Surrogate-assisted evolutionary algorithms have been developed mainly for solving expensive optimization problems where only a small number of real fitness evaluations are allowed. Most existing surrogate-assisted evolutionary algorithms are designed for solving low-dimensional single or multi-objective optimization problems, which are not well suited for many-objective optimization. This paper proposes a surrogate-assisted many-objective evolutionary algorithm that uses an artificial neural network to predict the dominance relationship between candidate solutions and reference solutions instead of approximating the objective values separately. The uncertainty information in prediction is taken into account together with the dominance relationship to select promising solutions to be evaluated using the real objective functions. Our simulation results demonstrate that the proposed algorithm outperforms the state-of-the-art evolutionary algorithms on a set of many-objective optimization test problems.

In this work, we propose a framework to accelerate the computational efficiency of evolutionary algorithms on large-scale multi-objective optimization. The main idea is to track the Pareto optimal set directly via problem reformulation. To begin with, the algorithm obtains a set of reference directions in the decision space and associates them with a set of weight variables for locating the Pareto optimal set. Afterwards, the original large-scale multi-objective optimization problem is reformulated into a low-dimensional single-objective optimization problem. In the reformulated problem, the decision space is reconstructed by the weight variables and the objective space is reduced by an indicator function. Thanks to the low dimensionality of the weight variables and reduced objective space, a set of quasi-optimal solutions can be obtained efficiently. Finally, a multi-objective evolutionary algorithm is used to spread the quasi-optimal solutions over the approximate Pareto optimal front evenly. Experiments have been conducted on a variety of large-scale multi-objective problems with up to 5000 decision variables. Four different types of representative algorithms are embedded into the proposed framework and compared with their original versions respectively. Furthermore, the proposed framework has been compared with two state-of-the-art algorithms for large-scale multi-objective optimization. Experimental results have demonstrated the significant improvement benefited from the framework in terms of its performance and computational efficiency in large-scale multi-objective optimization.

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs.

Only a small number of function evaluations can be afforded in many real-world multiobjective optimization problems (MOPs) where the function evaluations are economically/computationally expensive. Such problems pose great challenges to most existing multiobjective evolutionary algorithms (EAs), which require a large number of function evaluations for optimization. Surrogate-assisted EAs (SAEAs) have been employed to solve expensive MOPs. Specifically, a certain number of expensive function evaluations are used to build computationally cheap surrogate models for assisting the optimization process without conducting expensive function evaluations. The infill sampling criteria in most existing SAEAs take all requirements on convergence, diversity, and model uncertainty into account, which is, however, not the most efficient in exploiting the limited computational budget. Thus, this article proposes a Kriging-assisted two-archive EA for expensive many-objective optimization. The proposed algorithm uses one influential point-insensitive model to approximate each objective function. Moreover, an adaptive infill criterion that identifies the most important requirement on convergence, diversity, or uncertainty is proposed to determine an appropriate sampling strategy for reevaluations using the expensive objective functions. The experimental results on a set of expensive multi/many-objective test problems have demonstrated its superiority over five state-of-the-art SAEAs.

Recently, increasing works have been proposed to drive evolutionary algorithms using machine-learning models. Usually, the performance of such model-based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e., the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales due to the curse of dimensionality. To address this issue, we propose a multiobjective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on ten benchmark problems with up to 200 decision variables. The experimental results on these test problems demonstrate the effectiveness of the proposed algorithm.

Ratio error estimation of the voltage transformers plays an important role in modern power delivery systems. Existing ratio error estimation methods mainly focus on periodical calibration but ignore the time-varying property. Consequently, it is difficult to efficiently estimate the state of the voltage transformers in real time. To address this issue, we formulate a time-varying ratio error estimation (TREE) problem into a large-scale multiobjective optimization problem, where the multiple objectives and inequality constraints are formulated by statistical and physical rules extracted from the power delivery systems. Furthermore, a set of TREE problems from different substations are systematically formulated into a benchmark test suite for characterizing their different properties. The formulation of these TREE problems not only transfers an expensive ratio error estimation task to a relatively cheaper optimization problem, but also promotes the research in large-scale multiobjective optimization by providing a real-world benchmark test suite with complex variable interactions and correlations to different objectives. To the best of our knowledge, this is the first time to formulate a real-world problem into a benchmark test suite for large-scale multiobjective optimization, and it is also the first work proposing to solve TREE problems via evolutionary multiobjective optimization.