chemical_balance_sat.py

#!/usr/bin/env python3
# Copyright 2010-2022 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""We are trying to group items in equal sized groups.

Each item has a color and a value. We want the sum of values of each group to be
as close to the average as possible. Furthermore, if one color is an a group, at
least k items with this color must be in that group.
"""

import math
from typing import Sequence
from absl import app
from ortools.sat.python import cp_model


def chemical_balance():
    """Solves the chemical balance problem."""
    # Data
    max_quantities = [
        ["N_Total", 1944],
        ["P2O5", 1166.4],
        ["K2O", 1822.5],
        ["CaO", 1458],
        ["MgO", 486],
        ["Fe", 9.7],
        ["B", 2.4],
    ]

    chemical_set = [
        ["A", 0, 0, 510, 540, 0, 0, 0],
        ["B", 110, 0, 0, 0, 160, 0, 0],
        ["C", 61, 149, 384, 0, 30, 1, 0.2],
        ["D", 148, 70, 245, 0, 15, 1, 0.2],
        ["E", 160, 158, 161, 0, 10, 1, 0.2],
    ]

    num_products = len(max_quantities)
    all_products = range(num_products)

    num_sets = len(chemical_set)
    all_sets = range(num_sets)

    # Model

    model = cp_model.CpModel()

    # Scale quantities by 100.
    max_set = [
        int(
            math.ceil(
                min(
                    max_quantities[q][1] * 1000 / chemical_set[s][q + 1]
                    for q in all_products
                    if chemical_set[s][q + 1] != 0
                )
            )
        )
        for s in all_sets
    ]

    set_vars = [model.NewIntVar(0, max_set[s], f"set_{s}") for s in all_sets]

    epsilon = model.NewIntVar(0, 10000000, "epsilon")

    for p in all_products:
        model.Add(
            sum(int(chemical_set[s][p + 1] * 10) * set_vars[s] for s in all_sets)
            <= int(max_quantities[p][1] * 10000)
        )
        model.Add(
            sum(int(chemical_set[s][p + 1] * 10) * set_vars[s] for s in all_sets)
            >= int(max_quantities[p][1] * 10000) - epsilon
        )

    model.Minimize(epsilon)

    # Creates a solver and solves.
    solver = cp_model.CpSolver()
    status = solver.Solve(model)
    print(f"Status = {solver.StatusName(status)}")
    # The objective value of the solution.
    print(f"Optimal objective value = {solver.ObjectiveValue() / 10000.0}")

    for s in all_sets:
        print(f"  {chemical_set[s][0]} = {solver.Value(set_vars[s]) / 1000.0}", end=" ")
        print()
    for p in all_products:
        name = max_quantities[p][0]
        max_quantity = max_quantities[p][1]
        quantity = sum(
            solver.Value(set_vars[s]) / 1000.0 * chemical_set[s][p + 1]
            for s in all_sets
        )
        print(f"{name}: {quantity} out of {max_quantity}")


def main(argv: Sequence[str]) -> None:
    if len(argv) > 1:
        raise app.UsageError("Too many command-line arguments.")
    chemical_balance()


if __name__ == "__main__":
    app.run(main)