Module pywrapknapsack_solver
Expand source code
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# Import the lowlevel C/C++ module
if __package__ or "." in __name__:
from . import _pywrapknapsack_solver
else:
import _pywrapknapsack_solver
try:
import builtins as __builtin__
except ImportError:
import __builtin__
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def set_instance_attr(self, name, value):
if name == "thisown":
self.this.own(value)
elif name == "this":
set(self, name, value)
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set(self, name, value)
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set(cls, name, value)
else:
raise AttributeError("You cannot add class attributes to %s" % cls)
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"""Class decorator for adding a metaclass to a SWIG wrapped class  a slimmed down version of six.add_metaclass"""
def wrapper(cls):
return metaclass(cls.__name__, cls.__bases__, cls.__dict__.copy())
return wrapper
class _SwigNonDynamicMeta(type):
"""Meta class to enforce nondynamic attributes (no new attributes) for a class"""
__setattr__ = _swig_setattr_nondynamic_class_variable(type.__setattr__)
class KnapsackSolver(object):
r"""
This library solves knapsack problems.
Problems the library solves include:
 01 knapsack problems,
 Multidimensional knapsack problems,
Given n items, each with a profit and a weight, given a knapsack of
capacity c, the goal is to find a subset of items which fits inside c
and maximizes the total profit.
The knapsack problem can easily be extended from 1 to d dimensions.
As an example, this can be useful to constrain the maximum number of
items inside the knapsack.
Without loss of generality, profits and weights are assumed to be positive.
From a mathematical point of view, the multidimensional knapsack problem
can be modeled by d linear constraints:
ForEach(j:1..d)(Sum(i:1..n)(weight_ij * item_i) <= c_j
where item_i is a 01 integer variable.
Then the goal is to maximize:
Sum(i:1..n)(profit_i * item_i).
There are several ways to solve knapsack problems. One of the most
efficient is based on dynamic programming (mainly when weights, profits
and dimensions are small, and the algorithm runs in pseudo polynomial time).
Unfortunately, when adding conflict constraints the problem becomes strongly
NPhard, i.e. there is no pseudopolynomial algorithm to solve it.
That's the reason why the most of the following code is based on branch and
bound search.
For instance to solve a 2dimensional knapsack problem with 9 items,
one just has to feed a profit vector with the 9 profits, a vector of 2
vectors for weights, and a vector of capacities.
E.g.:
**Python**:
.. codeblock:: c++
profits = [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]
weights = [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
]
capacities = [ 34, 4 ]
solver = pywrapknapsack_solver.KnapsackSolver(
pywrapknapsack_solver.KnapsackSolver
.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
'Multidimensional solver')
solver.Init(profits, weights, capacities)
profit = solver.Solve()
**C++**:
.. codeblock:: c++
const std::vectorint64 profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
const std::vectorstd::vector<int64 weights =
{ { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
const std::vectorint64 capacities = { 34, 4 };
KnapsackSolver solver(
KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
"Multidimensional solver");
solver.Init(profits, weights, capacities);
const int64 profit = solver.Solve();
**Java**:
.. codeblock:: c++
final long[] profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
final long[][] weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
final long[] capacities = { 34, 4 };
KnapsackSolver solver = new KnapsackSolver(
KnapsackSolver.SolverType.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
"Multidimensional solver");
solver.init(profits, weights, capacities);
final long profit = solver.solve();
"""
thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc="The membership flag")
__repr__ = _swig_repr
KNAPSACK_BRUTE_FORCE_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_BRUTE_FORCE_SOLVER
r"""
Brute force method.
Limited to 30 items and one dimension, this
solver uses a brute force algorithm, ie. explores all possible states.
Experiments show competitive performance for instances with less than
15 items.
"""
KNAPSACK_64ITEMS_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_64ITEMS_SOLVER
r"""
Optimized method for single dimension small problems
Limited to 64 items and one dimension, this
solver uses a branch & bound algorithm. This solver is about 4 times
faster than KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER.
"""
KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER
r"""
Dynamic Programming approach for single dimension problems
Limited to one dimension, this solver is based on a dynamic programming
algorithm. The time and space complexity is O(capacity *
number_of_items).
"""
KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER
r"""
CBC Based Solver
This solver can deal with both large number of items and several
dimensions. This solver is based on Integer Programming solver CBC.
"""
KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER
r"""
Generic Solver.
This solver can deal with both large number of items and several
dimensions. This solver is based on branch and bound.
"""
def __init__(self, *args):
_pywrapknapsack_solver.KnapsackSolver_swiginit(self, _pywrapknapsack_solver.new_KnapsackSolver(*args))
__swig_destroy__ = _pywrapknapsack_solver.delete_KnapsackSolver
def Init(self, profits: "std::vector< int64 > const &", weights: "std::vector< std::vector< int64 > > const &", capacities: "std::vector< int64 > const &") > "void":
r"""Initializes the solver and enters the problem to be solved."""
return _pywrapknapsack_solver.KnapsackSolver_Init(self, profits, weights, capacities)
def Solve(self) > "int64":
r"""Solves the problem and returns the profit of the optimal solution."""
return _pywrapknapsack_solver.KnapsackSolver_Solve(self)
def BestSolutionContains(self, item_id: "int") > "bool":
r"""Returns true if the item 'item_id' is packed in the optimal knapsack."""
return _pywrapknapsack_solver.KnapsackSolver_BestSolutionContains(self, item_id)
def set_use_reduction(self, use_reduction: "bool") > "void":
return _pywrapknapsack_solver.KnapsackSolver_set_use_reduction(self, use_reduction)
def set_time_limit(self, time_limit_seconds: "double") > "void":
r"""
Time limit in seconds.
When a finite time limit is set the solution obtained might not be optimal
if the limit is reached.
"""
return _pywrapknapsack_solver.KnapsackSolver_set_time_limit(self, time_limit_seconds)
# Register KnapsackSolver in _pywrapknapsack_solver:
_pywrapknapsack_solver.KnapsackSolver_swigregister(KnapsackSolver)
class KnapsackSolver (*args)

