A novel modified binary differential evolution algorithm and its applications

Differential Evolution (DE) is a simple yet efficient global optimization algorithm. However, the standard DE and most of its variants operate in the continuous space, which cannot solve the binary-coded optimization problems directly. To tackle this problem, this paper proposes a novel modified binary differential evolution algorithm (NMBDE) inspired by the concept of Estimation of Distribution Algorithm and DE. A novel probability estimation operator is developed for NMBDE, which can efficiently maintain diversity of population and achieve a better tradeoff between the exploration and exploitation capabilities by cooperating with the selection operator. Furthermore, the parameter study of NMBDE is run and the analysis is performed to improve the global search ability and scalability of algorithm. The effectiveness and efficiency of NMBDE was verified in applications to the numerical optimization and multidimensional knapsack problems. The experimental results demonstrate that NMBDE has the better global search ability and outperforms the discrete binary DE, the modified binary DE, the discrete binary Particle Swarm Optimization and the binary Ant System in terms of accuracy and convergence speed.