Tsp

class Tsp(graph)

Bases: GraphOptimizationApplication

Optimization application for the “traveling salesman problem” [1] based on a NetworkX graph.

References

[1]: “Travelling salesman problem”, https://en.wikipedia.org/wiki/Travelling_salesman_problem

Parameters:

graph (nx.Graph | np.ndarray | list) – A graph representing a problem. It can be specified directly as a NetworkX graph, or as an array or list format suitable to build out a NetworkX graph.

Attributes

graph

Getter of the graph

Returns:

A graph for a problem

Methods

static create_random_instance(n, low=0, high=100, seed=None)

Create a random instance of the traveling salesman problem

Parameters:

• n (int) – the number of nodes.

• low (int) – The minimum value for the coordinate of a node.

• high (int) – The maximum value for the coordinate of a node.

• seed (int | None) – the seed for the random coordinates.

Returns:

A Tsp instance created from the input information

Return type:

Tsp

draw(result=None, pos=None)

Draw a graph with the result. When the result is None, draw an original graph without colors.

Parameters:

• result (OptimizationResult | np.ndarray | None) – The calculated result for the problem

• pos (dict[int, np.ndarray] | None) – The positions of nodes

interpret(result)

Interpret a result as a list of node indices

Parameters:

result (OptimizationResult | np.ndarray) – The calculated result of the problem

Returns:

A list of nodes whose indices correspond to its order in a prospective cycle.

Return type:

list[int | list[int]]

static parse_tsplib_format(filename)

Read a graph in TSPLIB format from file and return a Tsp instance.

Only the EUC_2D edge weight format is supported.

Parameters:

filename (str) – the name of the file.

Raises:

• QiskitOptimizationError – If the type is not “TSP”

• QiskitOptimizationError – If the edge weight type is not “EUC_2D”

Returns:

A Tsp instance data.

Return type:

Tsp

static sample_most_likely(state_vector)

Compute the most likely binary string from state vector.

Parameters:

state_vector (QuasiDistribution | Statevector | np.ndarray | dict) – state vector or counts or quasi-probabilities.

Returns:

binary string as numpy.ndarray of ints.

Raises:

ValueError – if state_vector is not QuasiDistribution, Statevector, np.ndarray, or dict.

Return type:

np.ndarray

to_quadratic_program()

Convert a traveling salesman problem instance into a QuadraticProgram

Returns:

The QuadraticProgram created from the traveling salesman problem instance.

Return type:

QuadraticProgram

static tsp_value(z, adj_matrix)

Compute the TSP value of a solution. :param z: list of cities. :param adj_matrix: adjacency matrix.

Returns:

value of the total length

Return type:

float