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doc/OnlineDocs/contributed_packages/alternative_solutions.rst
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############################################### | ||
Generating Alternative (Near-)Optimal Solutions | ||
############################################### | ||
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Optimization solvers are generally designed to return a feasible solution | ||
to the user. However, there are many applications where a user needs | ||
more context than this result. For example, | ||
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* alternative solutions can support an assessment of trade-offs between competing objectives; | ||
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* if the optimization formulation may be inaccurate or untrustworthy, then comparisons amongst alternative solutions provide additional insights into the reliability of these model predictions; or | ||
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* the user may have unexpressed objectives or constraints, which only are realized in later stages of model analysis. | ||
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The *alternative-solutions library* provides a variety of functions that | ||
can be used to generate optimal or near-optimal solutions for a pyomo | ||
model. Conceptually, these functions are like pyomo solvers. They can | ||
be configured with solver names and options, and they return a list of | ||
solutions for the pyomo model. However, these functions are independent | ||
of pyomo's solver interface because they return a custom solution object. | ||
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The following functions are defined in the alternative-solutions library: | ||
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* ``enumerate_binary_solutions`` | ||
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* Finds alternative optimal solutions for a binary problem using no-good cuts. | ||
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* ``enumerate_linear_solutions`` | ||
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* Finds alternative optimal solutions for a (mixed-integer) linear program. | ||
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* ``enumerate_linear_solutions_soln_pool`` | ||
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* Finds alternative optimal solutions for a (mixed-binary) linear program using Gurobi's solution pool feature. | ||
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* ``gurobi_generate_solutions`` | ||
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* Finds alternative optimal solutions for discrete variables using Gurobi's built-in solution pool capability. | ||
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* ``obbt_analysis_bounds_and_solutions`` | ||
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* Calculates the bounds on each variable by solving a series of min and max optimization problems where each variable is used as the objective function. This can be applied to any class of problem supported by the selected solver. | ||
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Usage Example | ||
------------- | ||
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Many of functions in the alternative-solutions library have similar options, so we simply illustrate the ``enumerate_binary_solutions`` function. We define a simple knapsack example whose alternative solutions have integer objective values ranging from 0 to 90. | ||
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.. doctest:: | ||
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>>> import pyomo.environ as pyo | ||
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>>> values = [10, 40, 30, 50] | ||
>>> weights = [5, 4, 6, 3] | ||
>>> capacity = 10 | ||
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>>> m = pyo.ConcreteModel() | ||
>>> m.x = pyo.Var(range(4), within=pyo.Binary) | ||
>>> m.o = pyo.Objective(expr=sum(values[i] * m.x[i] for i in range(4)), sense=pyo.maximize) | ||
>>> m.c = pyo.Constraint(expr=sum(weights[i] * m.x[i] for i in range(4)) <= capacity) | ||
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We can execute the ``enumerate_binary_solutions`` function to generate a list of ``Solution`` objects that represent alternative optimal solutions: | ||
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.. doctest:: | ||
:skipif: not glpk_available | ||
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>>> import pyomo.contrib.alternative_solutions as aos | ||
>>> solns = aos.enumerate_binary_solutions(m, num_solutions=100, solver="glpk") | ||
>>> assert len(solns) == 10 | ||
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Each ``Solution`` object contains information about the objective and variables, and it includes various methods to access this information. For example: | ||
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.. doctest:: | ||
:skipif: not glpk_available | ||
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>>> print(solns[0]) | ||
{ | ||
"fixed_variables": [], | ||
"objective": "o", | ||
"objective_value": 90.0, | ||
"solution": { | ||
"x[0]": 0, | ||
"x[1]": 1, | ||
"x[2]": 0, | ||
"x[3]": 1 | ||
} | ||
} | ||
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Interface Documentation | ||
----------------------- | ||
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.. currentmodule:: pyomo.contrib.alternative_solutions | ||
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.. autofunction:: enumerate_binary_solutions | ||
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.. autofunction:: enumerate_linear_solutions | ||
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.. autofunction:: enumerate_linear_solutions_soln_pool | ||
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.. autofunction:: gurobi_generate_solutions | ||
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.. autofunction:: obbt_analysis_bounds_and_solutions | ||
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.. autoclass:: Solution | ||
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