optimize: memoize wrapping

Closes stevengj#57

NEWS.md

@@ -6,6 +6,8 @@
 
 * Dropped unused LD_LBFGS_NOCEDAL enum value.
 
+* Fixed COBYLA not returning the optimum ([#57])
+
 * Various minor bugfixes ([#570], [#368], [#563], [#504])
 
 ## NLopt 2.8

src/api/optimize.c

@@ -394,6 +394,69 @@ static int elimdim_wrapcheck(nlopt_opt opt)
     }
 }
 
+/*********************************************************************/
+/* wrapper functions for algorithms not considering all evaluated points as candidates
+ * or returning only the last evaluation which might not be optimum */
+
+typedef struct {
+    nlopt_func f;
+    void *f_data;
+    const double *lb, *ub;      /* bounds, of length n */
+    double minf;
+    double *bestx;
+} memoize_data;
+
+
+static double memoize_func(unsigned n, const double *x, double *grad, void *d_)
+{
+    memoize_data *d = (memoize_data *) d_;
+    const double *lb = d->lb, *ub = d->ub;
+    double val;
+    unsigned i, feasible = 1;
+
+    val = d->f(n, x, grad, d->f_data);
+
+    for (i = 0; i < n; ++ i)
+    {
+        if (lb && (x[i] < lb[i]))
+            feasible = 0;
+        if (ub && (x[i] > ub[i]))
+            feasible = 0;
+    }
+    if (feasible && (val < d->minf))
+    {
+        d->minf = val;
+        for (i = 0; i < n; ++ i)
+            d->bestx[i] = x[i];
+    }
+    return val;
+}
+
+
+/* return whether to use memoize wrapping. */
+static int memoize_wrapcheck(nlopt_opt opt)
+{
+    if (!opt)
+        return 0;
+
+    /* constraints not supported */
+    if ((opt->m > 0) || (opt->p > 0))
+        return 0;
+
+    switch (opt->algorithm) {
+    case NLOPT_LN_COBYLA:
+    case NLOPT_LD_TNEWTON:
+    case NLOPT_LD_TNEWTON_RESTART:
+    case NLOPT_LD_TNEWTON_PRECOND:
+    case NLOPT_LD_TNEWTON_PRECOND_RESTART:
+        return 1;
+
+    default:
+        return 0;
+    }
+}
+
+
 /*********************************************************************/
 
 #define POP(defaultpop) (opt->stochastic_population > 0 ? (int)opt->stochastic_population : (nlopt_stochastic_population > 0 ? nlopt_stochastic_population : (defaultpop)))
@@ -863,6 +926,7 @@ nlopt_result NLOPT_STDCALL nlopt_optimize(nlopt_opt opt, double *x, double *opt_
     void *f_data;
     nlopt_precond pre;
     f_max_data fmd;
+    memoize_data mmzd;
     int maximize;
     nlopt_result ret;
 
@@ -891,6 +955,18 @@ nlopt_result NLOPT_STDCALL nlopt_optimize(nlopt_opt opt, double *x, double *opt_
         opt->maximize = 0;
     }
 
+    if (memoize_wrapcheck(opt))
+    {
+        mmzd.f = opt->f;
+        mmzd.f_data = opt->f_data;
+        mmzd.lb = opt->lb;
+        mmzd.ub = opt->ub;
+        mmzd.minf = DBL_MAX;
+        mmzd.bestx = (double *) calloc(opt->n, sizeof(double));
+        opt->f = memoize_func;
+        opt->f_data = &mmzd;
+    }
+
     { /* possibly eliminate lb == ub dimensions for some algorithms */
         nlopt_opt elim_opt = opt;
         if (elimdim_wrapcheck(opt)) {
@@ -916,6 +992,17 @@ nlopt_result NLOPT_STDCALL nlopt_optimize(nlopt_opt opt, double *x, double *opt_
     }
 
