pyCIAP

This a tiny 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

Thanks to to the wheels, you can install the package like this

pip3 install pyCIAP

Alternatively, you can build and install from source

pip3 install git+https://github.com/jhelgert/pyCIAP

However, note that the latter requires Cython and a installed C++ compiler.

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.