Quadratic Assignment Problem - Formal Mathematical Definition

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 × PR and a distance function d : L × LR. Find the bijection f : PL ("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:

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