# pywrapknapsack_solver

## View Source

# This file was automatically generated by SWIG (http://www.swig.org). # Version 4.0.2 # # Do not make changes to this file unless you know what you are doing--modify # the SWIG interface file instead. from sys import version_info as _swig_python_version_info if _swig_python_version_info < (2, 7, 0): raise RuntimeError("Python 2.7 or later required") # Import the low-level 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__ def _swig_repr(self): try: strthis = "proxy of " + self.this.__repr__() except __builtin__.Exception: strthis = "" return "<%s.%s; %s >" % (self.__class__.__module__, self.__class__.__name__, strthis,) def _swig_setattr_nondynamic_instance_variable(set): def set_instance_attr(self, name, value): if name == "thisown": self.this.own(value) elif name == "this": set(self, name, value) elif hasattr(self, name) and isinstance(getattr(type(self), name), property): set(self, name, value) else: raise AttributeError("You cannot add instance attributes to %s" % self) return set_instance_attr def _swig_setattr_nondynamic_class_variable(set): def set_class_attr(cls, name, value): if hasattr(cls, name) and not isinstance(getattr(cls, name), property): set(cls, name, value) else: raise AttributeError("You cannot add class attributes to %s" % cls) return set_class_attr def _swig_add_metaclass(metaclass): """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: - 0-1 knapsack problems, - Multi-dimensional 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 multi-dimensional 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 0-1 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 NP-hard, i.e. there is no pseudo-polynomial 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 2-dimensional 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**: .. code-block:: python 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, 'Multi-dimensional solver') solver.Init(profits, weights, capacities) profit = solver.Solve() **C++**: .. code-block:: c++ const std::vector<int64_t> profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }; const std::vector<std::vector<int64_t>> weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, { 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; const std::vector<int64_t> capacities = { 34, 4 }; KnapsackSolver solver( KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER, "Multi-dimensional solver"); solver.Init(profits, weights, capacities); const int64_t profit = solver.Solve(); **Java**: .. code-block:: java 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, "Multi-dimensional 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. """ KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER r""" SCIP based solver This solver can deal with both large number of items and several dimensions. This solver is based on Integer Programming solver SCIP. """ 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_t > const &", weights: "std::vector< std::vector< int64_t > > const &", capacities: "std::vector< int64_t > 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_t": 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)

## View Source

class KnapsackSolver(object): r""" This library solves knapsack problems. Problems the library solves include: - 0-1 knapsack problems, - Multi-dimensional 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 multi-dimensional 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 0-1 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 NP-hard, i.e. there is no pseudo-polynomial 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 2-dimensional 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**: .. code-block:: python 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, 'Multi-dimensional solver') solver.Init(profits, weights, capacities) profit = solver.Solve() **C++**: .. code-block:: c++ const std::vector<int64_t> profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }; const std::vector<std::vector<int64_t>> weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, { 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; const std::vector<int64_t> capacities = { 34, 4 }; KnapsackSolver solver( KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER, "Multi-dimensional solver"); solver.Init(profits, weights, capacities); const int64_t profit = solver.Solve(); **Java**: .. code-block:: java 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, "Multi-dimensional 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. """ KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER r""" SCIP based solver This solver can deal with both large number of items and several dimensions. This solver is based on Integer Programming solver SCIP. """ 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_t > const &", weights: "std::vector< std::vector< int64_t > > const &", capacities: "std::vector< int64_t > 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_t": 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)

This library solves knapsack problems.

Problems the library solves include:

- 0-1 knapsack problems,
- Multi-dimensional 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 multi-dimensional 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 0-1 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 NP-hard, i.e. there is no pseudo-polynomial 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 2-dimensional 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**:

.. code-block:: python

```
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,
'Multi-dimensional solver')
solver.Init(profits, weights, capacities)
profit = solver.Solve()
```

**C++**:

.. code-block:: c++

```
const std::vector<int64_t> profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
const std::vector<std::vector<int64_t>> weights =
{ { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
const std::vector<int64_t> capacities = { 34, 4 };
KnapsackSolver solver(
KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
"Multi-dimensional solver");
solver.Init(profits, weights, capacities);
const int64_t profit = solver.Solve();
```

**Java**:

.. code-block:: java

```
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,
"Multi-dimensional solver");
solver.init(profits, weights, capacities);
final long profit = solver.solve();
```

## View Source

def __init__(self, *args): _pywrapknapsack_solver.KnapsackSolver_swiginit(self, _pywrapknapsack_solver.new_KnapsackSolver(*args))

The membership flag

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.

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.

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).

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.

Generic Solver.

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

SCIP based solver

This solver can deal with both large number of items and several dimensions. This solver is based on Integer Programming solver SCIP.

## View Source

def Init(self, profits: "std::vector< int64_t > const &", weights: "std::vector< std::vector< int64_t > > const &", capacities: "std::vector< int64_t > const &") -> "void": r"""Initializes the solver and enters the problem to be solved.""" return _pywrapknapsack_solver.KnapsackSolver_Init(self, profits, weights, capacities)

Initializes the solver and enters the problem to be solved.

## View Source

def Solve(self) -> "int64_t": r"""Solves the problem and returns the profit of the optimal solution.""" return _pywrapknapsack_solver.KnapsackSolver_Solve(self)

Solves the problem and returns the profit of the optimal solution.

## View Source

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)

Returns true if the item 'item_id' is packed in the optimal knapsack.

## View Source

def set_use_reduction(self, use_reduction: "bool") -> "void": return _pywrapknapsack_solver.KnapsackSolver_set_use_reduction(self, use_reduction)

## View Source

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)

Time limit in seconds.

When a finite time limit is set the solution obtained might not be optimal if the limit is reached.