基于二次搜索的改进粒子群算法

针对标准粒子群优化（PSO）算法在求解复杂优化问题中出现的早熟收敛问题，提出一种结合梯度下降法的二次搜索粒子群算法。首先，当全局极值超过预设的最大不变迭代次数时，判断全局极值点处于极值陷阱中；然后，采用梯度下降法进行二次搜索，并以最优极值点为中心、某一具体半径设定禁忌区域，防止粒子重复搜索该区域；最后，依据种群多样性准则生成新粒子，替代被淘汰的粒子。将二次搜索粒子群算法及其他四种典型的改进粒子群算法分别应用于四种典型测试函数的优化，仿真结果表明，二次搜索粒子群算法收敛精度最高提升了10个数量级，并且收敛速度较快更容易寻找全局最优解。

Improved particle swarm optimization algorithm based on twice search

Aiming at the premature convergence problem of standard Particle Swarm Optimization (PSO) in solving complex optimization problem, a new search PSO algorithm based on gradient descent method was proposed. Firstly, when the global extremum exceeds the preset maximum number of unchanged iterations, the global extremum was judged to be in the extreme trap. Then, the gradient descent method was used to proceed twice search, a tabu area was constituted with the center of optimal extremum point and the radius of specific length to prevent particles repeatedly search the same area. Finally, new particles were generated based on the population diversity criteria to replace the particles that would be eliminated. The twice search algorithm and other four improved algorithms were applied to the optimization of four typical test functions. The simulation results show that the convergence accuracy of the twice search particle swarm algorithm is higher up to 10 orders of magnitude, the convergence speed is faster and it is easier to find the global optimal solution.