.57021e-11, |f - minf| / |minf| = 2.588742e-13
vs. global minimum f = -176.542 at x = [ -1.30671 -1.42513]
-----------------------------------------------------------
Optimizing 1d oscillating function with a single minimum (1 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ -5]
upper bounds at ub = [ 5]
Starting guess x = [ -0.41489]
Starting function value = 0.926593
ISRES: Using updated version of indeces.
finished after 0.034017 seconds.
return code 5 from nlopt_minimize
Found minimum f = -1 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 1.23457]
|f - minf| = 0, |f - minf| / |minf| = 0.000000e+00
vs. global minimum f = -1 at x = [ 1.23457]
-----------------------------------------------------------
Optimizing 4d function with minimum at corner (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0 0 0 0]
upper bounds at ub = [ 1 1 1 1]
Starting guess x = [ 0.458511 0.610162 0.250057 0.401166]
Starting function value = 3.48162
ISRES: Using updated version of indeces.
finished after 0.089929 seconds.
return code 5 from nlopt_minimize
Found minimum f = 1 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 3.11425e-09 3.91903e-16 1.69425e-16 3.77083e-16]
|f - minf| = 0, |f - minf| / |minf| = 0.000000e+00
vs. global minimum f = 1 at x = [ 0 0 0 0]
-----------------------------------------------------------
Optimizing 4d function with minimum at side (4 dims) using ISRES evolutionary constrained optimization (global, no-derivative) algorithm
lower bounds at lb = [ 0.1 -1 -1 -1]
upper bounds at ub = [ 1 1 1 1]
Starting guess x = [ 0.51266 0.220324 -0.499886 -0.197667]
Starting function value = -23.7322
ISRES: Using updated version of indeces.
finished after 0.091347 seconds.
return code 5 from nlopt_minimize
Found minimum f = -141.285 after 300000 evaluations (numevals = 300000).
Minimum at x = [ 0.1 0.102971 0.0760521 -0.0497099]
|f - minf| = 4.78678e-10, |f - minf| / |minf| = 3.388034e-12
vs. global minimum f = -141.285 at x = [ 0.1 0.102971 0.0760521 -0.0497099]

What is your opinion about that?

[stevengj]

What stopping criteria are you using? I would use something like -m 1e-2 so that it stops when it is within 0.01 of the optimum, and check how many iterations this took.

It would be good to try it on a problem with a nonlinear constraint, e.g. https://github.com/stevengj/nlopt/blob/master/test/t_tutorial.cxx (probably after #591 is merged so that you can see the evaluation count).

Update: I tried the old and new versions of isres.c with t_tutorial.cxx, after merging the PR, above. Running it 1000 times and collecting the evaluation counts with repeat 1000 test/t_tutorial 35 |cut -d' ' -f18, I got a median of 14618 iterations for the old version and 15237 iterations for the new version (the std. dev was about ±3000 iterations for both, but the difference is larger than stddev/sqrt(1000) so it seems significant). So it's certainly not an obvious improvement, and may even be worse.

(As I said, I don't remember this code very well; I'd have to go back and read it and the paper carefully to be sure what was intended here.)