A Hybrid Genetic Algorithm for the Quadratic Assignment Problem
Zakir Hussain Ahmed, Hachemi Bennaceur,
Mohammad Habib Vulla and Furat Altukhaim
Department of Computer Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU),
P.O. Box No. 5701, Riyadh 11432, Kingdom of Saudi Arabia.
e-mail: {zhahmed, hachemi, habeebvulla}@ccis.imamu.edu.sa
Abstract. A hybrid genetic algorithm is proposed to find heuristic solution to the quadratic assignment
problem. (QAP) is a NP-hard combinatorial optimization problem. Our algorithm uses an improved initial
population generated by sequential sampling algorithm and a combined mutation operator, sequential
constructive crossover, an adaptive mutation, a local search method and an immigration method. Finally,
a comparative study is carried out against an improved genetic algorithm on some benchmark QAPLIB
instances which shows effectiveness of our proposed algorithm.
Keywords: Adaptive mutation, Combined mutation, Genetic algorithm, Quadratic assignment problem,
Sequential constructive crossover, Sequential sampling, Immigration.
1. Introduction
Genetic algorithms (GAs), first proposed by John Holland [1] based on Darwinian Theory of survival-of-the-fittest
among different species, are very powerful and robust heuristic artificial intelligent algorithms for solving complex
optimization problems [2]. To apply GA on any problem, solution space of the problem must be represented as a
chromosome and an objective function that measures the goodness of the solution must be defined. A basic GA
includes a randomly generated initial population of chromosomes, a selection operator that copies some chromosomes
to the next generation probabilistically based on their objective function value, a crossover operator that randomly
selects a pair of chromosomes and exchanges information between them, and a mutation operator that occasionally
alters random position value (called gene) of a chromosome. Crossover operator together with selection operator is the
most powerful process in the GA search and mutation operator diversifies the search space. The main feature of GAs
is that information is passed through generations. Moreover, in GAs, the learning process can be viewed as a search
whose main function is to exploit the knowledge embodied in the good structures so far created and the exploration,
through the combining operators of regions in the solution space. All this process is performed in parallel, in a sense,
on a pool of strings; this prevents the algorithm from being trapped in a local minimum and, perhaps most importantly,
by allowing for movements in the search space, which are non-optimal, to reach regions which could not be reached
by a conventional descent algorithm.
Crossover operator plays very important role in GAs, and hence, many crossover operators have been proposed for
different optimization problems as well as the quadratic assignment problem. Still, most of the crossovers have some
drawbacks including premature convergence, evolutionary stagnation, and time consuming. To overcome them, local
search method is incorporated to improve their performance. Hybrid GAs, also called memetic algorithms [3], are GAs
with a local search algorithm applied on the offspring produced by crossover operator before including them into the
population.
In this paper, we propose an improved initial population using sequential sampling algorithm [4] which is then
improved by a combined mutation operator [4] for our hybrid GA (HGA). For the crossover operator, we use
sequential constructive crossover [5], which is further improved by using the combined mutation operator [4].
As regards the mutation operator, we use an adaptive mutation operator [5] to diversify the search space intelligently.
As an immigration method, we use sequential sampling algorithm [4] to occasionally insert into the population.
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