The environments of the dynamic multiobjective optimization problems (DMOPs), such as Pareto optimal front (POF) or Pareto optimal set (POS), usually frequently change with the evolution process. This kind of problem poses a higher challenge for evolutionary algorithms because it requires the population to quickly track (i.e., converge) to the position of a new environment and be widely distributed in the search space. The prediction-based response mechanism is a commonly used method to deal with environmental changes, but it’s only suitable for predictable changes. Moreover, the imbalance of population diversity and convergence in the process of tracking the dynamically changing POF has aggravated. In this paper, we proposed a new change response mechanism that combines a hybrid prediction strategy and a precision controllable mutation strategy (HPPCM) to solve the DMOPs. Specifically, the hybrid prediction strategy coordinates the center point-based prediction and the guiding individual-based prediction to make accurate predictions. Thus, the population can quickly adapt to the predictable environmental changes. Additionally, the precision controllable mutation strategy handles unpredictable environmental changes. It improves the diversity exploration of the population by controlling the variation degree of solutions. In this way, our change response mechanism can adapt to various environmental changes of DMOPs, such as predictable and unpredictable changes. This paper integrates the HPPCM mechanism into a prevalent regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) to optimize DMOPs. The results of comparative experiments with some state-of-the-art algorithms on various test instances have demonstrated the effectiveness and competitiveness of the change response mechanism proposed in this paper. 

/pdf/combining-a-hybrid-prediction-strategy-and-a-mutation-3qqbfsh5.pdf

Combining a hybrid prediction strategy and a mutation strategy for dynamic multiobjective optimization

/pdf/multiple-source-transfer-learning-for-dynamic-multiobjective-7k27g1q7.pdf

Multiple source transfer learning for dynamic multiobjective optimization

Dynamic multiobjective optimization poses great challenges to evolutionary algorithms due to the change of optimal solutions or Pareto front with time. Learning-based methods are popular to extract the changing pattern of optimal solutions for predicting new solutions. They tend to use all variables as features (i.e., inputs) to build prediction models. However, there are usually some irrelevant and redundant variables, which increase training difficulty and decrease prediction accuracy. This paper proposes a new interaction-based prediction method, which captures the correlation of variables with prediction targets and selects the most relevant variables to build prediction models using neural networks. In particular, the interaction between variables is detected to remove redundant variables. In addition, a correction procedure is developed to further improve predicted solutions according to the prediction error in past environments. The predicted solutions are used to update the population according to a specifically designed update strategy. Integrating the interaction-based prediction (IP) method into the framework of multiobjective evolutionary algorithm based on decomposition (MOEA/D), a new algorithm named IP-DMOEA is put forward. Experimental results on a typical dynamic multiobjective test suite demonstrate the better performance of the proposed IPDMOEA than state-of-the-art algorithms in terms of convergence speed and solution quality. The proposed IP-DMOEA is also successfully applied to the multirobot task scheduling problem. 

Interaction-based Prediction for Dynamic Multiobjective Optimization

In recent years, researchers have made significant progress in handling dynamic multi-objective optimization problems (DMOPs), particularly for environmental changes with predictable characteristics. However, little attention has been paid to DMOPs with stochastic changes. It may be difficult for existing dynamic multi-objective evolutionary algorithms (DMOEAs) to effectively handle this kind of DMOPs because most DMOEAs assume that environmental changes follow regular patterns and consecutive environments are similar. This paper presents a Mahalanobis Distance-based approach (MDA) to deal with DMOPs with stochastic changes. Specifically, we make an all-sided assessment of search environments via Mahalanobis distance on saved information to learn the relationship between the new environment and historical ones. Afterward, a change response strategy applies the learning to the new environment to accelerate the convergence and maintain the diversity of the population. Besides, the change degree is considered for all decision variables to alleviate the impact of stochastic changes on the evolving population. MDA has been tested on stochastic DMOPs with 2 to 4 objectives. The results show that MDA performs significantly better than the other latest algorithms in this paper, suggesting that MDA is effective for DMOPs with stochastic changes. 

https://dora.dmu.ac.uk/bitstream/2086/22586/1/IEEETEVC23.pdf

A Mahalanobis Distance-based Approach for Dynamic Multi-objective Optimization with Stochastic Changes

Dynamic multiobjective optimization problems (DMOPs) are widely encountered in real-world applications and have received considerable attention in recent years. During the process of solving DMOPs, tracking the constantly changing Pareto optimal set (POS) quickly is the main task, and numerous methods have been proposed to achieve this task from different perspectives. However, how to improve the evolution of static optimizers via using historical information from past environments gets little attention. In fact, with adequate historical evolution information to learn, the trend of population evolution in the historical environments is promising to guide the future evolution and thus enhance the search ability. Therefore, in this paper, a historical evolution learning based framework is proposed to assist the static optimizers in fully using the historical evolution direction and POSs distribution. Specifically, two new models are designed with a purpose of generating offsprings and environmental selection, respectively. For enhancing the contribution of offsprings, a direction guidance model is developed to guide the offsprings according to the direction tendency of historical evolution. Furthermore, to improve the robustness of static optimizers and avoid the disturbance caused by misleading solutions, a manifold revise model is proposed to produce promising solutions via consulting historical POSs distribution. The proposed framework employs these two models collaboratively, and it is flexible and readily to be embedded into various dynamic response mechanisms and static optimizers in coping with DMOPs. The superiority of the framework has been comprehensively demonstrated by experimental comparison results on a variety of benchmark test problems. 

A Framework Based on Historical Evolution Learning for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization problems are challenging due to their fast convergence and diversity maintenance requirements. Prediction-based evolutionary algorithms currently gain much attention for meeting these requirements. However, it is not always the case that an elaborate predictor is suitable for different problems and the quality of historical solutions is sufficient to support prediction, which limits the availability of prediction-based methods over various problems. Faced with these issues, this article proposes a knowledge learning strategy for change response in the dynamic multiobjective optimization. Unlike prediction approaches that estimate the future optima from previously obtained solutions, in the proposed strategy, we react to changes via learning from the historical search process. We introduce a method to extract the knowledge within the previous search experience. The extracted knowledge can accelerate convergence as well as introduce diversity for the optimization of the future environment. We conduct a comprehensive experiment on comparing the proposed strategy with the state-of-the-art algorithms. Results demonstrate the better performance of the proposed strategy in terms of solution quality and computational efficiency.

Evolutionary Dynamic Multiobjective Optimization via Learning From Historical Search Process.

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Evolutionary Dynamic Multiobjective Optimization via Learning From Historical Search Process.