Class KnapsackSolver

java.lang.Object
com.google.ortools.algorithms.KnapsackSolver
public class KnapsackSolver extends Object
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 = 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();

  • Field Details

    • swigCMemOwn

      protected transient boolean swigCMemOwn

  • Constructor Details

    • KnapsackSolver

      protected KnapsackSolver(long cPtr, boolean cMemoryOwn)

    • KnapsackSolver

      public KnapsackSolver(String solver_name)

    • KnapsackSolver

      public KnapsackSolver(KnapsackSolver.SolverType solver_type, String solver_name)

  • Method Details

    • getCPtr

      protected static long getCPtr(KnapsackSolver obj)

    • swigRelease

      protected static long swigRelease(KnapsackSolver obj)

    • finalize

      protected void finalize()
      Overrides:
      finalize in class Object

    • 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

      public String getName()

    • 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.