FICO Xpress Optimization Examples Repository: Create a problem with general constraints that use operator abs

FICO Xpress Optimization Examples Repository

Create a problem with general constraints that use operator abs

Description

Create a simple problem using the modeling methods abs, And and max, as well as their corresponding modeling constructs using the API method problem.addgencons, for creating general constraints.

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

general_constraints.zip

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Source Files

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general_constraints_abs.py	[download]
general_constraints_logic.py	[download]
general_constraints_max.py	[download]

general_constraints_logic.py

# General constraints example using the Xpress And/Or operators and
# the problem.addgencons() API method.
#
# Solves a simple SAT problem by finding the solution with the fewest
# 'True' variables that satisfy all clauses.
#
# (C) 1983-2025 Fair Isaac Corporation

import xpress as xp

formulate_using_andor = True  # If True - will use xpress operators, else - will use problem.addgencons.

p = xp.problem()

N = 10
k = 5

x = [p.addVariable(vartype=xp.binary) for _ in range(N)]

if formulate_using_andor:
    # Here we use the And/Or operators of the Python interface to create a new
    # optimization problem.

    # At most one of each pair can be True.
    con0 = [(x[i] & x[i+1]) == 0 for i in range(0, N-1, 2)]

    # At least a quarter of all OR clauses on continuous groups of k
    # clauses must be True.
    con1 = xp.Sum(xp.Or(*(x[i:i+k])) for i in range(N-k)) >= N/4

    p.addConstraint(con0, con1)

else:
    # Here we use the API function problem.addgencons().

    # Creates a continuous list despite the 2 step in range().
    y_and = [p.addVariable(vartype=xp.binary) for i in range(0, N - 1, 2)]

    y_or = [p.addVariable(vartype=xp.binary) for i in range(N - k)]

    p.addGenCons([xp.gencons_and] * (N // 2) + [xp.gencons_or] * (N - k),
                 y_and + y_or,  # two list of resultants
                 [2 * i for i in range(N // 2)] +  # colstart is the list [0, 2, 4...] for the AND constraint
                 [2 * (N // 2) + k * i for i in range(N - k)],  # ... and then the list [0, k, 2*k...] displaced by 2N
                 x[:2 * (N // 2)] +  # consider all original variables in this order
                 [x[i + j] for j in range(k) for i in range(N - k)])  # and then variables [0..k-1, 1..k, 2..k+1, ...]

# Set time limit to 5 seconds.
p.controls.timelimit = 5
p.optimize()

print("Solution: x = ", p.getSolution())