源码实验优化圆圈
from gurobipy import * from math import * import random import time import sys # Work on a circle defined on a million constraints t0 = time.time() n = 1024 * 1024 m = Model('Circle Optimization') X = m.addVars(2,lb=-2,ub=2) Wb = 0 Wc = 0 Wd = 0 maxdiff = 0 niter = 0 margin = 1.01 m.addConstrs(X[0]*cos((2*pi*i)/n) + X[1]*sin((2*pi*i)/n) <= 1 for i in range(n)) print('Added 2 Vars and %d constraints in %.2f seconds' % (n, time.time()-t0)) m.Params.OutputFlag = 0 m.Params.Presolve = 0 # Now select random objectives and optimize.Resulting optimal # solution must be in the circle for i in range(4096): theta=2*pi*random.random() a = cos(theta) b = sin(theta) m.setObjective(X[0] * a + X[1] * b) m.optimize() niter += m.IterCount # See how far is the solution from the boundary of a circle of # radius one, if we minimize (a,b) the optimal solution should be (-a,-b) error = (X[0].X+a)*(X[0].X+a) + (X[1].X+b)*(X[1].X+b) # Display most inacurate solution if (error > margin * maxdiff or m.BoundVio > margin * Wb or m.ConstrVio > margin * Wc or m.DualVio > margin * Wd ): maxdiff = max(maxdiff, error) Wb = max(Wb, m.BoundVio) Wc = max(Wb, m.ConstrVio) Wd = max(Wd, m.DualVio) print('Errors: %g %g %g %g Iter %d %d Kappa %g' % (maxdiff, Wb, Wc, Wd, i, niter, m.KappaExact)) sys.stdout.flush()
