演化优化的自适应约束处理机理及在生化过程中的应用

Most real-world optimization problems involve constraints mainly due to physical limitations or functional requirements. It is difficult to choose a reasonable value for the penalty factor of the traditional penalty function method or the penalty probability of the stochastic ranking method in evolutionary constrained optimization because of the potential risks of over-penalization and under-penalization. In this project, two adaptive mechanisms of handling constraints which can dynamically control the penalty factor and the penalty probability respectively in evolutionary constrained optimization are studied by borrowing ideas from bi-objective optimization and annealing. On one hand, a non-dominated fitting model is built so that the critical information such as the adaptive penalty factor can be mined from the non-dominated front in the bi-objective space in this project. Further, an adaptive constraint-handling mechanism of non-dominated fitting is designed to guide search processes towards the optimal feasible solutions by taking advantage of the non-dominated front to adaptively control the penalty factor. On the other hand, an adaptive constraint-handling mechanism of stochastic ranking is also designed by introducing the metropolis acceptance criteria in annealing. This mechanism can adaptively choose an appropriate penalty probability for stochastic ranking according to the evolutionary process and the overall constraint violation in order to overcome the blindness at a microscopic as well as a macroscopic level. As a result, evolutionary algorithms with two adaptive constraint-handling mechanisms are applied to efficiently solve the constrained parameter estimation problems in biochemical pathways such as Threestep model and HIV model.

现实世界的大多数优化问题由于物理限制或功能需求往往都涉及到约束，演化约束优化的传统惩罚函数法和有前景的随机排序法中分别存在惩罚因子和惩罚概率难以选定合适的参数值，存在欠惩罚或过惩罚风险。本项目分别借鉴二目标优化和退火过程研究演化约束优化中可动态控制惩罚因子与惩罚概率的两种自适应约束处理机理。本项目一方面拟建立非劣拟合信息抽取模型有效挖掘二目标非劣前沿蕴含的自适应惩罚因子等关键信息，进而设计自适应非劣拟合约束处理机制利用非劣前沿自适应地控制惩罚因子引导算法搜索到最优的可行解。另一方面，借鉴退火过程中Metropolis接受准则设计自适应随机排序约束处理机制，使算法能根据进化进程与约束违反量自适应地合理确定惩罚概率, 克服随机排序在宏观和微观上的盲目性。最后将采用两种自适应约束处理机制的演化算法应用于生化学中ThreeStep过程和HIV过程等参数估计问题，使其可高效求得这些问题的最优可行解。

现实世界的大多数优化问题由于物理限制或功能需求往往都涉及到约束，演化约束优化的传统惩罚函数法和有前景的随机排序法中分别存在惩罚因子和惩罚概率难以选定合适的参数值，存在欠惩罚或过惩罚风险。本项目分别借鉴二目标优化和退火过程研究了演化约束优化中有效规避欠惩罚或过惩罚风险的两种自适应约束处理机理。本项目一方面揭示了约束优化的惩罚函数法与二目标法的深层理论联系，借鉴锥面积进化算法对二目标空间中的非劣前沿进行锥形采样，建立演化约束优化中锥面积约束分解二目标非劣拟合模型，进而提出了采用锥面积约束分解二目标非劣拟合模型的双种群锥面积自适应非劣拟合约束处理机制，采用双种群结构依据锥面积指标同时搜索多个锥形子区域，既利用非劣拟合信息自适应地并行尝试许多个不同大小的惩罚因子避免了设置惩罚因子的困难，又充分利用了二目标前沿上不可行解蕴含的有效信息引导种群向全局最优解收敛。另一方面，本项目借鉴退火过程中Metropolis接受准则设计了自适应随机排序约束处理机制，当选择约束违反程度作为比较依据时，综合考虑个体间的约束违反程度差异性和进化进程等因素，让约束违反程度大的个体也能有机会以某个自适应的概率被保留，从而改善进化过程中种群的多样性，提高种群的全局搜索约束处理能力。最后将采用两种自适应随机排序约束处理机制的演化算法应用于工程设计中压力容器设计和焊接梁设计等工程约束优化问题并与CMODE等演化约束优化流行算法进行对比分析，结果表明采用自适应随机排序约束处理机制的算法与CMODE求解性能近似，而采用双种群锥面积自适应非劣拟合约束处理机制的算法在这些工程问题上都取得了比CMODE更好的求解性能与明显更高的运行效率。