This library solves knapsack problems.
Problems the library solves include:  01 knapsack problems,  Multidimensional knapsack problems,
Given n items, each with a profit and a weight, given a knapsack of capacity c, the goal is to find a subset of items which fits inside c and maximizes the total profit. The knapsack problem can easily be extended from 1 to d dimensions. As an example, this can be useful to constrain the maximum number of items inside the knapsack. Without loss of generality, profits and weights are assumed to be positive.
From a mathematical point of view, the multidimensional knapsack problem can be modeled by d linear constraints:
ForEach(j:1..d)(Sum(i:1..n)(weight_ij * item_i) <= c_j where item_i is a 01 integer variable.
Then the goal is to maximize:
Sum(i:1..n)(profit_i * item_i).
There are several ways to solve knapsack problems. One of the most efficient is based on dynamic programming (mainly when weights, profits and dimensions are small, and the algorithm runs in pseudo polynomial time). Unfortunately, when adding conflict constraints the problem becomes strongly NPhard, i.e. there is no pseudopolynomial algorithm to solve it. That's the reason why the most of the following code is based on branch and bound search.
For instance to solve a 2dimensional knapsack problem with 9 items, one just has to feed a profit vector with the 9 profits, a vector of 2 vectors for weights, and a vector of capacities. E.g.:
Python:
.. codeblock:: c++
profits = [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] weights = [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ] capacities = [ 34, 4 ] solver = pywrapknapsack_solver.KnapsackSolver( pywrapknapsack_solver.KnapsackSolver .KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER, 'Multidimensional solver') solver.Init(profits, weights, capacities) profit = solver.Solve()
C++:
.. codeblock:: c++
const std::vectorint64 profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }; const std::vectorstd::vector<int64 weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, { 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; const std::vectorint64 capacities = { 34, 4 }; KnapsackSolver solver( KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER, "Multidimensional solver"); solver.Init(profits, weights, capacities); const int64 profit = solver.Solve();
Java:
.. codeblock:: c++
final long[] profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }; final long[][] weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, { 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; final long[] capacities = { 34, 4 }; KnapsackSolver solver = new KnapsackSolver( KnapsackSolver.SolverType.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER, "Multidimensional solver"); solver.init(profits, weights, capacities); final long profit = solver.solve();
Expand source code
class KnapsackSolver(object): r""" This library solves knapsack problems. Problems the library solves include:  01 knapsack problems,  Multidimensional knapsack problems, Given n items, each with a profit and a weight, given a knapsack of capacity c, the goal is to find a subset of items which fits inside c and maximizes the total profit. The knapsack problem can easily be extended from 1 to d dimensions. As an example, this can be useful to constrain the maximum number of items inside the knapsack. Without loss of generality, profits and weights are assumed to be positive. From a mathematical point of view, the multidimensional knapsack problem can be modeled by d linear constraints: ForEach(j:1..d)(Sum(i:1..n)(weight_ij * item_i) <= c_j where item_i is a 01 integer variable. Then the goal is to maximize: Sum(i:1..n)(profit_i * item_i). There are several ways to solve knapsack problems. One of the most efficient is based on dynamic programming (mainly when weights, profits and dimensions are small, and the algorithm runs in pseudo polynomial time). Unfortunately, when adding conflict constraints the problem becomes strongly NPhard, i.e. there is no pseudopolynomial algorithm to solve it. That's the reason why the most of the following code is based on branch and bound search. For instance to solve a 2dimensional knapsack problem with 9 items, one just has to feed a profit vector with the 9 