A greedy genetic algorithm for the quadratic assignment problem

Abstract

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. Scope and purpose Genetic Algorithms (GAs) are one of the most popular heuristic algorithms to solve optimization problems and is an extremely useful tool in an OR toolkit. For solving combinatorial optimization problems, GAs in their elementary forms are not competitive with other heuristic algorithms such as simulated annealing and tabu serach. In this paper, we have investigated the use of several possible enhancements to GAs and illustrated them using the Quadratic Assignment Problem (QAP), one of the hardest nut in the field of combinatorial optimization. Most of our enhancements use some greedy criteria to improve the quality of individuals in the population. We found that the overall performance of the GA for the QAP improves by using greedy methods but not their overuse. Overuse of greedy methods adversely affects the diversity in the population. By striking a right balance between the greedy methods that improve the quality of the solution and the methods that promote diversity, we can obtain fairly effective heuristic algorithms for solving combinatorial optimization problems.