One of the major distinguishing features of the Dynamic Multiobjective Optimization Problems (DMOPs) is that optimization objectives will change over time, thus tracking the varying Pareto-Optimal Front (POF) becomes a challenge. One of the promising solutions is reusing “experiences” to construct a prediction model via statistical machine learning approaches. However, most existing methods neglect the non-independent and identically distributed nature of data to construct the prediction model. In this paper, we propose an algorithmic framework, called Tr-DMOEA, which integrates transfer learning and population-based evolutionary algorithms (EAs) to solve the DMOPs. This approach exploits the transfer learning technique as a tool to generate an effective initial population pool via reusing past experience to speed up the evolutionary process, and at the same time any population based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this idea, we incorporate the proposed approach into the development of three well-known evolutionary algorithms, nondominated sorting genetic algorithm II (NSGA-II), multiojective particle swarm optimization (MOPSO), and the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA). We employ twelve benchmark functions to test these algorithms as well as compare them with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed design for DMOPs.

Dynamic multiobjective optimization problems (DMOPs) are optimization problems with multiple conflicting optimization objectives, and these objectives change over time. Transfer learning-based approaches have been proven to be promising; however, a slow solving speed is one of the main obstacles preventing such methods from solving real-world problems. One of the reasons for the slow running speed is that low-quality individuals occupy a large amount of computing resources, and these individuals may lead to negative transfer. Combining high-quality individuals, such as knee points, with transfer learning is a feasible solution to this problem. However, the problem with this idea is that the number of high-quality individuals is often very small, so it is difficult to acquire substantial improvements using conventional transfer learning methods. In this paper, we propose a knee point-based transfer learning method, called KT-DMOEA, for solving dynamic multiobjective optimization problems. In the proposed method, a trend prediction model (TPM) is developed for producing the estimated knee points. Then, an imbalance transfer learning method is proposed to generate a high-quality initial population by using these estimated knee points. The advantage of this approach is that the seamless integration of a small number of high-quality individuals and the imbalance transfer learning technique can greatly improve the computational efficiency while maintaining the quality of the solution. The experimental results and performance comparisons with some chosen state-of-the-art algorithms demonstrate that the proposed design is capable of significantly improving the performance of dynamic optimization.

Dynamic multiobjective optimization problems (DMOPs) are characterized by optimization functions that change over time in varying environments. The DMOP is challenging because it requires the varying Pareto-optimal sets (POSs) to be tracked quickly and accurately during the optimization process. In recent years, transfer learning has been proven to be one of the effective means to solve dynamic multiobjective optimization. However, the negative transfer will lead the search of finding the POS to a wrong direction, which greatly reduces the efficiency of solving optimization problems. Minimizing the occurrence of negative transfer is thus critical for the use of transfer learning in solving DMOPs. In this article, we propose a new individual-based transfer learning method, called an individual transfer-based dynamic multiobjective evolutionary algorithm (IT-DMOEA), for solving DMOPs. Unlike existing approaches, it uses a presearch strategy to filter out some high-quality individuals with better diversity so that it can avoid negative transfer caused by individual aggregation. On this basis, an individual-based transfer learning technique is applied to accelerate the construction of an initial population. The merit of the IT-DMOEA method is that it combines different strategies in maintaining the advantages of transfer learning methods as well as avoiding the occurrence of negative transfer; thereby greatly improving the quality of solutions and convergence speed. The experimental results show that the proposed IT-DMOEA approach can considerably improve the quality of solutions and convergence speed compared to several state-of-the-art algorithms based on different benchmark problems.

The key task in dynamic multiobjective optimization problems (DMOPs) is to find Pareto-optima closer to the true one as soon as possible once a new environment occurs. Previous dynamic multiobjective evolutionary algorithms (DMOEAs) normally focus on DMOPs with regular environmental changes, but neglect widespread random one, limiting their applications in real-world fields. To address this issue, a knowledge guided transfer strategy based DMOEA is proposed in the paper. First, knowledge described as a two-tuple is extracted under each historical environment and preserved to a knowledge pool. Redundant knowledge is recognized and adaptively removed so as to guarantee the diversity of the pool. Second, a knowledge matching strategy is developed to re-evaluate the representative of each stored knowledge under a new environment, with the purpose of finding the most valuable one to promote positive knowledge transfer. Third, an improved knowledge transfer mechanism based on subspace alignment is introduced. By integrating it with knowledge reuse mechanism, a hybrid transfer strategy is constructed to adaptively select the most suitable one in terms of the similarity degree of selected knowledge on the current environment, and then generate a new initial population. Experiments on 20 benchmark problems demonstrate that the knowledge guided transfer strategy outperforms five state-of-the-art algorithms, achieving good versatility in solving DMOPs with both regular and random changes.

Recently, evolutionary multitasking (EMT) has been successfully used in the field of high-dimensional classification. However, the generation of multiple tasks in the existing EMT-based feature selection (FS) methods is relatively simple, using only the Relief-F method to collect related features with similar importance into one task, which cannot provide more diversified tasks for knowledge transfer. Thus, this paper devises a new EMT algorithm for FS in high-dimensional classification, which first adopts different filtering methods to produce multiple tasks and then modifies a competitive swarm optimizer to efficiently solve these related tasks via knowledge transfer. First, a diversified multiple task generation method is designed based on multiple filtering methods, which generates several relevant low-dimensional FS tasks by eliminating irrelevant features. In this way, useful knowledge for solving simple and relevant tasks can be transferred to simplify and speed up the solution of the original high-dimensional FS task. Then, a competitive swarm optimizer is modified to simultaneously solve these relevant FS tasks by transferring useful knowledge among them. Numerous empirical results demonstrate that the proposed EMT-based FS method can obtain a better feature subset than several state-of-the-art FS methods on eighteen high-dimensional datasets.

Dynamic multiobjective optimization requires the robust tracking of varying Pareto-optimal solutions (POS) in a changing environment. When a change is detected in the environment, prediction mechanisms estimate the POS by utilizing information from previous populations to accelerate search toward the true POS. To achieve a robust prediction of POS, a mixture-of-experts-based ensemble framework is proposed. Unlike existing approaches, the framework utilizes multiple prediction mechanisms to improve the overall prediction. A gating network is applied to manage switching among the various predictors based on performance of the predictors at different time intervals of the optimization process. The efficacy of the proposed framework is validated through experimental studies based on 13 dynamic multiobjective benchmark optimization problems. The simulation results show that the proposed framework improves the dynamic optimization performance significantly, particularly for: 1) problems with distinct dynamic POS in decision space over time and 2) problems with highly nonlinear decision variable linkages.