Solving Quadratic Assignment Problems by Differential Evolution

Differential evolution (DE) was introduced by Stone and Price in 1995 as a population-based stochastic search technique for solving optimization problems in a continuous space. DE has been successfully applied to various real world numerical optimization problems. In recent years not only continuous real-valued function, the applications of DE on combinatorial optimization problems with discrete decision variables are reported. However, genetic operator in the standard DE can not directly applied to discrete space. In this paper, we propose a method to solve quadratic assignment problems (QAP) by DE. The QAP is a well-known combinatorial optimization problem with a wide variety of practical applications. It is NP-hard and is considered to be one of the most difficult problems. In the QAP, a candidate solution can represented a permutation of integer. The proposed method employs permutation representation for individuals in DE. Therefore, a individual vector is encoded directly as a permutation. In discrete space, to realize effcient solution search like standard DE which have continuous nature, we modify differential operator to handle permutation encoding. Additionally, in order to maintain diversity of population, restart strategy and tabu list are introduced to proposed method instead of crossover operator. Finally, we show the experimental results using instances of QAPLIB and the efficacy of proposed method.