top_final_solution_cvxpy.py

def optimize(data_models, train_limit, ob_cost_factor=2, container_cost_factor=10):
    results = {}
    containers = data_models['containers']
    shippers = data_models['shippers']
    orig_ports = data_models['orig_port']
    transp = data_models['transp']
    transp_train_map = data_models['transp_train_map']
    shipper_trade_spaces = data_models['shipper_trade_spaces']
    overbooking_spaces = shipper_trade_spaces.matrix
    dest_shipper_map = data_models['dest_shipper_map']
    orig_transp_map = data_models['orig_transp_map']
    dest_shipper_and_orig = data_models['dest_shipper_and_orig']
    trade_shipper_and_trade_map = data_models['trade_shipper_and_trade_map']
    shipper_shipper_and_trade_map = data_models['shipper_shipper_and_trade_map']
    dest_trade_map = data_models['dest_trade_map']
    orig_shipper_map = data_models['orig_shipper_map']
    orig_shipper_and_orig_map = data_models['orig_shipper_and_orig_map']
    shipper_shipper_and_orig_map = data_models['shipper_shipper_and_orig_map']
    factory_orig_and_transp_cost = data_models['factory_orig_and_transp_cost']
    factory_orig_and_transp_map = data_models['factory_orig_and_transp_map']
    orig_orig_and_transp_map = data_models['orig_orig_and_transp_map']
    transp_orig_and_transp_map = data_models['transp_orig_and_transp_map']

    dests_arr = np.asarray(containers.matrix[:, 1].todense()).flatten().astype(np.int32)
    dest_trades_arr = dest_trade_map.matrix[dests_arr]
    # This matrix is a mapping from trades to shippers and trades. This allows us to
    # convert everything to spaces later on as spaces are defined at the shipper and
    # trade level.
    trade_shipper_trade_matrix = dest_trades_arr @ trade_shipper_and_trade_map.matrix

    factories_arr = np.asarray(containers.matrix[:, 0].todense()).flatten().astype(
        np.int32)
    # Each factory have only a few available options for transportation and which origins
    # it may attend. This variable is used to make sure the origin and transport chosen
    # by the algorithm are available for the factory of each container
    factories_origs_transp_arr = factory_orig_and_transp_map.matrix[factories_arr]
    orig_and_transp_costs_matrix = factory_orig_and_transp_cost.matrix[factories_arr]

    container_costs_arr = np.asarray(containers.matrix[:, 2].todense()).flatten()

    n_containers = len(containers)
    n_shippers = len(shippers)
    n_origins = len(orig_ports)
    n_transp = len(transp)

    # cvxpy variables.
    x_shippers = cx.Variable((n_containers, n_shippers), boolean=True, name='Shippers')
    x_ob_shippers = cx.Variable((n_containers, n_shippers), boolean=True,
                                name='OverBooking Shippers')
    x_origins = cx.Variable((n_containers, n_origins), boolean=True, name='Origins')
    x_transp = cx.Variable((n_containers, n_transp), boolean=True, name='Transports')

    # cvxpy "AND" variables.
    y_shipper_and_origin = cx.Variable(
        (n_containers, shipper_shipper_and_orig_map.matrix.shape[1]),
        boolean=True,
        name='Shippers AND Origins'
    )
    y_shipper_ob_and_origin = cx.Variable(
        (n_containers, shipper_shipper_and_orig_map.matrix.shape[1]),
        boolean=True,
        name='Shippers Overbooking AND Origins'
    )
    y_origin_and_transp = cx.Variable(
        (n_containers, orig_orig_and_transp_map.matrix.shape[1]),
        boolean=True,
        name='Orig Ports AND Transportation'
    )

    constraints = []
    # x_shippers constraints
    shipper_shipper_trade_arr = x_shippers @ shipper_shipper_and_trade_map.matrix
    shipper_trade_consumed = cx.sum(
        cx.multiply(trade_shipper_trade_matrix, shipper_shipper_trade_arr),
        axis=0, keepdims=True
    )
    constr00 = shipper_trade_consumed <= shipper_trade_spaces.matrix
    constr01 = cx.sum(x_shippers + x_ob_shippers, axis=1) <= 1
    constr02 = (x_shippers + x_ob_shippers) <= dest_shipper_map.matrix[dests_arr]
    constr03 = cx.sum(shipper_trade_consumed) <= n_containers

    constraints.extend([constr00, constr01, constr02, constr03])

    # x_origins constraints
    constr10 = cx.sum(x_origins, axis=1) <= 1
    constr11 = (x_shippers + x_ob_shippers) <= x_origins @ orig_shipper_map.matrix
    constr12 = cx.sum(x_shippers + x_ob_shippers, axis=1) == cx.sum(x_origins, axis=1)

    constraints.extend([constr10, constr11, constr12])

