The Black-Box Optimization Solver

The problem in this example is to minimize the six-hump camelback function (Michalewicz 1996, Appendix B). Minimize

subject to

Providing derivative-free algorithms with good estimates for lower and upper bounds often greatly improves performance because it prevents the algorithm from unnecessarily sampling in regions that you do not want to explore. For this problem, the following statements add the explicit variable bounds and :

proc optmodel;
   var x {1..2} >= -2 <= 2;
   con a1: 2*x[1] +   x[2] <=  2;
   con a2:   x[1] -   x[2] >= -2;
   con a3:   x[1] + 2*x[2] >= -2;
   min f = (4 - 2.1*x[1]^2 + x[1]^4/3)*x[1]^2 + x[1]*x[2]
           + (-4 + 4*x[2]^2)*x[2]^2;
   solve with blackbox / nthreads=2;
   print x;
quit;

Output 10.2.1 shows the output from running these steps.