   done:
+
+    if (memoize_wrapcheck(opt))
+    {
+        for (unsigned i = 0; i < opt->n; ++ i)
+            x[i] = mmzd.bestx[i];
+        free(mmzd.bestx);
+        *opt_f = mmzd.minf;
+        opt->f = mmzd.f;
+        opt->f_data = mmzd.f_data;
+    }
+
     if (maximize) { /* restore original signs */
         opt->maximize = maximize;
         opt->stopval = -opt->stopval;

test/CMakeLists.txt

@@ -71,6 +71,8 @@ if (Python_FOUND AND NUMPY_FOUND AND (SWIG_FOUND OR (EXISTS ${PROJECT_SOURCE_DIR
     set_tests_properties (test_python${algo_index} PROPERTIES ENVIRONMENT "${PYINSTALLCHECK_ENVIRONMENT}")
   endforeach()
 
+  add_test (NAME test_memoize COMMAND ${Python_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/t_memoize.py ${algo_index})
+  set_tests_properties (test_memoize PROPERTIES ENVIRONMENT "${PYINSTALLCHECK_ENVIRONMENT}")
 endif ()
 
 if (OCTAVE_FOUND)

test/t_memoize.py

@@ -0,0 +1,72 @@
+import nlopt
+import math as m
+
+numFuncEval = [0]
+minf_ext = [1e300]
+
+lb = [-10., -10.]
+ub = [+10., +10.]
+
+
+def myfunc(x, grad):
+    for j in range(2):
+        if m.isnan(x[j]) or x[j] < lb[j] or x[j] > ub[j]:
+            return 1.e10
+    numFuncEval[0] += 1
+
+    x1 = x[0]
+    x2 = x[1]
+
+    # http://al-roomi.org/benchmarks/unconstrained/2-dimensions/65-powell-s-badly-scaled-function
+    # Powell's Badly Scaled Function
+    # Range of initial points: -10 < xj < 10 , j=1,2
+    # Global minima: (x1,x2)=(1.098...e-5, 9.106...)
+    # f(x1,x2)=0
+    f1 = (10000. * x1 * x2 - 1.)**2
+    f2 = (m.exp(-x1) + m.exp(-x2) - 1.0001)**2
+    retval = f1 + f2
+
+    if grad.size > 0:
+        # raise ValueError('Cannot suppply gradient values')
+        grad[0] = 2.0 * (10000. * x1 * x2 - 1.) * 10000. * x2 + 2.0 * (m.exp(-x1) + m.exp(-x2) - 1.0001) * -1.0
+        grad[1] = 2.0 * (10000. * x1 * x2 - 1.) * 10000. * x1 + 2.0 * (m.exp(-x1) + m.exp(-x2) - 1.0001) * -1.0
+
+    # print("myfunc: x:", x, ", val:", retval)
+
+    if retval < minf_ext[0]:
+        minf_ext[0] = retval
+
+    return retval
+
+
+for algo in range(nlopt.NUM_ALGORITHMS):
+    if algo in [nlopt.LD_LBFGS, nlopt.LD_VAR1, nlopt.LD_VAR2]:
+        continue
+    opt = nlopt.opt(algo, 2)
+
+    print('-'*40)
+    print("Algo:", opt.get_algorithm_name(), algo)
+    numFuncEval[0] = 0
+    minf_ext = [1e300]
+
+    opt.set_min_objective(myfunc)
+    opt.set_lower_bounds(lb)
+    opt.set_upper_bounds(ub)
+    opt.set_maxeval(int(1e4))
+    opt.set_xtol_rel(1e-4)
+    local_opt = nlopt.opt(nlopt.LD_MMA, 2)
+    opt.set_local_optimizer(local_opt)
+    x0 = [0.0, 0.0]
+    print("x0:", x0)
+    try:
+        x = opt.optimize(x0)
+        minf = opt.last_optimum_value()
+        print("optimum at ", x[0], x[1])
+        print("minimum value = ", minf)
+        print("result code = ", opt.last_optimize_result())
+        print("num function evaluations:", numFuncEval[0])
+        if minf_ext[0] < minf:
+            raise ValueError(f"minimum value {minf} is not the true minimum {minf_ext[0]}")
+    except nlopt.invalid_argument:
+        # stogo/ags might not be enabled
+        pass