Conventional evolutionary algorithms are not well suited for solving expensive optimization problems due to the fact that they often require a large number of fitness evaluations to obtain acceptable solutions. To alleviate the difficulty, this paper presents a multi-tasking evolutionary optimization framework for solving computationally expensive problems. In the framework, knowledge is transferred from a number of computationally cheap optimization problems to help the solution of the expensive problem on the basis of the recently proposed multifactorial evolutionary algorithm, leading to a faster convergence of the expensive problem. However, existing multifactorial evolutionary algorithms do not work well in solving multi-tasking problems whose optimums do not lie in the same location or when the dimensions of the decision space are not the same. To address the above issues, the existing multifactorial evolutionary algorithm is generalized by proposing two strategies, one for decision variable translation and the other for decision variable shuffling, to facilitate knowledge transfer between optimization problems having different locations of the optimums and different numbers of decision variables. To assess the effectiveness of the generalized multifactorial evolutionary algorithm, empirical studies have been conducted on eight multi-tasking instances and eight test problems for expensive optimization. The experimental results demonstrate that the proposed generalized multifactorial evolutionary algorithm works more efficiently for multi-tasking optimization and successfully accelerates the convergence of expensive optimization problems compared to single-task optimization.

Gaussian processes (GPs) are the most popular model used in surrogate-assisted evolutionary optimization of computationally expensive problems, mainly because GPs are able to measure the uncertainty of the estimated fitness values, based on which certain infill sampling criteria can be used to guide the search and update the surrogate model. However, the computation time for constructing GPs may become excessively long when the number of training samples increases, which makes it inappropriate to use them as surrogates in evolutionary optimization. To address this issue, this paper proposes to use ensembles as surrogates and infill criteria for model management in evolutionary optimization. A heterogeneous ensemble consisting of a least square support vector machine and two radial basis function networks is constructed to enhance the reliability of ensembles for uncertainty estimation. In addition to the original decision variables, a selected subset of the decision variables and a set of transformed variables are used as inputs of the heterogeneous ensemble to further promote the diversity of the ensemble. The proposed heterogeneous ensemble is compared with a GP and a homogeneous ensemble for infill sampling criteria in evolutionary multiobjective optimization. Experimental results demonstrate that the heterogeneous ensemble is competitive in performance compared with GPs and much more scalable in computational complexity to the increase in search dimension.

Gaussian processes (GPs) are widely used in surrogate-assisted evolutionary optimization of expensive problems mainly due to the ability to provide a confidence level of their outputs, making it possible to adopt principled surrogate management methods, such as the acquisition function used in the Bayesian optimization. Unfortunately, GPs become less practical for high-dimensional multiobjective and many-objective optimization as their computational complexity is cubic in the number of training samples. In this article, we propose a computationally efficient dropout neural network (EDN) to replace the Gaussian process and a new model management strategy to achieve a good balance between convergence and diversity for assisting evolutionary algorithms to solve high-dimensional multiobjective and many-objective expensive optimization problems. While the conventional dropout neural network needs to save a large number of network models during the training for calculating the confidence level, only one single network model is needed in the EDN to estimate the fitness and its confidence level by randomly ignoring neurons in both training and testing the neural network. Extensive experimental studies on benchmark problems with up to 100 decision variables and 20 objectives demonstrate that, compared to state of the art, the proposed algorithm is not only highly competitive in performance but also computationally more scalable to high-dimensional many-objective optimization problems. Finally, the proposed algorithm is validated on an operational optimization problem of crude oil distillation units, further confirming its capability of handling expensive problems given a limited computational budget.

This article is concerned with the trajectory tracking control problem for the wheeled mobile robots (WMRs) subject to actuator faults. The challenge lies in the partial loss of effectiveness of the actuated wheels which results in the loss of strong controllability of the WMR, rendering the classical fault-tolerant control methods infeasible. To overcome this obstacle, a novel mixed-gain adaption technique is put forward and is skillfully combined with the robust prescribed performance control method. The resulting control achieves trajectory tracking of the WMR with the predefined settling time and accuracy, against the actuator faults, the model uncertainties, and the disturbances. Moreover, it exhibits significant simplicity, without parameter identification, function approximation, disturbance estimation, or fault estimation. The theoretical findings are illustrated by a comparative simulation.

This paper presents a robust event-triggered model predictive control (MPC) strategy for multiple high-speed trains (MHSTs) with random switching topologies. Due to the complicated operation environment of high-speed railways, the communication topology of MHSTs system is time-varying and changes among a set of directed graphs, which can be characterized as a Markov chain. By adopting the concept of MPC, this paper studies the distributed cooperative leader-following consensus control for MHSTs, in which a novel event-triggered strategy is introduced to determine when information exchange among neighboring trains and control update are executed. Firstly, the leader-following consensus problem of MHSTs system is transformed to the stabilization of a Markov jump system and a sufficient condition for leader-following consensus is derived with stability analysis of the Markov jump system based on the robust event-triggered MPC scheme. Then, the robust event-triggered MPC algorithm which minimizes the objective function is proposed. By optimizing the objective function, the deviation of states and amplitude of the control force are optimized. The effectiveness of the proposed robust event-triggered MPC method on cooperative cruise control of MHSTs is illustrated by numerical examples.

Obtaining accurate point prediction of industrial processes' key variables is challenging due to the outliers and noise that are common in industrial data. Hence the prediction intervals (PIs) have been widely adopted to quantify the uncertainty related to the point prediction. In order to improve the prediction accuracy and quantify the level of uncertainty associated with the point prediction, this article estimates the PIs by using ensemble stochastic configuration networks (SCNs) and bootstrap method. The estimated PIs can guarantee both the modeling stability and computational efficiency. To encourage the cooperation among the base SCNs and improve the robustness of the ensemble SCNs when the training data are contaminated with noise and outliers, a simultaneous robust training method of the ensemble SCNs is developed based on the Bayesian ridge regression and M-estimate. Moreover, the hyperparameters of the assumed distributions over noise and output weights of the ensemble SCNs are estimated by the expectation-maximization (EM) algorithm, which can result in the optimal PIs and better prediction accuracy. Finally, the performance of the proposed approach is evaluated on three benchmark data sets and a real-world data set collected from a refinery. The experimental results demonstrate that the proposed approach exhibits better performance in terms of the quality of PIs, prediction accuracy, and robustness.