Introduction

Complex systems, which are composed of many interconnected and interactive functional parts, widely exist in the nature and human society. Significant efforts are needed to be made to reveal the relationship among the system structure and its function, evolution and regulation from both theoretical and practical points of view. Moreover, modern systems, such as social systems, industrial systems, transportation systems, ecosystems, communication systems, urban traffic systems, and power systems, become complex and large scale due to the increasing demands of quality and efficiency. This brings new challenges to optimization, intelligent control, analysis and integration of modern complex systems.

As an active research area in machine learning, the computational intelligence including neural networks, fuzzy logic, evolutionary and other intelligent-related algorithms is a prominent solution to these problems. Due to its unprecedented capabilities of function approximation, model prediction, pattern recognition, decision-making, and optimization, the computational intelligence is an extremely effective way to harvest and reveal valuable knowledge from tremendous data and growing information hidden in complex systems.

This special issue aims to share most recent developments on computational intelligence in complex systems. After a double-blinded peer-review process, a series of 19 qualified papers, which discuss the computational intelligence-based analysis, integration, prediction, control, optimization of complex systems and their implementations, have been accepted and included in this special issue.

Computational intelligence in analysis and integration of complex systems

Nineteen accepted papers in this special issue can be categorized into three groups, i.e., decision-making and analysis, system integration and prediction, and control and optimization. Next, we will introduce them briefly.

Decision-making and analysis

Six papers have focused on the computational intelligence-based decision-making and analysis of complex systems.

In the first paper, A deep learning-based computer-aided diagnosis method of X-ray images for bone age assessment, the authors proposed a deep learning-based computer-aided diagnosis method for performing bone age assessment. The proposed method is sufficiently potential to create a fully automated bone age assessment system with accurate and authentic results with less time tendency.

In the second paper, A game strategy model in the digital curling system based on NFSP, the authors regarded the digital curling game as a two-player zero-sum extensive game in a continuous action space. Then, they combined the neural fictitious self-play (NFSP) and the kernel regression-upper confidence bounds applied to trees (KR-UCT) to obtain the Nash equilibrium.

In the third paper, An integrated fuzzy model for evaluation and selection of mobile banking (m-banking) applications using new fuzzy-BWM and fuzzy-TOPSIS, the authors proposed an m-banking application selection model based on a combined fuzzy best-worst method and fuzzy technique for order of preference by similarity to ideal solution. Moreover, the proposed model can assist financial institutions and customers to overcome the challenges of choosing an appropriate m-banking application.

In the fourth paper, Collision-free path planning for welding manipulator via hybrid algorithm of deep reinforcement learning and inverse kinematics, the authors established a deep learning-based path planner for welding manipulators in high-dimensional continuous state and action spaces. The method cannot only improve the convergence rate, but also is superior in terms of optimality, robustness and less sensitive to state dimension.

In the fifth paper, Reinforcement learning for the traveling salesman problem with refueling, the authors employed the reinforcement learning (RL) as a potential method to solve the best-known traveling salesman problem with refueling. By comparing two RL algorithms, i.e., Q-learning and SARSA, the proposed method achieved the best solution in 15 out of 16 case studies.

In the sixth paper, Remote sensing image building detection method based on Mask R-CNN, the authors proposed a remote sensing image-based building extraction method which combined traditional digital image processing methods and convolution neural networks to improve detection accuracy and reduce the computational time.

System integration and prediction

Seven papers have concentrated on the computational intelligence-based integration and prediction of complex systems.

In the first paper, A neuro-swarming intelligent heuristic for second order nonlinear Lane–Emden multi-pantograph delay differential system, the authors presented a neuro-swarming intelligent heuristic, i.e., ANN-PSOIP scheme, for nonlinear second-order Lane–Emden multi-pantograph delay differential model using artificial neural networks, particle swarm optimization and interior-point approach. The approach presents a reliable, steadfast and consistent arrangement for soft computing optimization to handle inspiring classifications.

In the second paper, A novel sEMG-based force estimation method using deep learning algorithm, the authors proposed a linear regression and long short-term memory integrated method to estimate the muscle force using the channel and temporal dimensions of the surface electromyography signals collected from an armband-like collection device. By combining the linear regression and the long short-term memory, the efficient utilization of both channels and time information drives an accurate force evaluation.

