Abstract: Most of the basic multi-objective evolutionary algorithm is one kind of similar random search algorithm based on the concept of Pareto optimization,which with the slowly speed,especially for dynamic multi-objective problems.Accordingly,the hybrid optimization algorithm based on single and multi-objective gradient information (HSMGOA) is proposed.The algorithm confirms the direction of variation on each individual by using the gradient information.Firstly,the negative gradient direction information of each target in the population is calculated,those operation guarantees the individual species moving to the optimization declining direction for each of the single objective value effectively.Due to the conflict between each objective of multi-objective problem,it may cause the increase of the other objective function value if only considering the fall direction of one target.Therefore,this article also joins in the random weighted integration method,which fusing the gradient direction information of multiple goals to one search direction.Also,based on the traditional crowding distance selection method,this paper proposes a new select scatter point method to further speed up the optimization algorithm and provide the best initial population.Through the simulation of ZDT series test function and the analysis results with the NSGA2,it can be seen that the performance of the proposed algorithm is much better than the NSGA2 algorithm with less run times.It also shows that this algorithm has faster convergence.Finally a new algorithm was proposed by mixing the algorithm with NSGA2,and it is applied to dynamic multi-objective optimization of fed-batch bioreactor,the preferable Pareto optimal solution set is obtained.Compared with NSGA2 and MOPSO,the new algorithm shows better performance.

Key words: multi-objective, optimization algorithm, gradient information, selection and collocation method, fed-batch bioreactor, dynamic optimization

摘要： 传统的多目标进化算法多是基于Pareto最优概念的类随机搜索算法，求解速度较慢，特别是针对动态多目标优化问题。就此提出了一种新的基于梯度信息的多目标寻优算法（hybrid optimization algorithm based on single and multi-objective gradient information，HSMGOA），该算法首先利用种群中每个个体对各目标的负梯度方向，以有效保证种群个体能沿单个目标函数值减小的方向加快搜索；同时为避免由于多目标问题之间的冲突性而导致其他目标函数的显著增大，将多个目标的梯度信息方向整合为一个方向进行协同搜索；并且还提出了一种新的选择置点法，以加快算法初始寻优速度并提供优良的初始种群。通过对ZDT系列测试函数的仿真可以看出，HSMGOA在较少的运行次数下，其性能远远优于NSGA2算法。最后将HSMGOA与NSGA2混合以解决补料分批生化反应过程的动态多目标优化问题，并将取得的Pareto最优解集与NSGA2、MOPSO比较可知，该混合算法在解决该化工问题时表现出了更好的性能。

关键词: 多目标, 优化算法, 梯度信息, 选择置点法, 补料分批生化反应器, 动态优化