Prediction-based Dynamic Multi-objective Evolutionary Optimization

Dynamic multi-objective optimization problems(DMOPs)have found an increasing number of applications in engineering and science,such as power system management,financial asset allocation,rescue path planning of robots,routing selection of mobile ad hoc network,and workshop production scheduling.Resulted from actual running environment,there might be time-related variables in the objectives or(and)constraints of DMOPs.One of the most effective methods of this kind of problems is to track the moving Pareto set(PS).It responds to changes whenever detecting the environment occurs on purpose of finding the changing optima in a rapid and accurate way.As a representative,prediction methods aim to generate the reinitialized populations which are hopefully close to or even covering the true optimal regions of the new environment.Prediction works from the aspect of seeking intrinsic changing patterns and is widely employed to solve DMOPs due to its great performance in tracking changes.Currently,there are a variety of prediction-based dynamic multi-objective optimization methods.However,these methods focus on DMOPs with a translational Pareto optimal set.For DMOPs whose PS changing type is rotation,composite move,or their combination,these methods will lose their effectiveness.In addition,a handful of them have the capability in handling dynamic constraints,which are very popular in real-world DMOPs.Based on these observations,this paper proposes prediction-based dynamic multi-objective evolutionary optimization methods for DMOPs with changing objectives or(and)constraints.Firstly,a multi-directional prediction method for dynamic multi-objective evolutionary optimization method(MDP)is proposed to deal with DMOPs with unchanged constraints.MDP predicts the number of clusters based on the objective variance of PS before and after the change.It determines the number of guiding directions for subsequent process.A computationally efficient clustering method is presented and employed to categorize individuals of PS and calculate the center for each cluster.Based on the changes of cluster centers between the nearest two time instances,MDP predicts the guiding direction for each cluster by utilizing the linear time sequence model.Individuals in the same cluster evolve along the corresponding guiding direction and find their new locations.MDP has good performance in maintaining the diversity of the reinitialized population.The proposed method is compared with commonly used approaches like dNSGA-II and SGEA for nine dynamic test instances.Experimental results demonstrate its superiority in obtaining Pareto optimal sets with good convergence and diversity.Secondly,a multi-model prediction method for dynamic multi-objective evolutionary optimization method(MMP)is proposed to solve DMOPs with unchanged constraints.In MMP,four types of the PS change are defined to determine the provided PS changing type.Based on the changes of detectors,MMP makes an estimation of the PS changing type under the current environment.According to the PS changing type,MMP selects the most appropriate prediction model to generate the reinitialized population.This method takes the PS changing type into account when predicting new locations of individuals,which improves the pertinence of prediction.Comparisons are conducted with commonly used dynamic methods like DMOPSO and PPS for eleven dynamic test instances.Experimental results show that MMP has good performance in tracking the changing PS.Thirdly,a prediction and niching-based evolutionary algorithm for dynamic constrained multi-objective evolutionary optimization method(P-NEA)is proposed to handle dynamic constrained multi-objective optimization problems with changing constraints.This method detects whether a change occurs in constraints based on the behavior of PS.In response to the change,two sub-populations,i.e.the prediction and maintenance sub-populations,are employed to generate the whole reinitialized population with expectedly good diversity,convergence,and feasibility.The former works based on the autoregressive time sequence model whereas the latter takes advantages of differential mutation.Based on a niching strategy,the population can be directed towards the feasible region.This method has good performance in dynamic constraint handling.It is compared with a number of commonly used methods like C-TAEA and CH.Experimental results indicate that P-NEA has the capability of tracking the constrained PS.Finally,the prediction-based dynamic multi-objective optimization method discussed above is applied into robot rescue path planning.A mathematical optimization model is formulated and a prediction and niching-based path planning method is proposed.In the experimental section,the proposed method is compared with dNSGA-II and DMOPSO under a designed representative scenario.Experimental results show that this method is able to adapt itself and obtain good rescue path when the environment changes.The advantages of all these proposed methods have been experimentally validated in the corresponding DMOPs.The study not only enriches the existing dynamic multi-objective evolutionary optimization theory,but also improves the performance of dynamic multi-objective evolutionary optimization methods and provides efficient solutions to complex DMOPs.Therefore,this study has theoretical significance and application value.There are totally 19 figures,20 tables,and 118 references in this paper.