An adaptive Bayesian approach to surrogate-assisted evolutionary multi-objective optimization

A two-stage dominance-based surrogate-assisted evolution algorithm for high-dimensional expensive multi-objective optimization

In the past decades, surrogate-assisted evolutionary algorithms (SAEAs) have become one of the most popular methods to solve expensive multi-objective optimization problems (EMOPs). However, most existing methods focus on low-dimensional EMOPs because a large number of training samples are required to build accurate surrogate models, which is unrealistic for high-dimensional EMOPs. Therefore, this paper develops a two-stage dominance-based surrogate-assisted evolution algorithm (TSDEA) for high-dimensional EMOPs which utilizes the RBF model to approximate each objective function. First, a two-stage selection strategy is applied to select individuals for re-evaluation. Then considering the training time of the model, proposing a novel archive updating strategy to limit the number of individuals for updating. Experimental results show that the proposed algorithm has promising performance and computational efficiency compared to the state-of-the-art five SAEAs.

Choose Appropriate Subproblems for Collaborative Modeling in Expensive Multiobjective Optimization

In dealing with the expensive multiobjective optimization problem, some algorithms convert it into a number of single-objective subproblems for optimization. At each iteration, these algorithms conduct surrogate-assisted optimization on one or multiple subproblems. However, these subproblems may be unnecessary or resolved. Operating on such subproblems can cause server inefficiencies, especially in the case of expensive optimization. To overcome this shortcoming, we propose an adaptive subproblem selection (ASS) strategy to identify the most promising subproblems for further modeling. To better leverage the cross information between the subproblems, we use the collaborative multioutput Gaussian process surrogate to model them jointly. Moreover, the commonly used acquisition functions (also known as infill criteria) are investigated in this article. Our analysis reveals that these acquisition functions may cause severe imbalances between exploitation and exploration in multiobjective optimization scenarios. Consequently, we develop a new acquisition function, namely, adaptive lower confidence bound (ALCB), to cope with it. The experimental results on three different sets of benchmark problems indicate that our proposed algorithm is competitive. Beyond that, we also quantitatively validate the effectiveness of the ASS strategy, the CoMOGP model, and the ALCB acquisition function.

Surrogated-assisted multimodal multi-objective optimization for hybrid renewable energy system

Hybrid renewable energy system (HRES) is an effective tool to improve the utilization of renewable energy so as to enhance the quality of energy supply. The optimization of HRES includes a simulation process during a long time span, which is time-consuming. So far, introducing a surrogate model to replace the objective evaluation is an effective way to solve such problems. However, existing methods focused few on the diversity of solutions in the decision space. Based on this motivation, we proposed a novel surrogated-assisted multi-objective evolutionary algorithm that focuses on solving multimodal and time-expensive problems, termed SaMMEA. Specifically, we use a Gaussian process model to replace the calculation of the objective values. In addition, a special environmental selection strategy is proposed to enhance the diversity of solutions in the decision space and a model management method is proposed to better train the surrogate model. The proposed algorithm is then compared to several state-of-the-art algorithms on HRES problems, which indicates that the proposed algorithm is competitive.

A two-stage infill strategy and surrogate-ensemble assisted expensive many-objective optimization

Many optimization problems are expensive in practical applications. The surrogate-assisted optimization methods have attracted extensive attention as they can get satisfyingly optimal solutions in a limited computing resource. In this paper, we propose a two-stage infill strategy and surrogate-ensemble assisted optimization algorithm for solving expensive many-objective optimization problems. In this method, the population is optimized by a surrogate ensemble. Then a two-stage infill strategy is proposed to select individuals for real evaluations. The infill strategy considers individuals with better convergence or greater uncertainty. To calculate the uncertainty, we consider two aspects. One is the approximate variance of the current surrogate ensemble and the other one is the approximate variance of the historical surrogate ensemble. Finally, the population is revised by the recently updated surrogate ensemble. In experiments, we testify our method on two sets of many-objective benchmark problems. The results demonstrate the superiority of our proposed algorithm compared with the state-of-the-art algorithms for solving computationally expensive many-objective optimization problems.

A Lagrangian dual-based theory-guided deep neural network

The theory-guided neural network (TgNN) is a kind of method which improves the effectiveness and efficiency of neural network architectures by incorporating scientific knowledge or physical information. Despite its great success, the theory-guided (deep) neural network possesses certain limits when maintaining a tradeoff between training data and domain knowledge during the training process. In this paper, the Lagrangian dual-based TgNN (TgNN-LD) is proposed to improve the effectiveness of the training process. We convert the original loss function into a constrained form with several items, in which partial differential equations (PDEs), engineering controls (ECs), and expert knowledge (EK) are regarded as constraints, with one Lagrangian variable per constraint. These Lagrangian variables are incorporated to achieve an equitable trade-off between observation data and corresponding constraints, to improve prediction accuracy and training efficiency. To investigate the performance of the proposed method, the original TgNN model with a set of optimized weight values adjusted by ad-hoc procedures is compared on a subsurface flow problem, with their L2 error, R square (R2), and computational time being analyzed. Experimental results demonstrate the superiority of the Lagrangian dual-based TgNN.

Simplified Phasmatodea population evolution algorithm for optimization

This work proposes a population evolution algorithm to deal with optimization problems based on the evolution characteristics of the Phasmatodea (stick insect) population, called the Phasmatodea population evolution algorithm (PPE). The PPE imitates the characteristics of convergent evolution, path dependence, population growth and competition in the evolution of the stick insect population in nature. The stick insect population tends to be the nearest dominant population in the evolution process, and the favorable evolution trend is more likely to be inherited by the next generation. This work combines population growth and competition models to achieve the above process. The implemented PPE has been tested and analyzed on 30 benchmark functions, and it has better performance than similar algorithms. This work uses several engineering optimization problems to test the algorithm and obtains good results.