In the third paper, Deep transfer learning: a novel glucose prediction framework for new subjects with Type 2 diabetes, the authors designed a novel cross-subject glucose prediction framework by integrating instance-based and network-based deep transfer learning via segmented continuous glucose monitoring time series. The experimental results illustrated that the proposed deep transfer learning framework achieved a more accurate glucose prediction for new subjects with type 2 diabetes.

In the fourth paper, DensePILAEA feature reuse Pseudoinverse learning algorithm for deep stacked Autoencoder, the authors proposed a dense connection pseudoinverse learning autoencoder (DensePILAE) from reuse perspective. This scheme can greatly reduce the time cost since the pseudoinverse learning autoencoder can extract features in the form of analytic solution. Meanwhile, the information of all previous layers has not only no loss, but also can be strengthened and refound, thus a better feature performance can be obtained.

In the fifth paper, Dueling deep Q-networks for social-awareness aided spectrum sharing, the authors developed a social awareness-aided transmit power control policy in overlapping spectrum sharing for secondary users to overcome the challenge in correctly sensing the usage of the spectrum in real time due to the complexity of cognitive environment. This method provided a higher spectrum sharing success rate and improved the comprehensive performance. Moreover, the performance of dueling deep Q-network is more stable on this problem than other deep reinforcement learning algorithms.

In the sixth paper, FSD-SLAM: a fast semi-direct SLAM algorithm, the authors proposed a fast semi-direct simultaneous localization and mapping (SLAM) algorithm by combining the feature point method with the direct method to avoid the feature loss caused by fast motion and unstructured scene in complex environments.

In the seventh paper, ResCaps: An improved capsule network and its application in ultrasonic image classification of thyroid papillary carcinoma, the authors developed a capsule network (CapsNet)-based network model, i.e., ResCaps network, which employed residual modules and enhanced the abstract expression of the model. It not only improves the accuracy of CapsNet significantly, but also provides an effective method for the classification of lesion characteristics of thyroid papillary carcinoma ultrasonic images.

Control and optimization

Six papers have devoted to the computational intelligence-based decision-making and analysis of complex systems.

In the first paper, A tractor-trailer parking control scheme using adaptive dynamic programming, the authors developed an online learning control scheme of a truck-trailer parallel parking problem by adaptive dynamic programming (ADP). At the same time, the parameterized nonlinear uncertainties can be handled during the online learning.

In the second paper, Compensator-critic structure based event-triggered decentralized tracking control of modular robot manipulators theory and experimental verification, the authors presented an event-triggered decentralized tracking control scheme via compensator-critic structure for modular robot manipulators based on the joint torque feedback technique. Through the Lyapunov stability analysis, the closed-loop system can be guaranteed to be ultimately uniformly bounded.

In the third paper, Neural network based asynchronous synchronization for fuzzy hidden Markov jump complex dynamical networks, the authors investigated the drive-response synchronization problem for Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks to cope with mismatched hidden jumping modes. They established a sufficient conditions to ensure mean-square synchronization performance with disturbances.

In the fourth paper, Sliding mode-based online fault compensation control for modular reconfigurable robots through adaptive dynamic programming, the authors developed an ADP-based online fault compensation control scheme based on sliding mode technique for modular reconfigurable robots (MRRs) with actuator failures. The controller consisted of a sliding mode-based iterative control, an adaptive robust term and an online fault compensator. The closed-loop faulty MRR system was ensured to be asymptotically stable under the proposed method.

In the fifth paper, Sliding-mode observers based distributed consensus control for nonlinear multi-agent systems with disturbances, the authors investigated the distributed consensus control problem for nonlinear multi-agent systems with external disturbances under switching directed topologies. The established distributed sliding mode observers were superior in estimating states by considering both nonlinear dynamics and external disturbances simultaneously.

In the sixth paper, Self-adaptive opposition-based differential evolution with subpopulation strategy for numerical and engineering optimization problems, the authors proposed a subpopulation-based opposition-based learning with a self-adaptive parameter control strategy, which presented a more excellent performance than other algorithms in terms of benchmark functions and constrained optimization problems.

Conclusions

We would like to thank Prof. Yaochu Jin, the Editor-in-Chief, for providing us the opportunity to guest-edit this special issue. We would also like to thank all the authors and anonymous reviewers for their contributions and great efforts which make the publication of this special issue possible. We hope this special issue has provided a useful resource of innovate ideas, advanced techniques, and implementable methods for the significant computational intelligence of analysis and integration in complex systems.