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operations_research::KnapsackSolver Class Reference

Detailed Description

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:

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++:

const std::vector<int64> profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
const std::vector<std::vector<int64>> weights =
{ { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
const std::vector<int64> capacities = { 34, 4 };
KnapsackSolver solver(
KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
"Multi-dimensional solver");
solver.Init(profits, weights, capacities);
const int64 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();

Definition at line 120 of file knapsack_solver.h.

Public Types

enum  SolverType {
  KNAPSACK_BRUTE_FORCE_SOLVER = 0, KNAPSACK_64ITEMS_SOLVER = 1, KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER = 2, KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER = 3,
  KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER = 5, KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER = 6
}
 Enum controlling which underlying algorithm is used. More...
 

Public Member Functions

 KnapsackSolver (const std::string &solver_name)
 
 KnapsackSolver (SolverType solver_type, const std::string &solver_name)
 
virtual ~KnapsackSolver ()
 
void Init (const std::vector< int64 > &profits, const std::vector< std::vector< int64 > > &weights, const std::vector< int64 > &capacities)
 Initializes the solver and enters the problem to be solved. More...
 
int64 Solve ()
 Solves the problem and returns the profit of the optimal solution. More...
 
bool BestSolutionContains (int item_id) const
 Returns true if the item 'item_id' is packed in the optimal knapsack. More...
 
bool IsSolutionOptimal () const
 Returns true if the solution was proven optimal. More...
 
std::string GetName () const
 
bool use_reduction () const
 
void set_use_reduction (bool use_reduction)
 
void set_time_limit (double time_limit_seconds)
 Time limit in seconds. More...
 

Member Enumeration Documentation

◆ SolverType

enum operations_research::KnapsackSolver::SolverType

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.

Enumerator
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.

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.

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).

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_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.

KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER 

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.

Definition at line 127 of file knapsack_solver.h.

Constructor & Destructor Documentation

◆ KnapsackSolver() [1/2]

operations_research::KnapsackSolver::KnapsackSolver ( const std::string &  solver_name)
explicit

◆ KnapsackSolver() [2/2]

operations_research::KnapsackSolver::KnapsackSolver ( SolverType  solver_type,
const std::string &  solver_name 
)

◆ ~KnapsackSolver()

virtual operations_research::KnapsackSolver::~KnapsackSolver ( )
virtual

Member Function Documentation

◆ BestSolutionContains()

bool operations_research::KnapsackSolver::BestSolutionContains ( int  item_id) const

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

◆ GetName()

std::string operations_research::KnapsackSolver::GetName ( ) const

◆ Init()

void operations_research::KnapsackSolver::Init ( const std::vector< int64 > &  profits,
const std::vector< std::vector< int64 > > &  weights,
const std::vector< int64 > &  capacities 
)

Initializes the solver and enters the problem to be solved.

◆ IsSolutionOptimal()

bool operations_research::KnapsackSolver::IsSolutionOptimal ( ) const
inline

Returns true if the solution was proven optimal.

Definition at line 201 of file knapsack_solver.h.

◆ set_time_limit()

void operations_research::KnapsackSolver::set_time_limit ( double  time_limit_seconds)
inline

Time limit in seconds.

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

Definition at line 212 of file knapsack_solver.h.

◆ set_use_reduction()

void operations_research::KnapsackSolver::set_use_reduction ( bool  use_reduction)
inline

Definition at line 205 of file knapsack_solver.h.

◆ Solve()

int64 operations_research::KnapsackSolver::Solve ( )

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

◆ use_reduction()

bool operations_research::KnapsackSolver::use_reduction ( ) const
inline

Definition at line 204 of file knapsack_solver.h.

The documentation for this class was generated from the following file: