**1. Introduction**

In recent years, many important ye<sup>t</sup> complex problems, either continuous or combinatorial, suffer the intractability of the problem of nature. This is because the classic exact methods are constrained with strict assumptions, such as differentiability or linearity for continuous objective functions or constrained size for combinatorial problems. Instead of using exact methods such as calculus or mathematical programming, heuristics have been used as alternatives for seeking approximation solutions. However, it is argued that the error bound of the solutions obtained by heuristics to the optimal ones is usually loose and it is not acceptable for some accuracy-critical applications, as in finance and security domains. Moreover, the heuristics are problem-dependent and lack generalization for solving various genuine problems. Applied Metaheuristic Computing (AMC) has emerged as a prevailing optimization technique for tackling perplexing engineering and business problems. This is partly due to AMC's ability to guide the search course beyond the local optimality, which impairs the capability of traditional heuristics, and partly due to AMC providing general frameworks which can be applied to solve a broad range of problems. We have witnessed many successful AMC applications in various domains, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, renewable energy, portfolio optimization, classification, and forecasting, among others. The aim of this topic series was to collect quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC. The manuscript submission to this topic series was closed on 31 March 2022. We received 116 submissions and 33 papers were published. The acceptance rate is 28%. Due to the success of this topic series, we are launching the second volume to collect more cutting-edge papers in the field of AMC.

#### **2. Special Features on AMC**

The most commonly seen AMC algorithms include genetic algorithm (GA), genetic programming (GP), evolutionary strategy (ES), evolutionary programming (EP), memetic algorithm (MA), particle swarm optimization (PSO), ant colony optimization (ACO), artificial bee colony (ABC), differential evolution (DE), firefly algorithm (FA), simulated annealing (SA), tabu search (TS), scatter search (SS), variable neighborhood search (VNS), and GRASP, to name a few. In this topic series, we considered special features which have been adopted to enhance the effectiveness of AMC. One notable feature is to apply metaheuristics to learn the architecture of neural networks or to optimize the hyperparameters of machine learning algorithms. The first paper, authored by J. Chou, T. Pham, and C. Ho, developed a metaheuristic-optimized machine-learning algorithm for multi-level classification in civil and construction engineering [1]. In particular, the FA fine-tunes the hyperparameters of the least squares support vector machine (LSSVM) to construct an optimized LSSVM multilevel classification model. The second paper, authored by R. Caraka, H. Yasin, R. Chen, N. Goldameir, B. Supatmanto, T. Toharudin, M. Basyuni, P. Gio, and B. Pardamean, used

**Citation:** Yin, P.-Y.; Chang, R.-I. Special Features and Applications on Applied Metaheuristic Computing. *Appl. Sci.* **2022**, *12*, 9342. https:// doi.org/10.3390/app12189342

Received: 14 September 2022 Accepted: 14 September 2022 Published: 18 September 2022

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GA to evolve a hybrid cascade neural network for space–time pollution data forecasting [2]. The third paper, authored by S. Jiao, C. Wang, R. Gao, Y. Li, and Q. Zhang, improved the Harris Hawks optimization algorithm by a multi-strategy search. The proposed method was used to optimize the LSSVM to model the reactive power output [3].

The other fast-growing research direction in AMC is developing a multi-objective optimization framework for various metaheuristics. The paper authored by I. Masich, M. Kulachenko, P. Stanimirovi´c, A. Popov, E. Tovbis, A. Stupina, and I. Kazakovtsev proposed a multi-criteria genetic algorithm for pattern generation in logical data analysis. The proposed method has a flexibility of allowing the pattern to maximally cover the objects in the target class and minimize the covered objects in the opposite class. The generated patterns by using the multi-criteria genetic algorithm are more meaningful than using the traditional fuzzy approaches [4]. The paper by A. Alqaili, M. Qais, and A. Al-Mansour developed a new discrete multi-objective integer search algorithm to optimize the road pavement performance and minimize the maintenance cost at the same time [5]. The paper by B. Changaival, K. Lavangnananda, G. Danoy, D. Kliazovich, F. Guinand, M. Brust, J. Musial, and P. Bouvry applied the NSGA-II, which is a famous multi-objective version of GA, for determining the optimal station locations of carsharing fleet service [6]. The objectives for setting fleet stations include maximum user coverage, least walking distance, and flexibility for returning. The paper authored by R. Díaz, E. Solares, V. de-León-Gómez, and F. Salas tackled the portfolio optimization problem by using a three-phase multiobjective approach [7]. In the first phase, an artificial neural network was constructed to predict the stock price. Then, an EA was applied to select the stocks. Finally, MOEA/D, which is a multi-objective EA, was adopted to optimize the stock portfolio considering multiple criteria.

