OR-Toolsで瓶パッキング問題を解く

ortools  v9.0.9048
Copyright (c) 2000 The Apache Software Foundation.  All rights
Released under the Apache Software License
http://www.apache.org/licenses/LICENSE-1.1
This product includes software developed by the Apache Software Foundation (http://www.apache.org/).
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def create_data_model():
    """Create the data for the example."""
    data = {}
    weights = [20,20,40,40,60,60,60,60,60,60,60,60,60,60,60,60,60,60,80,80,94,94]
    weights.sort(reverse=True)
    data['weights'] = weights
    data['items'] = list(range(len(weights)))
    data['bins'] = data['items']
    data['bin_capacity'] = 180
    return data

def main():
    data = create_data_model()

    # Create the mip solver with the SCIP backend.
    solver = pywraplp.Solver.CreateSolver('SCIP')


    # Variables
    # x[i, j] = 1 if item i is packed in bin j.
    x = {}
    for i in data['items']:
        for j in data['bins']:
            x[(i, j)] = solver.IntVar(0, 1, 'x_%i_%i' % (i, j))

    # y[j] = 1 if bin j is used.
    y = {}
    for j in data['bins']:
        y[j] = solver.IntVar(0, 1, 'y[%i]' % j)

    # Constraints
    # Each item must be in exactly one bin.
    for i in data['items']:
        solver.Add(sum(x[i, j] for j in data['bins']) == 1)

    # The amount packed in each bin cannot exceed its capacity.
    for j in data['bins']:
        solver.Add(
            sum(x[(i, j)] * data['weights'][i] for i in data['items']) <= y[j] *
            data['bin_capacity'])

    # Objective: minimize the number of bins used.
    solver.Minimize(solver.Sum([y[j] for j in data['bins']]))

    status = solver.Solve()

    if status == pywraplp.Solver.OPTIMAL:
        num_bins = 0.
        for j in data['bins']:
            if y[j].solution_value() == 1:
                bin_items = []
                bin_weight = 0
                for i in data['items']:
                    if x[i, j].solution_value() > 0:
                        bin_items.append(i)
                        bin_weight += data['weights'][i]
                if bin_weight > 0:
                    num_bins += 1
                    print('Bin number', j)
                    print('  Items packed:', bin_items)
                    print('  Total weight:', bin_weight)
                    print()
        print()
        print('Number of bins used:', num_bins)
        print('sumLength: ', data['bin_capacity'] * (num_bins - 1) + bin_weight)
        print('Time = ', solver.WallTime(), ' milliseconds')
    else:
        print('The problem does not have an optimal solution.')