Formal Mathematical Definition
The formal definition of the quadratic assignment problem is as follows:
- Given two sets, P ("facilities") and L ("locations"), of equal size, together with a weight function w : P × P → R and a distance function d : L × L → R. Find the bijection f : P → L ("assignment") such that the cost function:
-
- is minimized.
Usually weight and distance functions are viewed as square real-valued matrices, so that the cost function is written down as:
Read more about this topic: Quadratic Assignment Problem
Famous quotes containing the words formal, mathematical and/or definition:
“The spiritual kinship between Lincoln and Whitman was founded upon their Americanism, their essential Westernism. Whitman had grown up without much formal education; Lincoln had scarcely any education. One had become the notable poet of the day; one the orator of the Gettsyburg Address. It was inevitable that Whitman as a poet should turn with a feeling of kinship to Lincoln, and even without any association or contact feel that Lincoln was his.”
—Edgar Lee Masters (1869–1950)
“What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
—D.H. (David Herbert)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)