quadratic_assignment generator does not describe how to interpret the decision variable

[arcondello]

It maps facilities to location. See for instance:

import numpy as np

from dwave.optimization.generators import quadratic_assignment

distance_matrix = np.array([[0, 32, 68, 97, 75, 70, 75, 40, 24],
                            [32, 0, 42, 80, 53, 65, 82, 47, 29],
                            [68, 42, 0, 45, 15, 49, 79, 55, 50],
                            [97, 80, 45, 0, 30, 36, 65, 65, 73],
                            [75, 53, 15, 30, 0, 38, 69, 53, 53],
                            [70, 65, 49, 36, 38, 0, 31, 32, 46],
                            [75, 82, 79, 65, 69, 31, 0, 36, 56],
                            [40, 47, 55, 65, 53, 32, 36, 0, 19],
                            [24, 29, 50, 73, 53, 46, 56, 19, 0]])

flow_matrix = np.array([[0, 2, 4, 0, 0, 0, 2, 0, 0],
                        [2, 0, 3, 1, 0, 6, 0, 0, 2],
                        [4, 3, 0, 0, 0, 3, 0, 0, 0],
                        [0, 1, 0, 0, 1, 0, 1, 2, 0],
                        [0, 0, 0, 1, 0, 0, 0, 0, 0],
                        [0, 6, 3, 0, 0, 0, 0, 0, 2],
                        [2, 0, 0, 1, 0, 0, 0, 4, 3],
                        [0, 0, 0, 2, 0, 0, 4, 0, 0],
                        [0, 2, 0, 0, 0, 2, 3, 0, 0]])

model = quadratic_assignment(distance_matrix=distance_matrix, flow_matrix=flow_matrix)
model.states.resize(1)

x, = model.iter_decisions()


def qap(flow_matrix, distance_matrix, facilities):
    # facilities[i] == j => facility i is at location j

    n = flow_matrix.shape[0]

    out = 0
    for i in range(n):
        for j in range(n):
            out += flow_matrix[i, j] * distance_matrix[facilities[i], facilities[j]]

    return out


rng = np.random.default_rng(42)

facilities = np.arange(distance_matrix.shape[0])
for _ in range(10):
    rng.shuffle(facilities)

    x.set_state(0, facilities)
    print(model.objective.state(), qap(flow_matrix=flow_matrix, distance_matrix=distance_matrix, facilities=facilities))