Solving MINLP with PYOMO/PYSP

Question

team,

currently I am working on a nonlinear stochastic optimization problem. So far, the toolbox has been really helpful, thank you! However, adding a nonlinear constraint has caused an error. I use the gurobi solver. The problem results from the following constraint.

def max_pcr_power_rule(model, t):
    if t == 0:
        return 0 <= battery.P_bat_max-model.P_sc_max[t+1]-model.P_pcr
    else:       
        return model.P_trade_c[t+1] + np.sqrt(-2*np.log(rob_opt.max_vio)) \
        *sum(model.U_max_pow[t,i]**2 for i in set_sim.tme_dat_stp)**(0.5) \
        <= battery.P_bat_max-model.P_sc_max[t+1]-model.P_pcr
model.max_pcr_power = Constraint(set_sim.tme_dat_stp, rule=max_pcr_power_rule)

I receive this error message:

Initializing extensive form algorithm for stochastic programming problems. Exception encountered. Scenario tree manager attempting to shut down. Traceback (most recent call last): File "C:\Users\theil\Anaconda3\Scripts\runef-script.py", line 5, in sys.exit(pyomo.pysp.ef_writer_script.main()) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\pysp\ef_writer_script.py", line 863, in main traceback=options.traceback) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\pysp\util\misc.py", line 344, in launch_command rc = command(options, *cmd_args, **cmd_kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\pysp\ef_writer_script.py", line 748, in runef ef.solve() File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\pysp\ef_writer_script.py", line 430, in solve **solve_kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\parallel\manager.py", line 122, in queue return self._perform_queue(ah, *args, **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\parallel\local.py", line 59, in _perform_queue results = opt.solve(*args, **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\base\solvers.py", line 599, in solve self._presolve(*args, **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\solvers\plugins\solvers\GUROBI.py", line 224, in _presolve ILMLicensedSystemCallSolver._presolve(self, *args, **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\solver\shellcmd.py", line 196, in _presolve OptSolver._presolve(self, *args, **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\base\solvers.py", line 696, in _presolve **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\base\solvers.py", line 767, in _convert_problem **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\base\convert.py", line 110, in convert_problem problem_files, symbol_map = converter.apply(*tmp, **tmpkw) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\solvers\plugins\converter\model.py", line 96, in apply io_options=io_options) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\core\base\block.py", line 1681, in write io_options) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\repn\plugins\cpxlp.py", line 176, in call include_all_variable_bounds=include_all_variable_bounds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\repn\plugins\cpxlp.py", line 719, in _print_model_LP "with nonlinear terms." % (constraint_data.name)) ValueError: Cannot write legal LP file. Constraint '1.max_pcr_power[1]' has a body with nonlinear terms.

I thought, that the problem may lay within the nested formulation of the constraint, i.e. the combination of sum and exponential terms. Therefore, I put the sum()-term into a separate variable. This didn't change the core the characteristic of the nonlinear constraint, so that the error stayed the same. My other suspicion was, that the problem lays within the gurobi solver. So i tried to utilize ipopt, which produced the follwing error message:

Error evaluating constraint 1: can't evaluate pow'(0,0.5). ERROR: Solver (ipopt) returned non-zero return code (1) ERROR: See the solver log above for diagnostic information. Exception encountered. Scenario tree manager attempting to shut down. Traceback (most recent call last): File "C:\Users\theil\Anaconda3\Scripts\runef-script.py", line 5, in sys.exit(pyomo.pysp.ef_writer_script.main()) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\pysp\ef_writer_script.py", line 863, in main traceback=options.traceback) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\pysp\util\misc.py", line 344, in launch_command rc = command(options, *cmd_args, **cmd_kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\pysp\ef_writer_script.py", line 748, in runef ef.solve() File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\pysp\ef_writer_script.py", line 434, in solve **solve_kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\parallel\manager.py", line 122, in queue return self._perform_queue(ah, *args, **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\parallel\local.py", line 59, in _perform_queue results = opt.solve(*args, **kwds) File "C:\Users\theil\Anaconda3\lib\site-packages\pyomo\opt\base\solvers.py", line 626, in solve "Solver (%s) did not exit normally" % self.name) pyutilib.common._exceptions.ApplicationError: Solver (ipopt) did not exit normally

I am wondering now, if my mistake lays within the formulation of the constraint or the way i utilize the solver. Otherwise I have to simplify my problem to make it solvable.

I would be glad, if you can point me in the right direction. Thank you!

Best regards Philipp

Gurobi can only handle linear problems (and some quadratic problems). — Erwin Kalvelagen
The ipopt error is related to not being able to evaluate the gradient of the pow function at zero. Usually this can be solved by setting a small lower bound on the corresponding x variable. In your case you have an expression, so introduce a new variable and equality constraint so you can apply this bound. — Erwin Kalvelagen

Qi Chen Qi Chen · Accepted Answer · 2018-06-16T04:52:32

As Erwin mentioned in the comment, Gurobi is generally not intended for nonlinear problems.

Solving MINLP with PYOMO/PYSP

1 Answers