K. Li et al. (Eds.): LSMS/ICSEE 2010, Part II, LNCS 6329, pp. 49–57, 2010. © Springer-Verlag Berlin Heidelberg 2010 A Modified Binary Differential Evolution Algorithm Ling Wang, Xiping Fu, Muhammad Ilyas Menhas, and Minrui Fei Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronics and Automation, Shanghai University, 200072, Shanghai, China wangling@shu.edu.cn Abstract. Differential evolution (DE) is a simple, yet efficient global optimiza- tion algorithm. As the standard DE and most of its variants operate in the continuous space, this paper presents a modified binary differential evolution algorithm (MBDE) to tackle the binary-coded optimization problems. A novel probability estimation operator inspired by the concept of distribution of esti- mation algorithm is developed, which enables MBDE to manipulate binary- valued solutions directly and provides better tradeoff between exploration and exploitation cooperated with the other operators of DE. The effectiveness and efficiency of MBDE is verified in application to numerical optimization problems. The experimental results demonstrate that MBDE outperforms the discrete binary DE, the discrete binary particle swarm optimization and the bi- nary ant system in terms of both accuracy and convergence speed on the suite of benchmark functions. Keywords: Differential Evolution, Binary Encoding, Probability Estimation Operator, Multidimensional Knapsack Problem. 1 Introduction Differential Evolution (DE), an emerging population-based stochastic optimization technique first proposed by Storn and Price in 1995 [1], has become a new hotspot in evolutionary computation. The standard DE algorithm, which is simple yet efficient in global optimization, has been successfully applied in scientific and engineering fields. As a versatile evolutionary algorithm, DE does not need any gradient information so that it is capable of solving non-convex, nonlinear, non-differentiable and multimodal problems. Moreover, there are only two control parameters in the update formulas of DE, thus it is easy to implement and tune parameters. Literatures have reported that DE is superior to particle swarm optimization (PSO) and genetic algorithm (GA) in some real-world applications [2-4]. Due to its simplicity and effectiveness, DE has attracted much attention in recent years, and a number of improved variants have been proposed [5-7]. However, the standard DE and many of its improved variants operate in the continuous space, which are not suitable for solving discrete combinational optimization problems. Therefore, several binary DE algorithms are proposed to tackle this drawback. In- spired by angle modulated PSO algorithm [8], Pampará [9] proposed a new binary DE