Abstract: Due to the weak development ability, Particle Swarm Optimization (PSO) algorithms have the shortages of low precision and slow convergence. Comparatively weak exploration ability of Differential Evolution (DE) algorithm, might further lead to a trap in the local extremum. A particle swarm-differential evolution fusion algorithm based on fuzzy Gaussian learning strategy was proposed. On the basis of the standard particle swarm algorithm, the elite particle population was selected, and the fusion mechanism of elite particle swarm-evolution was constructed by using mutation, crossover and selection evolution operators to improve particle diversity and convergence. A fuzzy Gaussian learning strategy according with human thinking characteristics was introduced to improve particle optimization ability, and further generate an elite particle swarm and differential evolution fusion algorithm based on fuzzy Gaussian learning strategy. Nine benchmark functions were calculated and analyzed in this thesis. The results show that the mean values of the functions Schwefel.1.2, Sphere, Ackley, Griewank and Quadric Noise are respectively 1.5E-39, 8.5E-82, 9.2E-13, 5.2E-17, 1.2E-18, close to the minimum values of the algorithm. The convergences of Rosenbrock, Rastrigin, Schwefel and Salomon functions are 1~3 orders of magnitude higher than those of four contrast particle swarm optimization algorithms. At the same time, the convergence of the proposed algorithm is 5%-30% higher than that of the contrast algorithms. The proposed algorithm has significant effects on improving convergence speed and precision, and has strong capabilities in escaping from the local extremum and global searching.

Key words: fuzzy membership degree, Gaussian learning, particle swarm, differential evolution, fusion optimization

摘要： 针对粒子群优化（PSO）算法存在的开发能力不足，导致算法精度不高、收敛速度慢以及微分进化算法具有的探索能力偏弱，易陷入局部极值的问题，提出一种基于模糊高斯学习策略的粒子群-进化融合算法。在标准粒子群算法的基础上，选取精英粒子种群，运用变异、交叉、选择进化算子，构建精英粒子群-进化融合优化机制，提高粒子种群多样性与收敛性；引入符合人类思维特性的模糊高斯学习策略，提高粒子寻优能力，形成基于模糊高斯学习策略的精英粒子群和微分进化融合算法。对9个标准测试函数进行了计算测试和对比分析，结果表明函数Schwefel.1.2、Sphere、Ackley、Griewank与Quadric Noise计算平均值分别为1.5E-39、8.5E-82、9.2E-13、5.2E-17、1.2E-18，接近算法最小值；Rosenbrock、Rastrigin、Schwefel及Salomon函数收敛平均值较四种对比粒子群优化算法计算结果提高了1~3个数量级；同时，收敛性显示算法收敛速度较对比算法提高了5%~30%。算法在提高计算收敛速度和精度上效果明显，具有较强的逃离局部极值的能力和全局搜索能力。

关键词: 模糊隶属度, 高斯学习, 粒子群, 微分进化, 融合优化