Algorithm for partially distributed outer approximation of MICPs. This code uses the open-source tool CasADi:
https://web.casadi.org/
Input problem must be partitioned:
obj_funs: cell array of CasADi functions
cons_funs: cell array of CasADi functions
lb: cell array of vectors
ub: cell array of vectors
A: cell array of matrices
B: cell array of matrices
c: vector
x0: cell array of vectors
z0: cell array of vectors
params: struct
opts: struct
Params will assume default values if left empty. Possible params to set:
update_hyper_planes_with_U: 1,0. Whether or not to add hyperplanes only when an MINLP solution improves the upper bound. Default: 1
remove_inac_hyperplanes: 1,0. Whether or not to check active hyperplanes at the MILP solutio and remove those that are inactive. Default: 1
limited_hyperplane_gen: 1,0. Whether to add 1 instead of N hyperplanes from each MINLP solution. Default: 0
upper_bound_MILP_epigraph: 1,0. Whether or or not to add an upper bound on the MILP. Default: 0
lower_bound_MILP_epigraph: 1,0. Whether or or not to add a lower bound on the MILP. Default: 1
max_hyperplanes: double. Start discarding old hyperplanes after this amount has been added to the MILP. Default: inf
Us: vector. User provided upper bounds on each MINLP subproblem. Default: inf(N,1);
Ls: vector. User provided lower bounds on each MINLP subproblem. Default: -inf(N,1);
eps: double. Termination tolerance. Default: 10^-3;
maxiter: int. Iteration limit. Default: 100;
Opts must be set. Algorithm options are:
MILP_solver: 'ipopt', 'bonmin', 'gurobi', 'cplex'
MINLP_solver: 'ipopt', 'bonmin', 'gurobi', 'cplex'
MINLPsolver_opts: used to pass options to the MINLP solver
milp_opts: used to pass options to the MILP solver
The syntax for using PaDOA is shown in the EXAMPLE_MIP.
To cite use:
@Article{Murray_2019,
author = {Murray, A. and Faulwasser, T. and Hagenmeyer, V. and Villanueva, M.E. and Houska, B.},
title = {Partially Distributed Outer Approximation},
journal = {Journal of Global Optimization},
year = {2020},
}