profits, a vector of 2 vectors for weights, and a vector of capacities. E.g.: **Python**: .. codeblock:: c++ profits = [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] weights = [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ] capacities = [ 34, 4 ] solver = pywrapknapsack_solver.KnapsackSolver( pywrapknapsack_solver.KnapsackSolver .KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER, 'Multidimensional solver') solver.Init(profits, weights, capacities) profit = solver.Solve() **C++**: .. codeblock:: c++ const std::vectorint64 profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }; const std::vectorstd::vector<int64 weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, { 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; const std::vectorint64 capacities = { 34, 4 }; KnapsackSolver solver( KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER, "Multidimensional solver"); solver.Init(profits, weights, capacities); const int64 profit = solver.Solve(); **Java**: .. codeblock:: c++ final long[] profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }; final long[][] weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, { 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; final long[] capacities = { 34, 4 }; KnapsackSolver solver = new KnapsackSolver( KnapsackSolver.SolverType.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER, "Multidimensional solver"); solver.init(profits, weights, capacities); final long profit = solver.solve(); """ thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc="The membership flag") __repr__ = _swig_repr KNAPSACK_BRUTE_FORCE_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_BRUTE_FORCE_SOLVER r""" Brute force method. Limited to 30 items and one dimension, this solver uses a brute force algorithm, ie. explores all possible states. Experiments show competitive performance for instances with less than 15 items. """ KNAPSACK_64ITEMS_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_64ITEMS_SOLVER r""" Optimized method for single dimension small problems Limited to 64 items and one dimension, this solver uses a branch & bound algorithm. This solver is about 4 times faster than KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER. """ KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER r""" Dynamic Programming approach for single dimension problems Limited to one dimension, this solver is based on a dynamic programming algorithm. The time and space complexity is O(capacity * number_of_items). """ KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER r""" CBC Based Solver This solver can deal with both large number of items and several dimensions. This solver is based on Integer Programming solver CBC. """ KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER r""" Generic Solver. This solver can deal with both large number of items and several dimensions. This solver is based on branch and bound. """ def __init__(self, *args): _pywrapknapsack_solver.KnapsackSolver_swiginit(self, _pywrapknapsack_solver.new_KnapsackSolver(*args)) __swig_destroy__ = _pywrapknapsack_solver.delete_KnapsackSolver def Init(self, profits: "std::vector< int64 > const &", weights: "std::vector< std::vector< int64 > > const &", capacities: "std::vector< int64 > const &") > "void": r"""Initializes the solver and enters the problem to be solved.""" return _pywrapknapsack_solver.KnapsackSolver_Init(self, profits, weights, capacities) def Solve(self) > "int64": r"""Solves the problem and returns the profit of the optimal solution.""" return _pywrapknapsack_solver.KnapsackSolver_Solve(self) def BestSolutionContains(self, item_id: "int") > "bool": r"""Returns true if the item 'item_id' is packed in the optimal knapsack.""" return _pywrapknapsack_solver.KnapsackSolver_BestSolutionContains(self, item_id) def set_use_reduction(self, use_reduction: "bool") > "void": return _pywrapknapsack_solver.KnapsackSolver_set_use_reduction(self, use_reduction) def set_time_limit(self, time_limit_seconds: "double") > "void": r""" Time limit in seconds. When a finite time limit is set the solution obtained might not be optimal if the limit is reached. """ return _pywrapknapsack_solver.KnapsackSolver_set_time_limit(self, time_limit_seconds)
Class variablesvar KNAPSACK_64ITEMS_SOLVER

