Leveraging on fruitful intertask knowledge transfer, multitasking evolutionary algorithms (MTEAs) exhibit superior efficiency in handling multiple optimization tasks simultaneously. In practice, it is common that the fitness evaluation of tasks is computationally expensive, leading to a very limited number of fitness evaluations for MTEAs. With this in mind, we propose a radial basis functions-assisted MTEA (RAMTEA) in this paper to better solve expensive multitasking optimization problems. In the proposed method, radial basis functions are constructed to approximate each task's real function to guide the selection of new samples. Furthermore, an adaptive sampling strategy considering intertask similarities is applied to facilitate the convergence of multiple tasks and curb negative transfer. The efficacy of our proposal is demonstrated by experimental studies including ablation experiments and comparison with advanced MTEAs on widely used benchmark problems.

Principal Component Analysis (PCA) aims to acquire the principal component space containing the essential structure of data, instead of being used for mining and extracting the essential structure of data. In other words, the principal component space contains not only information related to the essential structure of data but also some unrelated information. This frequently occurs when the intrinsic dimensionality of data is unknown or when it has complex distribution characteristics such as multi-modalities, manifolds, etc. Therefore, it is unreasonable to identify noise and useful information based solely on reconstruction error. For this reason, PCA is unsuitable as a preprocessing technique for most applications, especially in noisy environment. To solve this problem, this paper proposes robust PCA based on fuzzy local information reservation (FLIPCA). By analyzing the impact of reconstruction error on sample discriminability, FLIPCA provides a theoretical basis for noise identification and processing. This not only greatly improves its robustness but also extends its applicability and effectiveness as a data preprocessing technique. Meanwhile, FLIPCA maintains consistent mathematical descriptions with traditional PCA while having few adjustable hyperparameters and low algorithmic complexity. Finally, we conducted comprehensive experiments on synthetic and real-world datasets, which substantiated the superiority of our proposed algorithm.

Maintaining a balance between convergence and diversity is particularly crucial in evolutionary multiobjective optimization. Recently, a novel dominance relation called "strengthened dominance relation" (SDR) is proposed, which outperforms the existing dominance relations in balancing convergence and diversity. In this article, two points that influence the performance of SDR are studied and a new dominance relation, which is mainly based on SDR, is proposed (CSDR). An adaptation strategy is presented to dynamically adjust the dominance relation according to the current generation number. The CSDR is embedded into NSGA-II to substitute the Pareto dominance, labeled as NSGA-II/CSDR. The performance of our proposed method is validated by comparing it with five state-of-the-art algorithms on commonly used benchmark problems. NSGA-II/CSDR outperforms other algorithms in the most test instances considering both convergence and diversity.

This article addresses the problem of stabilizing a continuous-time switched system affected by a completely unknown disturbance, data quantization, and time-varying delay. In the sense of combined dwell-time and average dwell-time, it is assumed that the switching is slow enough. Suppose that the bound of delay is known but the one of disturbance is unknown. An estimation for the bound of disturbance is used to counteract the unknown disturbance. By extending the approach of the delay-free case, a communication and control strategy is developed by introducing a virtual system. On this basis, the exponential decay and practical stability of the closed-loop system are guaranteed by using a Lyapunov function. Two examples are illustrated to show the usefulness of the proposed framework for stability analysis of some classes of switched systems.

This paper proposes a radial basis functions (RBFs) assisted evolutionary algorithm for solving expensive many-objective problems where only a small number of real fitness evaluations are permitted. Two kinds of RBFs are applied in this algorithm, and the differences between the two kinds of RBFs are figured out to provide the estimated errors. By doing this, the estimated individual which has the maximum difference will be evaluated by real functions to strengthen the RBF models. In addition, for each objective, a more suitable RBF is selected for the purpose of making a more accurate approximation of the real functions. The simulation results demonstrate that the proposed algorithm not only performs well on many-objective problems with 10 decision variables, but also shows high efficiency. Besides, the proposed algorithm has good performance on problems with up to 30 decision variables.

In order to improve the performance of Water Cycle Algorithm (WCA), an alternative adaptation approach for enhancing the global searching ability is proposed. The proposed algorithm, named WCA-ALR, uses a new diversity enhancement approach to effectively improve the exploration capability of the WCA. The proposed approach consists of two major modifications: (1) an active selection method for choosing learning targets; (2) a promising position sifting and returning strategy. The benefits prove that actively selecting a learning target performs better than that of learning from a fixed one. A promising position sifting and returning strategy can also enhance the exploration ability. In order to verify the performance, numerical experiments on five basic benchmark problems are conducted. Then, a set of benchmark problems from the CEC2017 on 10 and 30 dimensions are used to prove the effectiveness of WCA-ALR. Experimental results affirm that the proposed approach can obtain better results, compared to the original WCA.

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for solving high-dimensional expensive problems. The basic idea of SAEAs is the integration of nature-inspired searching ability of evolutionary algorithms and prediction ability of surrogate models. This paper proposes a novel evolutionary sampling assisted optimization (ESAO) method which combines the two abilities to consider global exploration and local exploitation. Differential evolution is employed to generate offspring using mutation and crossover operators. A global radial basis functions surrogate model is built for prescreening of the offspring's objective function values and identifying the best one, which will be evaluated with the true function. The best offspring will replace its parent's position in the population if its function value is smaller than that of its parent. A local surrogate model is then built with selected current best solutions. An optimizer is applied to find the optimum of the local model. The optimal solution is then evaluated with the true function. Besides, a better point found in the local search will be added into the population in the global search. Global and local searches will alternate if one search cannot lead to a better solution. Comprehensive analysis is conducted to study the mechanism of ESAO and insights are gained on different local surrogates. The proposed algorithm is compared with two state-of-the-art SAEAs on a series of high-dimensional problems and results show that ESAO behaves better both in effectiveness and robustness on most of the test problems. Besides, ESAO is applied to an airfoil optimization problem to show its effectiveness.