pyCIAP

This a very simple package to solve the Combinatorial Integral Approximation Problem (CIAP) including dwell-time constraints by a dwell-time sum-up rounding algorithm, see 1 for the theoretical results.

Install

Clone this repo and then run

python3 setup.py install

inside the repo directory.

Example:

from pyCIAP import DSUR, solveCIAPMDT
import numpy as np

# Relaxed control fulfilling SOS1-constraint
b_rel = np.array([[
    0.47131227, 0.78736104, 0.97325193, 0.53496864, 
    0.73187786, 0.07838749, 0.48948843, 0.64580892],
    [0.52868773, 0.21263896, 0.02674807, 0.46503136, 
    0.26812214, 0.92161251, 0.51051157, 0.35419108]])

# time grid
dt = 1.0
time = np.arange(0, b_rel.shape[1], dt)

# Computes a binary control fulfilling the minimum dwell times
# The dwell times are always in number of time steps, i.e. multiples of dt
b_bin = DSUR(b_rel, 1.0, time, min_up_time=3, min_down_time=3)

gives

array([[1, 1, 1, 0, 0, 0, 1, 1],
       [0, 0, 0, 1, 1, 1, 0, 0]])

In order to compare the DSUR solution to the global optimum, one can solve the CIAP by Gurobi and use the solution as MIP start:

runtime, eps_opt, eps_dsur = solveCIAPMDT(b_rel, dt, 3, 3, start_sol=b_bin)

Here eps_opt and eps_dsur denote the objective values of the corresponding CIAP, i.e. the integrality gap.