Optimized method for single dimension small problems
Limited to 64 items and one dimension, this solver uses a branch & bound algorithm. This solver is about 4 times faster than KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER.
var KNAPSACK_BRUTE_FORCE_SOLVER

Brute force method.
Limited to 30 items and one dimension, this solver uses a brute force algorithm, ie. explores all possible states. Experiments show competitive performance for instances with less than 15 items.
var KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER

Dynamic Programming approach for single dimension problems
Limited to one dimension, this solver is based on a dynamic programming algorithm. The time and space complexity is O(capacity * number_of_items).
var KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER

Generic Solver.
This solver can deal with both large number of items and several dimensions. This solver is based on branch and bound.
var KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER

CBC Based Solver
This solver can deal with both large number of items and several dimensions. This solver is based on Integer Programming solver CBC.
KNAPSACK_64ITEMS_SOLVER
KNAPSACK_BRUTE_FORCE_SOLVER
KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER
KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER
KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER
Instance variablesvar thisown

The membership flag
Expand source code
thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc="The membership flag")
thisown
Methodsdef BestSolutionContains(self, item_id: int) > bool

Returns true if the item 'item_id' is packed in the optimal knapsack.
Expand source code
def BestSolutionContains(self, item_id: "int") > "bool": r"""Returns true if the item 'item_id' is packed in the optimal knapsack.""" return _pywrapknapsack_solver.KnapsackSolver_BestSolutionContains(self, item_id)
def Init(self, profits: std::vector< int64 > const &, weights: std::vector< std::vector< int64 > > const &, capacities: std::vector< int64 > const &) > 'void'

Initializes the solver and enters the problem to be solved.
Expand source code
def Init(self, profits: "std::vector< int64 > const &", weights: "std::vector< std::vector< int64 > > const &", capacities: "std::vector< int64 > const &") > "void": r"""Initializes the solver and enters the problem to be solved.""" return _pywrapknapsack_solver.KnapsackSolver_Init(self, profits, weights, capacities)
def Solve(self) > 'int64'

Solves the problem and returns the profit of the optimal solution.
Expand source code
def Solve(self) > "int64": r"""Solves the problem and returns the profit of the optimal solution.""" return _pywrapknapsack_solver.KnapsackSolver_Solve(self)
def set_time_limit(self, time_limit_seconds: double) > 'void'

Time limit in seconds.
When a finite time limit is set the solution obtained might not be optimal if the limit is reached.
Expand source code
def set_time_limit(self, time_limit_seconds: "double") > "void": r""" Time limit in seconds. When a finite time limit is set the solution obtained might not be optimal if the limit is reached. """ return _pywrapknapsack_solver.KnapsackSolver_set_time_limit(self, time_limit_seconds)
def set_use_reduction(self, use_reduction: bool) > 'void'

Expand source code
def set_use_reduction(self, use_reduction: "bool") > "void": return _pywrapknapsack_solver.KnapsackSolver_set_use_reduction(self, use_reduction)
BestSolutionContains
Init
Solve
set_time_limit
set_use_reduction