    # x_ob_shippers constraints
    constr20 = cx.sum(x_ob_shippers, axis=1) <= 1
    constr21 = cx.sum(x_shippers + x_ob_shippers) <= n_containers

    shipper_ob_shipper_ob_trade_arr = (
        x_ob_shippers @ shipper_shipper_and_trade_map.matrix
    )
    shipper_ob_trade_consumed = cx.sum(
        cx.multiply(trade_shipper_trade_matrix, shipper_ob_shipper_ob_trade_arr),
        axis=0, keepdims=True
    )
    shipper_ob_trade_indices = cx.max(
        cx.multiply(trade_shipper_trade_matrix, shipper_ob_shipper_ob_trade_arr),
        axis=0, keepdims=True
    )

    constr22 = shipper_ob_trade_consumed <= overbooking_spaces
    constr23 = (
        shipper_trade_consumed >=
        cx.multiply(shipper_trade_spaces.matrix, cx.max(shipper_ob_trade_indices, axis=0,
                    keepdims=True))
    )

    constraints.extend([constr20, constr21, constr22, constr23])

    # y_shipper_and_orig constraints.
    x1 = x_shippers @ shipper_shipper_and_orig_map.matrix
    x2 = x_origins @ orig_shipper_and_orig_map.matrix
    constr30 = y_shipper_and_origin >= x1 + x2 - 1
    constr31 = y_shipper_and_origin <= x1
    constr32 = y_shipper_and_origin <= x2
    constr33 = cx.sum(y_shipper_and_origin, axis=1) == cx.sum(x_shippers, axis=1)
    constr34 = y_shipper_and_origin >= 0

    x1 = x_ob_shippers @ shipper_shipper_and_orig_map.matrix
    constr35 = y_shipper_ob_and_origin >= x1 + x2 - 1
    constr36 = y_shipper_ob_and_origin <= x1
    constr37 = y_shipper_ob_and_origin <= x2
    constr38 = cx.sum(y_shipper_ob_and_origin, axis=1) == cx.sum(x_ob_shippers, axis=1)
    constr39 = y_shipper_ob_and_origin >= 0

    constraints.extend([constr30, constr31, constr32, constr33, constr34, constr35,
                        constr36, constr37, constr38, constr39])

    # x_transp constraints.
    constr40 = cx.sum(x_origins, axis=1) == cx.sum(x_transp, axis=1)
    constr41 = x_transp <= x_origins @ orig_transp_map.matrix
    constr42 = cx.sum(x_transp @ transp_train_map.matrix) <= train_limit

    constraints.extend([constr40, constr41, constr42])

    # y_origin_and_transp
    x1 = x_origins @ orig_orig_and_transp_map.matrix
    x2 = x_transp @ transp_orig_and_transp_map.matrix
    constr50 = y_origin_and_transp >= x1 + x2 - 1
    constr51 = y_origin_and_transp <= x1
    constr52 = y_origin_and_transp <= x2
    constr53 = cx.sum(y_origin_and_transp, axis=1) == cx.sum(x_origins, axis=1)
    constr54 = y_origin_and_transp >= 0
    constr55 = cx.sum(
        cx.multiply(factories_origs_transp_arr, y_origin_and_transp),
        axis=1) == cx.sum(x_origins, axis=1)

    constraints.extend([constr50, constr51, constr52, constr53, constr54, constr55])

    cost = (
        cx.sum(cx.multiply(
            y_shipper_and_origin,
            dest_shipper_and_orig.matrix[dests_arr]
        )) +
        cx.sum(
            cx.multiply(y_shipper_ob_and_origin,
                        dest_shipper_and_orig.matrix[dests_arr] * ob_cost_factor)
        ) +
        cx.sum(
            cx.multiply((1 - cx.sum(x_shippers + x_ob_shippers, axis=1)),
                        container_costs_arr * container_cost_factor)) +
        cx.sum(
            cx.multiply(y_origin_and_transp, orig_and_transp_costs_matrix))
    )
    objective = cx.Minimize(cost)
    problem = cx.Problem(objective, constraints)
    problem.solve()
    print(problem.solution)
    print(time() - t0)

    print('y_origin_and_transp ', y_origin_and_transp.value)
    print('y_shipper_and_origin ', y_shipper_and_origin.value)

    results['x_shippers'] = x_shippers.value
    results['x_ob_shippers'] = x_ob_shippers.value
    results['x_origins'] = x_origins.value
    results['x_transp'] = x_transp.value
    return results