Dynamic Multi-objective Optimization Algorithms Based On Knee Points Transfer

Dynamic multi-objective optimization problem is a complex optimization problem,which has attracted much attention because of its unique characteristics.With a change in time or environment,its optimization objectives and decision variables may also change,altering the final result of optimization.The objective function may change over time while the optimization process is taking place,thus the algorithm must take this into account in order to solve problems of this type.Among the many dynamic multi-objective optimization algorithms that have been presented,transfer learning-based methods show great prospects.However,the existing transfer learning-based algorithms typically ignore the trade-off between speed and performance,taking only a partial account of the algorithm’s performance.Therefore,on the one hand,we use the combination of partial feature information and transfer learning to improve the running speed of the algorithm.On the other hand,we focus on how to use the transfer solutions to generate more high-quality individuals and improve the quality of the initial population.In this paper,two optimization algorithms for dynamic multi-objective problems are proposed by using transfer solutions to guide the generation of high-quality initial population for new environment.The main works are as follows:(1)Dynamic Multiobjective Optimization With a Bi-stage Strategy(DMO-BS).The algorithm mainly consists of two stages,which are the transfer stage and the rest individual generation stage.In the first stage,the estimated knee points of the new environment are obtained according to the combination of the knee points in the historical environment and transfer learning.In the second stage,the estimated knee points are used to exploit and explore in the new environment to generate high-quality individuals respectively,so as to realize a dynamic multi-objective optimization algorithm with a two-stage strategy.The proposed method is tested on seven benchmark functions and compared with several representative algorithms.Experimental results show that the algorithm can improve the running speed while ensuring the quality of the initial population.(2)Dynamic multi-objective optimization algorithm based on contribution value analysis(DMO-CVA).The algorithm’s main idea is to analyze the contribution of special groups under two continuous moments and adopt a prediction method that satisfies the present requirements to generate more high-quality individuals to react to environmental changes.The two special groups,correspondingly,refer to historical knee points and estimated knee points produced by transfer.Due to different transfer groups will have different results,DMO-CVA put forward a non-repeated knee points selection strategy in order to guarantee that each individual is beneficial.According to the calculation results,different types of strategies are adopted to generate more high-quality individuals to meet the demand at the current changing environment.On various benchmark test problems,the experimental results demonstrate that DMO-CVA performs somewhat better than other algorithms.Additionally,the ablation experiment supports the algorithm’s non-repetitive knee point selection and prediction strategies as being effective.