求解黑箱优化问题的动态模式跟踪抽样算法

Dynamic mode-pursuing sampling method for black-box function optimization problems

针对当前复杂工业领域设计过程中存在的计算密集型黑箱优化问题,提出一种改进的动态模式跟踪抽样算法。算法基于线性样条函数进行全局近似,通过随机抽样过程产生逐步逼近全局最优区域的设计点,并利用二次响应面函数进行全局收敛判定。引入动态加速因子来增强算法的全局搜索能力和函数适应性,并采用改进的修正复相关系数进行动态加速因子更新和响应面拟合精度判定。标准测试函数表明,相比于遗传算法和模拟退火等启发式算法,动态模式跟踪抽样算法在减少目标函数评估次数和收敛成功率上均具有较大的优势。

To deal with the expensive black-box function optimization problems in the complex industrial design processes,an improved Dynamic Mode-Pursuing Sampling（DMPS）method was presented.The linear spline function was used for global approximation.Through random sampling process,the design points of approximate global optimal areas were generated,and quadratic regression function was performed to judge the global convergence.For improving the global search capability and function adaptability,a new dynamic acceleration factor was introduced.The modified multiple correlation coefficients were used to update the acceleration factor and to judge the fitting accuracy of response surface.Simulation results on standard test functions showed that DMPS method had better ability for finding global optimum and reducing the function evaluation times compared with genetic algorithm and simulated annealing algorithm.