# Quadratic Assignment Procedure (QAP)

In mathematics, the **quadratic bottleneck assignment problem** (**QBAP**) is one of fundamental problems in the branch of or , from the category of the problems.^{}

## On the Biquadratic Assignment Problem (BIQAP)

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### On the Biquadratic Assignment Problem (BIQAP)

The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. In this paper, we suggest a genetic algorithm for the QAP and report its computational behavior. The genetic algorithm incorporates many greedy principles in its design and, hence, we refer to it as a *greedy genetic algorithm*. The ideas we incorporate in the greedy genetic algorithm include (i) generating the initial population using a randomized construction heuristic; (ii) new crossover schemes; (iii) a special purpose immigration scheme that promotes diversity; (iv) periodic local optimization of a subset of the population; (v) tournamenting among different populations; and (vi) an overall design that attempts to strike a balance between diversity and a bias towards fitter individuals. We test our algorithm on all the benchmark instances of QAPLIB, a well-known library of QAP instances. Out of the 132 total instances in QAPLIB of varied sizes, the greedy genetic algorithm obtained the best known solution for 103 instances, and for the remaining instances (except one) found solutions within 1% of the best known solutions.

### Biquadratic Assignment Problem

Zoning a forest for different uses in a complex problem. Land of a particular suitability and location has to be assigned land use objectives in such a way that the highest value is derived from zoning. In this paper, the zoning problem has been formulated as a quadratic assignment problem. Assignment of forest land to land use objectives is based on the suitability rates of forest land for land use types on one hand, and resulting location of land use objectives in respect of each other and the forest environment on the other. Quadratic assignment problems can be solved using a technique known as simulated annealing. An application of the model is shown by means of a numerical example. By addressing the zoning problem separately, forest management decisions can be structured in a hierarchical way. This approach provides more opportunities for dealing with spatial considerations than common linear programming models.

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