Sched Square

This tutorial includes everything you need to set up decision optimization engines, build constraint programming models.

When you finish this tutorial, you'll have a foundational knowledge of Prescriptive Analytics.

This notebook is part of Prescriptive Analytics for Python

It requires either an installation of CPLEX Optimizers or it can be run on IBM Watson Studio Cloud (Sign up for a free IBM Cloud account and you can start using Watson Studio Cloud right away).

Table of contents:

Describe the business problem
How decision optimization (prescriptive analytics) can help
Use decision optimization
Summary

Describe the business problem

The aim of the square example is to place a set of small squares of different sizes into a large square.

How decision optimization can help

Prescriptive analytics technology recommends actions based on desired outcomes, taking into account specific scenarios, resources, and knowledge of past and current events. This insight can help your organization make better decisions and have greater control of business outcomes.
Prescriptive analytics is the next step on the path to insight-based actions. It creates value through synergy with predictive analytics, which analyzes data to predict future outcomes.
Prescriptive analytics takes that insight to the next level by suggesting the optimal way to handle that future situation. Organizations that can act fast in dynamic conditions and make superior decisions in uncertain environments gain a strong competitive advantage.
For example:
- Automate complex decisions and trade-offs to better manage limited resources.
- Take advantage of a future opportunity or mitigate a future risk.
- Proactively update recommendations based on changing events.
- Meet operational goals, increase customer loyalty, prevent threats and fraud, and optimize business processes.

Use decision optimization

Step 1: Download the library

Run the following code to install Decision Optimization CPLEX Modeling library. The DOcplex library contains the two modeling packages, Mathematical Programming and Constraint Programming, referred to earlier.



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import sys
try:
    import docplex.cp
except:
    if hasattr(sys, 'real_prefix'):
        #we are in a virtual env.
        !pip install docplex
    else:
        !pip install --user docplex

Note that the more global package docplex contains another subpackage docplex.mp that is dedicated to Mathematical Programming, another branch of optimization.

Step 2: Model the data



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from docplex.cp.model import *

Size of the englobing square



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SIZE_SQUARE = 112

Sizes of the sub-squares



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SIZE_SUBSQUARE = [50, 42, 37, 35, 33, 29, 27, 25, 24, 19, 18, 17, 16, 15, 11, 9, 8, 7, 6, 4, 2]

Step 3: Set up the prescriptive model



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mdl = CpoModel(name="SchedSquare")

Define the decision variables

Create array of variables for sub-squares



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x = []
y = []
rx = pulse((0, 0), 0)
ry = pulse((0, 0), 0)

for i in range(len(SIZE_SUBSQUARE)):
    sq = SIZE_SUBSQUARE[i]
    vx = interval_var(size=sq, name="X" + str(i))
    vx.set_end((0, SIZE_SQUARE))
    x.append(vx)
    rx += pulse(vx, sq)

    vy = interval_var(size=sq, name="Y" + str(i))
    vy.set_end((0, SIZE_SQUARE))
    y.append(vy)
    ry += pulse(vy, sq)

Express the business constraints

Create dependencies between variables



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for i in range(len(SIZE_SUBSQUARE)):
    for j in range(i):
        mdl.add((end_of(x[i]) <= start_of(x[j]))
                | (end_of(x[j]) <= start_of(x[i]))
                | (end_of(y[i]) <= start_of(y[j]))
                | (end_of(y[j]) <= start_of(y[i])))

Set other constraints



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mdl.add(always_in(rx, (0, SIZE_SQUARE), SIZE_SQUARE, SIZE_SQUARE))
mdl.add(always_in(ry, (0, SIZE_SQUARE), SIZE_SQUARE, SIZE_SQUARE))

Express the search phase



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mdl.set_search_phases([search_phase(x), search_phase(y)])

Solve with Decision Optimization solve service



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msol = mdl.solve(TimeLimit=20)

Step 4: Investigate the solution and then run an example analysis

Print Solution



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print("Solution: ")
msol.print_solution()

Import graphical tools



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import docplex.cp.utils_visu as visu
import matplotlib.pyplot as plt

You can set POP_UP_GRAPHIC=True if you prefer a pop up graphic window instead of an inline one.



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POP_UP_GRAPHIC=False



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if msol and visu.is_visu_enabled():
    import matplotlib.cm as cm
    from matplotlib.patches import Polygon
    
    if not POP_UP_GRAPHIC:
        %matplotlib inline
    
    # Plot external square
    print("Plotting squares....")
    fig, ax = plt.subplots()
    plt.plot((0, 0), (0, SIZE_SQUARE), (SIZE_SQUARE, SIZE_SQUARE), (SIZE_SQUARE, 0))
    for i in range(len(SIZE_SUBSQUARE)):
        # Display square i
        (sx, sy) = (msol.get_var_solution(x[i]), msol.get_var_solution(y[i]))
        (sx1, sx2, sy1, sy2) = (sx.get_start(), sx.get_end(), sy.get_start(), sy.get_end())
        poly = Polygon([(sx1, sy1), (sx1, sy2), (sx2, sy2), (sx2, sy1)], fc=cm.Set2(float(i) / len(SIZE_SUBSQUARE)))
        ax.add_patch(poly)
        # Display identifier of square i at its center
        ax.text(float(sx1 + sx2) / 2, float(sy1 + sy2) / 2, str(SIZE_SUBSQUARE[i]), ha='center', va='center')
    plt.margins(0)
    plt.show()

Summary

You learned how to set up and use the IBM Decision Optimization CPLEX Modeling for Python to formulate and solve a Constraint Programming model.

References

CPLEX Modeling for Python documentation
Decision Optimization on Cloud
Need help with DOcplex or to report a bug? Please go here
Contact us at dofeedback@wwpdl.vnet.ibm.com



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