Sarkar Debasis, Modak Jayant M
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560-012, India.
Bioprocess Biosyst Eng. 2004 Oct;26(5):295-306. doi: 10.1007/s00449-004-0366-0.
When using a genetic algorithm (GA) to solve optimal control problems that can arise in a fed-batch bioreactor, the most obvious direct approach is to rely on a finite dimensional discretization of the optimal control problem into a nonlinear programming problem. Usually only the control function is discretized, and the continuous control function is approximated by a series of piecewise constant functions. Even though the piecewise discretized controls that the GA produces for the optimal control problem may give good performances, the control policies often show very high activity and differ considerably from those obtained using a continuous optimization strategy. The present study introduces a few filters into a real-coded genetic algorithm as additional operators and investigates the smoothing capabilities of the filters employed. It is observed that inclusion of a filter significantly smoothens the optimal control profile and often encourages the convergence of the algorithm. The applicability of the technique is illustrated by solving two previously reported optimal control problems in fed-batch bioreactors that are known to have singular arcs.
当使用遗传算法（GA）来解决分批补料生物反应器中可能出现的最优控制问题时，最直接明显的方法是依靠将最优控制问题进行有限维离散化，转化为一个非线性规划问题。通常只对控制函数进行离散化，连续控制函数由一系列分段常数函数近似表示。尽管遗传算法为最优控制问题生成的分段离散控制可能具有良好的性能，但控制策略往往表现出非常高的活跃度，并且与使用连续优化策略获得的控制策略有很大差异。本研究将一些滤波器作为附加算子引入实编码遗传算法中，并研究了所采用滤波器的平滑能力。据观察，加入滤波器能显著平滑最优控制曲线，并常常促进算法的收敛。通过求解两个先前报道的分批补料生物反应器中的最优控制问题（已知存在奇异弧段），说明了该技术的适用性。
