GoemansWilliamsonOptimizer

class GoemansWilliamsonOptimizer(num_cuts, sort_cuts=True, unique_cuts=True, seed=0)

ベースクラス: OptimizationAlgorithm

Goemans-Williamson algorithm to approximate the max-cut of a problem. The quadratic program for max-cut is given by:

max sum_{i,j<i} w[i,j]*x[i]*(1-x[j])

Therefore the quadratic term encodes the negative of the adjacency matrix of the graph.

パラメータ:

• num_cuts (int) – Number of cuts to generate.

• sort_cuts (bool) – True if sort cuts by their values.

• unique_cuts (bool) – The solve method returns only unique cuts, thus there may be less cuts than num_cuts.

• seed (int) – A seed value for the random number generator.

Methods

get_compatibility_msg(problem)

Checks whether a given problem can be solved with the optimizer implementing this method.

パラメータ:

problem (QuadraticProgram) – The optimization problem to check compatibility.

戻り値:

Returns the incompatibility message. If the message is empty no issues were found.

戻り値の型:

str

is_compatible(problem)

Checks whether a given problem can be solved with the optimizer implementing this method.

パラメータ:

problem (QuadraticProgram) – The optimization problem to check compatibility.

戻り値:

Returns True if the problem is compatible, False otherwise.

戻り値の型:

bool

static max_cut_value(x, adj_matrix)

Compute the value of a cut from an adjacency matrix and a list of binary values.

パラメータ:

• x (ndarray) – a list of binary value in numpy array.

• adj_matrix (ndarray) – adjacency matrix.

戻り値:

value of the cut.

戻り値の型:

float

solve(problem)

Returns a list of cuts generated according to the Goemans-Williamson algorithm.

パラメータ:

problem (QuadraticProgram) – The quadratic problem that encodes the max-cut problem.

戻り値:

A list of generated cuts.

戻り値の型:

cuts