#### **3. Special Applications on AMC**

In addition to classic AMC applications, we saw some special applications in this topic series. There are four papers which address efficient methods of energy management. The first paper by H. Lin, P. Wang, W. Lin, K. Chao, and Z. Yang analyzed the attack sources of robot networks (botnets) for a renewable energy managemen<sup>t</sup> system [8]. The authors applied a revised locust swarm optimization algorithm to search near-global optima of the most probable attack paths via the internet protocol traceback schemes. The second paper, authored by M. Kara, A. Laouid, M. AlShaikh, M. Hammoudeh, A. Bounceur, R. Euler, A. Amamra, and B. Laouid proposed a multi-round Proof of Work (PoW) consensus algorithm for preserving energy consumption and resisting attacks [9]. The other two papers deal with power microgrid operations. The paper authored by T. Nguyen, T. Ngo, T. and Dao, T. Nguyen proposed an improved sparrow search algorithm by incorporating the mutation mechanism of the firefly algorithm [10]. The improved version ensures the share of green power generation and a safe symmetry power grid among distributed clean power sources. The last paper, authored by N. Ning, Y. Liu, H. Yang, and L. Li presented a scheme for efficiently running an energy storage station. An improved aquila optimizer for the optimal configuration of the combined cooling, heating, and power microgrid was proposed to symmetrically enhance the economic and environmental protection performance [11].

AMC has intensively contributed to improve information security. The paper by R. Abu Khurma, I. Almomani, and I. Aljarah, proposed an IoT botnet intrusion detection system (IDS) by hybridizing the salp swarm algorithm (SSA) and ant lion optimization (ALO) [12]. The proposed method outperformed several existing approaches in terms of standard performance measures. The paper authored by L. Wang, L. Gu, and Y. Tang developed an IDS to deal with massive redundant alarms when monitoring the frequent occurrence of network security events [13]. The proposed method uses the whale optimization algorithm to conduct an alarm hierarchical clustering. The results showed that the proposed algorithm can effectively reduce the load of IDS and staff. The paper authored by A. Aldallal, and F. Alisa presented another IDS to secure data in cloud cyberspace using a hybrid metaheuristic. The method combines a support vector machine and a GA to

enhance the detection rate [14]. The paper by M. Madbouly, Y. Mokhtar, and S. Darwish employed a quantum game theory approach to select the optimal recovery method for mobile databases as a response to environmental failures in mobile computing such as the number of processes, the time needed to send messages, and the number of messages logged-in time [15]. The paper authored by J. Pan, X. Sun, H. Yang, V. Snášel, and S. Chu introduced a two-level mechanism and look-up table approach to solve the problem of sufficient diversity of features for information hiding [16]. The method has better capacity and image quality such that the storage and security are ensured. The paper by M. Ali, A. Ismail, H. Elgohary, S. Darwish, and S. Mesbah employed fuzzy hash within blockchain for tracing Chain of Custody (CoC) in preserving digital evidence in cybercrime [17]. The fuzzy hash functions within blockchain can demonstrate the CoC evidence has not been tampered. Software reliability is also an important issue in information security. The paper authored by Y. Kim, K. Song, H. Pham, and I. Chang developed a software reliability model where the software failures are interdependent and a software failure, if not immediately detected, can cause a sequence of failures and resulting massive losses [18]. The paper authored by E. Sakalauskas, I. Timofejeva, and A. Kilciauskas presented a new sigmaidentification protocol based on matrix power function (MPF). The authors showed that the given protocol ensures the NP-completeness of MPF and it is resistant against direct and eavesdropping attacks [19].

