For solving large-scale multi-objective problems (LSMOPs), the transformation-based methods have shown promising search efficiency, which varies the original problem as a new simplified problem and performs the optimization in simplified spaces instead of the original problem space. Owing to the useful information provided by the simplified searching space, the performance of LSMOPs has been improved to some extent. However, it is worth noting that the original problem has changed after the variation, and there is thus no guarantee of the preservation of the original global or near-global optimum in the newly generated space. In this paper, we propose to solve LSMOPs via a multi-variation multifactorial evolutionary algorithm. In contrast to existing transformation-based methods, the proposed approach intends to conduct an evolutionary search on both the original space of the LSMOP and multiple simplified spaces constructed in a multi-variation manner concurrently. In this way, useful traits found along the search can be seamlessly transferred from the simplified problem spaces to the original problem space toward efficient problem-solving. Besides, since the evolutionary search is also performed in the original problem space, preserving the original global optimal solution can be guaranteed. To evaluate the performance of the proposed framework, comprehensive empirical studies are carried out on a set of LSMOPs with 2-3 objectives and 500-5000 variables. The experiment results highlight the efficiency and effectiveness of the proposed method compared to the state-of-the-art methods for large-scale multi-objective optimization.
Evolutionary multitasking optimization (EMTO) is an emerging paradigm for solving several problems simultaneously . Due to the flexible framework, EMTO has been naturally applied to multi-objective optimization to exploit synergy among distinct multi-objective problem domains. However, most studies barely take into account the scenario where some problems cannot converge under restrictive computational budgets with the traditional EMTO framework. T o dynamically allocate computational resources for multi-objective EMTO problems, this article proposes a generalized resource allocation (GRA) framework by concerning both theoretical grounds of conventional resource allocation and the characteristics of multi-objective optimization. normalized attainment function is designed for better quantifying convergence status, a multi-step nonlinear regression is proposed to serve as a stable performance estimator, and the algorithmic procedure of conventional resource allocation is refined for flexibly adjusting resource allocation intensity and including knowledge transfer information. It has been verified that the GRA framework can enhance the overall performance of the multi-objective EMTO algorithm in solving benchmark problems, complex problems, many-task problems, and a real-world application problem. Notably , the proposed GRA framework served as a crucial component for the winner algorithm in the Competition on Evolutionary Multi-T ask Optimization (Multi-objective Optimization Track) in IEEE 2020 W orld Congress on Computational Intelligence.
Solving a complex optimization task from scratch can be significantly expensive and/or time-consuming. Common knowledge obtained from different (but possibly related) optimization tasks may help enhance the solving of such tasks. In this regard, evolutionary multitasking optimization (EMTO) has been proposed to improve the solving of multiple optimization tasks simultaneously via knowledge transfer in the evolutionary algorithm framework. The effectiveness of knowledge transfer is crucial for the success of EMTO. Multifactorial evolutionary algorithm (MFEA) is one of the most representative EMTO algorithms, however, it suffers from negative knowledge transfer among the tasks with low correlation. To address this issue, in this study, inter-task gene-similarity-based knowledge transfer and mirror transformation are integrated into MFEA (termed as MFEA-GSMT). In the proposed inter-task gene-similarity-based knowledge transfer, a probabilistic model is used to feature each gene and the Kullback-Leibler divergence is employed to measure the inter-task dimension similarity. Guided by the inter-task gene similarity, a selective crossover is used to reproduce offspring solutions. The proposed inter-task knowledge transfer is based on online gene similarity evaluation, instead of individual similarity, to overcome the imprecise estimation of population distributions in a high-dimensional space with only a small number of samples. The proposed mirror transformation is an extension of opposition-based learning to avoid premature convergence and explore additional promising search areas. Experimental results on both single-objective and multi-objective multi-tasking problems demonstrate the effectiveness and efficiency of the proposed MFEA-GSMT.
