FICO
FICO Xpress Optimization Examples Repository
FICO Optimization Community FICO Xpress Optimization Home
Back to examples browserPrevious exampleNext example

Create an iterative algorithm cutting stock problem

Description
Use the modeling features to create an iterative solver for a cutting stock problem.

Further explanation of this example: 'Xpress Python Reference Manual'

cuttingstock.zip[download all files]

Source Files





cuttingstock.py

'''
Cutting stock model with column generation
(c) 2020 Fair Isaac Corporation
'''

import xpress as xp
import numpy as np

# Problem data
# widths = [17.0, 21.0, 22.5, 24.0, 29.5]
# demand = [150, 96, 48, 108, 227]
# max_width = 94.0
widths = [6, 11, 17, 21, 24, 28, 30, 33, 42, 49, 56, 69, 74, 87, 91]
demand = [9, 6, 20, 30, 17, 19, 25, 12, 8, 20, 5, 14, 15, 18, 10]
max_width = 100
eps = 1e-6
max_cols = 100


def solve_knapsack_problem(n_item_types, profit, resource_consumed, total_resource, demand):
    """
    Solve knapsack subproblem

    :param n_item_types: Total number of items
    :param profit: Profit of each item. 1-d numpy array
    :param resource_consumed: Resource consumed by each item. 1-d numpy array
    :param total_resource: total available resource
    :param demand: Demand for each item. 1-d numpy array
    :return:
        xbest: Number of items of type i used in an optimal solution
        zbest: Value of the optimial solution
    """
    N = range(n_item_types)
    p = xp.problem(name="knapsack")
    p.setControl('outputlog', 0)

    # Create a NumPy array of variable; specify dtype=xp.npvar to
    # ensure NumPy recognizes an array of Xpress variables rather than
    # objects.

    x = np.array([xp.var(name='use_{}'.format(i), lb=0, ub=demand[i], vartype=xp.integer) for i in N], dtype=xp.npvar)
    p.addVariable(x)
    p.addConstraint(xp.Dot(resource_consumed, x) <= total_resource)
    p.setObjective(xp.Dot(profit, x), sense=xp.maximize)
    p.solve()
    xbest = []
    p.getmipsol(xbest)
    return p.getObjVal(), xbest


def cutting_stock_model():
    """Solve a cutting stock problem by defining master problem and
    subproblem.

    :return:

    """
    n_widths = len(widths)
    N = range(n_widths)
    p = xp.problem(name='CutStock')
    patterns = np.zeros((n_widths, n_widths))
    for j in N:
        patterns[j][j] = int(max_width / widths[j])

    # Create array of variables using the dtype=xp.npvar keyword
    # argument.
    v_patterns = np.array([xp.var(name='pat_{}'.format(i), lb=0,
                                  ub=int(float(demand[i] / patterns[i][i]) + 1)) for i in N], dtype=xp.npvar)
    p.addVariable(v_patterns)
    p.setObjective(xp.Dot(np.ones(n_widths), v_patterns), sense=xp.minimize)
    p.addConstraint(xp.Dot(patterns, v_patterns) >= demand)
    p.setControl('outputlog', 0)

    for npass in range(max_cols):
        print('=============Iteration {}==========='.format(npass))
        p.solve()
        cs_lp_sol = []
        duals = []
        p.getlpsol(cs_lp_sol, None, duals, None)
        obj_val = p.getObjVal()
        #p.write('test_{}.lp'.format(npass), 'lp')
        z, x_best = solve_knapsack_problem(n_widths, np.array(duals), np.array(widths), max_width, demand)
        if z < 1 + eps:
            print('No profitable column found')
            break
        print('New pattern found with marginal cost {}'.format(z - 1));
        print(x_best)
        cur_pat = xp.var(name='pat_{}'.format(n_widths + npass), vartype=xp.continuous)
        p.addVariable(cur_pat)
        for i in N:
            p.chgcoef(i, cur_pat, x_best[i])
        p.chgobj([cur_pat], [1.0])

    print("LP Solution after column generation. Obj: {}, Sol = {}".format(obj_val, cs_lp_sol))
    n_final_patterns = p.getAttrib('cols')
    print('Number of patterns in the final LP = {}'.format(n_final_patterns))
    # Change the variables to integers
    p.chgcoltype([i for i in range(n_final_patterns)], ['I' for _ in range(n_final_patterns)])
    p.solve()
    integer_obj_val = p.getObjVal()
    int_sol = []
    p.getmipsol(int_sol)
    print("MIP Solution with final columns. Obj: {}, Sol = {}".format(integer_obj_val, int_sol))


if __name__ == '__main__':
    cutting_stock_model()

Back to examples browserPrevious exampleNext example