Class KnapsackSolver
java.lang.Object
com.google.ortools.algorithms.KnapsackSolver
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:
C++:
Java:
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:
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 = knapsack_solver.KnapsackSolver(
knapsack_solver.SolverType
.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
'Multi-dimensional solver')
solver.init(profits, weights, capacities)
profit = solver.solve()
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:
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();
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionstatic enum
Enum controlling which underlying algorithm is used.
This enum is passed to the constructor of the KnapsackSolver object.
It selects which solving method will be used. -
Field Summary
Fields -
Constructor Summary
ConstructorsModifierConstructorDescriptionprotected
KnapsackSolver
(long cPtr, boolean cMemoryOwn) KnapsackSolver
(KnapsackSolver.SolverType solver_type, String solver_name) KnapsackSolver
(String solver_name) -
Method Summary
Modifier and TypeMethodDescriptionboolean
bestSolutionContains
(int item_id) Returns true if the item 'item_id' is packed in the optimal knapsack.void
delete()
protected void
finalize()
protected static long
getCPtr
(KnapsackSolver obj) getName()
void
init
(long[] profits, long[][] weights, long[] capacities) Initializes the solver and enters the problem to be solved.boolean
Returns true if the solution was proven optimal.void
setTimeLimit
(double 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.void
setUseReduction
(boolean use_reduction) long
solve()
Solves the problem and returns the profit of the optimal solution.protected static long
boolean
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Field Details
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swigCMemOwn
protected transient boolean swigCMemOwn
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Constructor Details
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KnapsackSolver
protected KnapsackSolver(long cPtr, boolean cMemoryOwn) -
KnapsackSolver
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KnapsackSolver
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Method Details
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getCPtr
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swigRelease
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finalize
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delete
public void delete() -
init
public void init(long[] profits, long[][] weights, long[] capacities) Initializes the solver and enters the problem to be solved. -
solve
public long solve()Solves the problem and returns the profit of the optimal solution. -
bestSolutionContains
public boolean bestSolutionContains(int item_id) Returns true if the item 'item_id' is packed in the optimal knapsack. -
isSolutionOptimal
public boolean isSolutionOptimal()Returns true if the solution was proven optimal. -
getName
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useReduction
public boolean useReduction() -
setUseReduction
public void setUseReduction(boolean use_reduction) -
setTimeLimit
public void setTimeLimit(double 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.
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