Two papers were devoted to determining the optimal assembly sequence of mechanical parts. The first paper, authored by M. Suszy ´nski and K. Peta, determined the best assembly sequence model by clustering 10,000 artificial neural networks which were created by using various network-training methods and activation functions [20]. The proposed model can predict the optimal assembly time of mechanical parts. The second paper, authored by M. Suszy ´nski, K. Peta, V. Cernohl ˇ ávek, and M. Svoboda, on the other hand, creates a large number of artificial neural networks with a different means. It considers various criteria of Design for Assembly (DFA) as the input data and then predicts the assembly time [21].

Object detection and recognition has long been an interesting area for classic AMC applications. The paper by C. Ticala, C. Pintea, and O. Matei provided a new edge detection method for medical images [22]. The method is based on a sensitive ACO where a vector called pheromone sensitivity level is used to control the ant's sensibility to the pheromone attraction. The paper authored by D. Wang, J. Ni, and T. Du presented an image recognition method for coal gangue recognition [23]. The adaptive shrinking grid search chaos wolf optimization algorithm was proposed to optimize the parameters of the neural network to enhance the image recognition accuracy. The paper authored by A. Alzbier and C. Chen constructed a denoising network consisting of a kernel prediction network and a deep generative adversarial network. Compared with the state-of-the-art result, the proposed denoising network has a better denoising effect and shorter running time [24]. The paper by V. Hrytsyk, M. Medykovskyy, and M. Nazarkevych provided a subjective assessment of various edge-detection filters for reproducing the object image in a room under different lighting conditions during educational activity in Ukraine [25]. It was found that there exist dependencies between priority to certain filters and the lighting condition.

The rest of the papers in this topic series address miscellaneous applications. The paper authored by E. Matos, R. Parmezan Bonidia, D. Sipoli Sanches, R. Santos Pozza, and L. Dias Hiera Sampaio compared the performance of several heuristics including GA, PSO, and VNS for increasing the throughput of sequence allocation schemes in massive multi-user MIMO 5G networks [26]. The paper authored by L. Lara-Valencia, D. Caicedo, and Y. Valencia-Gonzalez presented a whale optimization algorithm (WOA) for the design of tuned mass dampers under earthquake excitations [27]. Multiple objectives including reducing the maximum horizontal displacement and the root mean square of displacements of the structures were implemented to improve the seismic safety. The paper by G. Csányi, D. Nagy, R. Vági, J. Vadász, and T. Orosz addressed the challenging issues and symmetrical problems of legal document anonymization. The existing methods are reviewed and illustrated by case studies from the Hungarian legal practice [28]. The paper authored

by S. Liu, Z. Zhou, S. Dai, I. Iqbal, and Y. Yang presented a fast computation method for the green function which represents the seismic fields [29]. The computation method was able to evaluate the Sommerfeld integral efficiently and accurately and the result showed that the computational time was reduced by about 40%. The paper authored by X. Shen and D. Ihenacho developed a hybrid metaheuristic algorithm by combining DE and PSO for resolving the complex mathematical models of gas cyclone design [30]. The paper by M. Li, H. Sang, P. Liu, and G. Huang provided new practical criteria for identifying the positive definiteness of H-tensors [31]. An application and several numerical examples were provided to illustrate the effectiveness of the method. The paper by Y. Alotaibi presents a new clustering algorithm based on tabu search (TS) and adaptive search memory (ASM) [32]. As k-means clustering result is easily spoiled by the biased initial seeds, the TS and ASM were applied to search the elite initial seeds and irritate k-means clustering from there. Finally, the paper by Z. Lian, D. Luo, B. Dai, and Y. Chen presented a new discrete search algorithm based on Levy random distribution in order to obtain an escape from the local optima. The simulation results showed the fast convergence and search effectiveness of the proposed scheme [33].

**Author Contributions:** Conceptualization, P.-Y.Y. and R.-I.C.; writing—original draft preparation, P.-Y.Y. and R.-I.C.; writing—review and editing, P.-Y.Y. and R.-I.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** I would like to thank all the contributing authors for their innovative and well managed works. This topic series would not be possible without their enthusiasm for charting advanced AMC research. My thanks are also given to the anonymous reviewers for their unselfish and professional reviews which have helped shape the standard of this topic series. Finally, I am grateful to all the gues<sup>t</sup> editors and the editorial team of MDPI.

**Conflicts of Interest:** The authors declare no conflict of interest.
