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)

title = {The Quadratic Assignment Problem: A Survey and Recent Developments},
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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.

A robust approach for quadratic assignment problem (RQAP) with budgeted uncertainty.
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The Quadratic Assignment Problem - CiteSeerX

The quadratic assignment problem (QAP) is one of the most studied NP-hard problems with various practical applications. In this work, we propose a powerful population-based memetic algorithm (called BMA) for QAP. BMA integrates an effective local optimization algorithm called Breakout Local Search (BLS) within the evolutionary computing framework which itself is based on a uniform crossover, a fitness-based pool updating strategy and an adaptive mutation procedure. Extensive computational studies on the set of 135 well-known benchmark instances from the QAPLIB revealed that the proposed algorithm is able to attain the best-known results for 133 instances and thus competes very favorably with the current most effective QAP approaches. A study of the search landscape and crossover operators is also proposed to shed light on the behavior of the algorithm.

Word Alignment via Quadratic Assignment - Washington

Quick overview of using quadratic assignment procedure (QAP) for social network analyses. Presented to the Human Evolutionary Ecology Group (Department of Anthropology, University College London).

A Survey of the Quadratic Assignment Problem, with Applications

Teaching–Learning-Based Optimization (TLBO) is a novel swarm intelligence metaheuristic that is reported as an efficient solution method for many optimization problems. It consists of two phases where all individuals are trained by a teacher in the first phase and interact with classmates to improve their knowledge level in the second phase. In this study, we propose a set of TLBO-based hybrid algorithms to solve the challenging combinatorial optimization problem, Quadratic Assignment. Individuals are trained with recombination operators and later a Robust Tabu Search engine processes them. The performances of sequential and parallel TLBO-based hybrid algorithms are compared with those of state-of-the-art metaheuristics in terms of the best solution and computational effort. It is shown experimentally that the performance of the proposed algorithms are competitive with the best reported algorithms for the solution of the Quadratic Assignment Problem with which many real life problems can be modeled.