Adaptive Differential Evolution Enhanced With Multiple Difference Vectors

The fittest creature in the nature survive, evolute from simple to complicated, and from lower to higher in quality.people learn from the law of evolution to construct some optimization algo-rithms. The optimization algorithm tries to find a optimal solution in the feasible region, and this solution can make some indicator of system achieve the minimal or maximal status. And the evo-lutionary algorithm means the optimization algorithm inspired from the biological evolution law. There are some representative evolutionary algorithm applied in many fields. For example, Ge-netic algorithm(GA), Simulated Annealing Algorithm(SAA), Particle Swarm Optimization(PSO), Ant Colony Algorithm(ACA) and Differential Evolution(DE). Among them, Differential Evolu-tion is a simple, but effective approach for numerical optimization. But the performance of DE is sensitive to rotation on the coordinate system. Several methods have been proposed to solve the rotated problem in DE but they may lose the diversity of population, and suffer from the problem of premature convergence.In this paper, a new adaptive differential evolution(DE) algorithm, aKDE, is proposed to im-prove optimization performance, especially on the rotated problem by implementing a new trial vector generating strategy "DE/current-to-pbest/K/pk". The proposed strategy, on the one hand, eliminates the rotationally variant crossover operator with a probability pk on generating trial vec-tors from mutant vectors, on the other hand, uses multiple difference vectors to enhance the potential diversity of population and to balance exploitation and exploration. The number of difference vec-tors in the strategy is determined by parameter K. Some methods for selection and adaptation of K are introduced to generate a proper value of K. And the parameter adaptation utilizes historical successful parameters to update the control parameters CR, F to appropriate values. Furthermore, aKDE is evaluated by comparison with other EAs on CEC2005 and CEC2013 benchmark sets. The experimental results show that aKDE outperforms other state-of-the-art DE algorithms, especially on the rotated problems.