基于Cauchy和Gaussian分布状态发生器的模拟退火算法

Simulated annealing with the state generator based on Cauchy and Gaussian distributions

模拟退火 (SA )算法是一种常用的概率性全局优化算法 ,但其搜索行为和优化性能对参数有严重的依赖性 ,其中状态发生器的设计最为关键。论文主要研究函数优化中基于 Cauchy分布的状态发生器 (SGC)和基于 Gaussian分布的状态发生器 (SGG)对 SA算法性能的影响。对分布机制的研究表明 ,SGC有利于大范围搜索和脱离极小区域 ,而SGG较适合于局部搜索。对不同复杂度的典型问题的仿真表明 ,优化简单单极小问题时 SGC的优化效率优于基于SGG,优化复杂多极小或存在平坦区的简单问题时 SGC的优化度和鲁棒性均优于 SGG。进而利用对尺度参数的“退温”控制 ,提出了 SGC的改进策略 ,较大程度上提高了优化度和鲁棒性。

Simulated annealing is a probabilistic global optimization algorithm, whose searching behavior and performance are very sensitive to the input parameters, especially to the state generator. The performances of state generators based on Cauchy distribution (SGC) and Gaussian distribution (SGG) for numerical optimization were compared in this paper. The distribution mechanism was analyzed, and it has been found that SGC is good at search in solution spaces while SGG is better at search in small local neighborhoods. Simulation results on benchmark problems show that SGC is more efficient than SGG for simple unimodal functions and that the optimization quality and robustness of SGC are superior to those of SGG for complex multimodal functions with many local minima and for simple functions with plateaus. An improved SGC was proposed using the annealing strategy to control the scale parameter which has better quality and robustness have been achieved.