quboResult2knapsack

Convert QUBO result to knapsack solution

Since R2025b

collapse all in page

    Installation Required: This functionality requires MATLAB Support Package for Quantum Computing.

    Syntax

    [items,totalValue,totalWeight] = quboResult2knapsack(result,v,w,M)

    Description

    [items,totalValue,totalWeight] = quboResult2knapsack(result,v,w,M) converts the result of solving the knapsack QUBO formulation to a solution for the corresponding problem. Use this function after solving a QUBO formulation created using the knapsack2qubo function.

    example

    Examples

    collapse all

    Open Live Script

    Define a knapsack problem by creating two 1-by-5 vectors that represent the values and weights of five items. Create a numeric scalar that represents the maximum weight capacity of the knapsack.

    v = [5 2 8 4 3];
w = [9 8 4 5 2];
M = 17;

    Convert the knapsack problem to a QUBO problem.

    qprob = knapsack2qubo(v,w,M)
    qprob = 
  qubo with properties:

    QuadraticTerm: [10×10 double]
       LinearTerm: [10×1 double]
     ConstantTerm: 289
     NumVariables: 10

    Solve the QUBO problem.

    result = solve(qprob)
    result = 
  quboResult with properties:

                BestX: [10×1 double]
    BestFunctionValue: -16
      AlgorithmResult: [1×1 tabuSearchResult]

    Convert the result of the QUBO problem to the knapsack formulation. The solution to the knapsack problem is to include the first, third, and fifth items in the list. These items have a total value of 16 and a total weight of 15, which is less than the specified maximum weight of 17.

    [items,totalValue,totalWeight] = quboResult2knapsack(result,v,w,M)
    items = 3×1

     1
     3
     5


    totalValue = 
16

    totalWeight = 
15

    Input Arguments

    collapse all

    Solution of the knapsack QUBO problem, specified as a quboResult object. Create result using the solve function for a QUBO problem generated using knapsack2qubo.

    Item values, specified as a numeric vector. Each element of v corresponds to the value of an item that can be placed in the knapsack. For example, the first item of those that can be placed in the knapsack has value v(1).

    Data Types: double

    Item weights, specified as a numeric vector. Each element of w corresponds to the weight of an item that can be placed in the knapsack. For example, the first item of those that can be placed in the knapsack has weight w(1).

    Data Types: double

    Maximum weight capacity of the knapsack, specified as a numeric scalar.

    Data Types: double

    Output Arguments

    collapse all

    Items selected, returned as a numeric vector. Each element of items corresponds to the index of an item from the original knapsack problem.

    Data Types: double

    Total value of all items selected, returned as a positive numeric scalar.

    Data Types: double

    Total weight of all items selected, returned as a positive numeric scalar.

    Data Types: double

    More About

    collapse all

    Version History

    Introduced in R2025b

    See Also

    Functions

    Objects

    Topics