Struct QuadraticAssignment 

pub struct QuadraticAssignment { /* private fields */ }

The Quadratic Assignment Problem (QAP).

Given n facilities and m locations, a cost matrix C (n x n) representing flows between facilities, and a distance matrix D (m x m) representing distances between locations, find an injective assignment of facilities to locations that minimizes:

f(p) = sum_{i != j} C[i][j] * D[p(i)][p(j)]

where p is an injective mapping from facilities to locations (a permutation when n == m).

Example

use problemreductions::models::algebraic::QuadraticAssignment;
use problemreductions::{Problem, Solver, BruteForce};

let cost_matrix = vec![
    vec![0, 1, 2],
    vec![1, 0, 3],
    vec![2, 3, 0],
];
let distance_matrix = vec![
    vec![0, 5, 8],
    vec![5, 0, 3],
    vec![8, 3, 0],
];
let problem = QuadraticAssignment::new(cost_matrix, distance_matrix);

let solver = BruteForce::new();
let best = solver.find_witness(&problem);
assert!(best.is_some());

Implementations

impl QuadraticAssignment

pub fn new(cost_matrix: Vec<Vec<i64>>, distance_matrix: Vec<Vec<i64>>) -> Self

Create a new Quadratic Assignment Problem.

Arguments

• cost_matrix - n x n matrix of flows/costs between facilities
• distance_matrix - m x m matrix of distances between locations

Panics

Panics if either matrix is not square, or if num_facilities > num_locations.

pub fn cost_matrix(&self) -> &[Vec<i64>]

Get the cost/flow matrix.

pub fn distance_matrix(&self) -> &[Vec<i64>]

Get the distance matrix.

pub fn num_facilities(&self) -> usize

Get the number of facilities.

pub fn num_locations(&self) -> usize

Get the number of locations.

Trait Implementations

impl Clone for QuadraticAssignment

fn clone(&self) -> QuadraticAssignment

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for QuadraticAssignment

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for QuadraticAssignment

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for QuadraticAssignment

const NAME: &'static str = "QuadraticAssignment"

Base name of this problem type (e.g., “MaximumIndependentSet”).

type Value = Min<i64>

The evaluation value type.

fn dims(&self) -> Vec<usize>

Configuration space dimensions. Each entry is the cardinality of that variable.

fn evaluate(&self, config: &[usize]) -> Min<i64>

Evaluate the problem on a configuration.

fn variant() -> Vec<(&'static str, &'static str)>

Returns variant attributes derived from type parameters.

fn num_variables(&self) -> usize

Number of variables (derived from dims).

fn problem_type() -> ProblemType

Look up this problem’s catalog entry.

impl ReduceTo<ILP> for QuadraticAssignment

type Result = ReductionQAPToILP

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl ReduceTo<QuadraticAssignment> for HamiltonianCircuit<SimpleGraph>

type Result = ReductionHamiltonianCircuitToQuadraticAssignment

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl Serialize for QuadraticAssignment

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl DeclaredVariant for QuadraticAssignment