Dynamic Multi-Objective Optimization Based On Brain Storm Optimization Algorithm

Many optimization problems in real production life need to take into account multiple objectives,and there are contradictions between the goals.There are often no solutions that can make all objectives reach the optimal solution,but only some compromise solutions can be found.The objective functions and constraints of these optimization problems often change with time.The optimization problem that satisfies the above characteristics is called Dynamic multi-objective optimization problem(DMOP).Unlike static multi-objective optimization problem,time-varying environmental variables lead to changes in the Pareto optimal solution sets and Pareto optimal fronts of dynamic multi-objective optimization problem.Therefore,the core of solving the dynamic multi-objective optimization problem is how to increase and maintain the population diversity after environmental change,and quickly and effectively track the Pareto optimal solution sets and the Pareto optimal fronts that change with time.In response to this problem,the researchers proposed a dynamic multi-objective optimization method based on prediction,which is used to generate the initial population under the new environment.While maintaining the diversity of the population,the historical information is fully utilized,which provide a correct guiding direction for the population search and effectively accelerate the rate of evolutionary convergence in the new environment.Based on the research of existing dynamic multi-objective optimization algorithms,this paper introduces the brain storm algorithm to solve the dynamic multi-objective optimization problem.(1)A grid-based dynamic multi-objective brainstorm optimization algorithm is presented to find the dynamic Pareto optimal solution set in the new environment,which makes the brainstorm optimization algorithm more suitable for solving dynamic multi-objective optimization problems.The method uses grid-based clustering method and mixed mutation operator to reduce the computational complexity of the algorithm and increase the diversity of the population.The grid-based clustering method uniformly divides the objective space along each objective,and marks the individuals in the same grid as a group,whose computational complexity is smaller than the existing K-means clustering method and group-based clustering method.Traditional Gaussian mutation,Cauchy mutation,and chaotic mutation have different mutation steps,resulting in new individuals with different diversity.In order to enhance diversity and avoid premature convergence,a mixed mutation strategy combining the above three mutation operators is given.Experimental results on different types of dynamic multi-objective test functions verify the effectiveness of the proposed algorithm.(2)For the dynamic multi-objective optimization problem,a dynamic multi-objective brainstorm optimization algorithm based on hybrid prediction is proposed to accelerate the evolutionary convergence.When the environment is detected to change,the initial population in the new environment consists of three parts,including: individuals generated based on the Kalman filter prediction model,individuals generated by the feedforward center point prediction method,and randomly initialized individuals.Among them,the proportion of individuals generated by the feedforward center point prediction model and the proportion of randomly initialized individuals are related to the degree of environmental change.For the dynamic multi-objective benchmark function,experiment analyses the effects of two different dimensions of Kalman filter model on the performance of the algorithm.At the same time,compared with several other prediction strategies,the Pareto optimal solution sets obtained by the prediction strategy proposed in this paper have better convergence and distribution.(3)The premise of constructing a predictive model is that there is a linear relationship between the dynamic Pareto optimal solution sets.When the environment changes aperiodically,the initial population generated based on the above prediction model has poor performance.Therefore,an improved dynamic multi-objective optimization algorithm framework based on transfer learning is presented.The proposed algorithm framework combines transfer learning with intelligent optimization algorithm to generate a more reasonable initial population under a new environment by transferring historical information at similar environment,effectively solving the dynamic multi-objective optimization problems.This method saves historical time information to the archive set.By comparing the Jensen-Shannon divergence,the historical environment most similar to the new environment is selected from the archive set,and correlation alignment is employed to extract the knowledge in the similar environment to generate a more effective initial population and accelerate the evolutionary convergence.In order to verify the validity of the algorithm framework,it is oriented to benchmark functions and fully compared with other algorithms.The experimental results show that the proposed algorithm can effectively solve the dynamic multi-objective optimization problems and obtain Pareto solution sets with better distribution and convergence.