I have a problem, where equation changes with problem instance size.
There are given n circles (centers and radiuses ). Circles dont intersect, they are separable. I need to visit every circle starting from the first circle and returning to the first circle. The sequence of visiting circles is known. The task is to find points on these circles (described by radius) to minimize the path.
For 3 circles we have to find P1 P2 and P3 that minimizes d=d(P1, P2)+d(P2, P3) + d(P3, P1) (for permutation (1, 2, 3)). When number of circles changes, the minimised equation changes.
I would like to have a module invoked from C++/Python that will solve such problem for me. I would like to send number of circles and its parameters, and solver should solves a problem and responds with P1, P2, P3,...Pn.
In the attachment you can find an image of two circles and some points P1, P2 (it is not optimal solution, of course).
http://www-01.ibm.com/support/docview.wss?uid=swg21400023
I think there is no thing to do with the solver (cplex, ..), what you need is a C++/Python code to construct the optimization problem depending on the size of the problem.
you can try something similar to this Python code which gets the points in "para" and then it defines the lp and solve it.
def main_lp( para):
"""
:param para:
:return:
"""
lp = cplex.Cplex()
lp.set_log_stream(None)
lp.set_results_stream(None)
lp.objective.set_sense(lp.objective.sense.maximize)
for p in sorted(para.points, key=str):
lp.linear_constraints.add(senses="L", rhs=[p.rhs], names=[p.name])
col_id = lp.variables.get_num() # get number of columns to know where to add the new variable
lp.variables.add(obj=[objective], names=['x' + str(col_id)]) # add a new variable
for t in sorted(c, key=str):
row_id = lp.linear_constraints.get_indices(t)
lp.linear_constraints.set_coefficients(row_id, col_id, 1.0) # set the coefficient of the new variable in the constraints
try:
lp.solve()
except CplexError, exe:
print "MainLP", exe
z = lp.solution.get_objective_value()
x = lp.solution.get_values()
y = lp.solution.get_dual_values()
I can recommend pyomo. http://pyomo.org
It allows you to create your optimization problem in plain python and calls the solver to solve it. It supports both Cplex and Gurobi but also many interesting open source solvers.
- Badges
- Science topic
- Similar topics
- Computer Science and Engineering
- Programming Languages
- Python