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In the last few years, the formulation of real-world optimization problems and their efficient solution via metaheuristic algorithms has been a catalyst for a myriad of research studies. In spite of decades of historical advancements on the design and use of metaheuristics, large difficulties still remain in regards to the understandability, algorithmic design uprightness, and performance verifiability of new technical achievements. A clear example stems from the scarce replicability of works dealing with metaheuristics used for optimization, which is often infeasible due to ambiguity and lack of detail in the presentation of the methods to be reproduced. Additionally, in many cases, there is a questionable statistical significance of their reported results. This work aims at providing the audience with a proposal of good practices which should be embraced when conducting studies about metaheuristics methods used for optimization in order to provide scientific rigor, value and transparency. To this end, we introduce a step by step methodology covering every research phase that should be followed when addressing this scientific field. Specifically, frequently overlooked yet crucial aspects and useful recommendations will be discussed in regards to the formulation of the problem, solution encoding, implementation of search operators, evaluation metrics, design of experiments, and considerations for real-world performance, among others. Finally, we will outline important considerations, challenges, and research directions for the success of newly developed optimization metaheuristics in their deployment and operation over real-world application environments.

Evolutionary algorithms (EA), a class of stochastic search methods based on the principles of natural evolution, have received widespread acclaim for their exceptional performance in various real-world optimization problems. While researchers worldwide have proposed a wide variety of EAs, certain limitations remain, such as slow convergence speed and poor generalization capabilities. Consequently, numerous scholars actively explore improvements to algorithmic structures, operators, search patterns, etc., to enhance their optimization performance. Reinforcement learning (RL) integrated as a component in the EA framework has demonstrated superior performance in recent years. This paper presents a comprehensive survey on integrating reinforcement learning into the evolutionary algorithm, referred to as reinforcement learning-assisted evolutionary algorithm (RL-EA). We begin with the conceptual outlines of reinforcement learning and the evolutionary algorithm. We then provide a taxonomy of RL-EA. Subsequently, we discuss the RL-EA integration method, the RL-assisted strategy adopted by RL-EA, and its applications according to the existing literature. The RL-assisted procedure is divided according to the implemented functions including solution generation, learnable objective function, algorithm/operator/sub-population selection, parameter adaptation, and other strategies. Additionally, different attribute settings of RL in RL-EA are discussed. In the applications of RL-EA section, we also demonstrate the excellent performance of RL-EA on several benchmarks and a range of public datasets to facilitate a quick comparative study. Finally, we analyze potential directions for future research., Comment: 28 pages, 16 figures

An efficient team is essential for the company to successfully complete new projects. To solve the team formation problem considering person-job matching (TFP-PJM), a 0-1 integer programming model is constructed, which considers both person-job matching and team members' willingness to communicate on team efficiency, with the person-job matching score calculated using intuitionistic fuzzy numbers. Then, a reinforcement learning-assisted genetic programming algorithm (RL-GP) is proposed to enhance the quality of solutions. The RL-GP adopts the ensemble population strategies. Before the population evolution at each generation, the agent selects one from four population search modes according to the information obtained, thus realizing a sound balance of exploration and exploitation. In addition, surrogate models are used in the algorithm to evaluate the formation plans generated by individuals, which speeds up the algorithm learning process. Afterward, a series of comparison experiments are conducted to verify the overall performance of RL-GP and the effectiveness of the improved strategies within the algorithm. The hyper-heuristic rules obtained through efficient learning can be utilized as decision-making aids when forming project teams. This study reveals the advantages of reinforcement learning methods, ensemble strategies, and the surrogate model applied to the GP framework. The diversity and intelligent selection of search patterns along with fast adaptation evaluation, are distinct features that enable RL-GP to be deployed in real-world enterprise environments., Comment: 16 pages

Reinforcement Learning (RL) has emerged as a highly effective technique for addressing various scientific and applied problems. Despite its success, certain complex tasks remain challenging to be addressed solely with a single model and algorithm. In response, ensemble reinforcement learning (ERL), a promising approach that combines the benefits of both RL and ensemble learning (EL), has gained widespread popularity. ERL leverages multiple models or training algorithms to comprehensively explore the problem space and possesses strong generalization capabilities. In this study, we present a comprehensive survey on ERL to provide readers with an overview of recent advances and challenges in the field. Firstly, we provide an introduction to the background and motivation for ERL. Secondly, we conduct a detailed analysis of strategies such as model selection and combination that have been successfully implemented in ERL. Subsequently, we explore the application of ERL, summarize the datasets, and analyze the algorithms employed. Finally, we outline several open questions and discuss future research directions of ERL. By offering guidance for future scientific research and engineering applications, this survey significantly contributes to the advancement of ERL., Comment: 34 pages

Non-parametric tests can determine the better of two stochastic optimization algorithms when benchmarking results are ordinal, like the final fitness values of multiple trials. For many benchmarks, however, a trial can also terminate once it reaches a pre-specified target value. When only some trials reach the target value, two variables characterize a trial's outcome: the time it takes to reach the target value (or not) and its final fitness value. This paper describes a simple way to impose linear order on this two-variable trial data set so that traditional non-parametric methods can determine the better algorithm when neither dominates. We illustrate the method with the Mann-Whitney U-test. A simulation demonstrates that U-scores are much more effective than dominance when tasked with identifying the better of two algorithms. We test U-scores by having them determine the winners of the CEC 2022 Special Session and Competition on Real-Parameter Numerical Optimization., Comment: 25 pages, 7 figures, 8 tables

Metaheuristics are popularly used in various fields, and they have attracted much attention in the scientific and industrial communities. In recent years, the number of new metaheuristic names has been continuously growing. Generally, the inventors attribute the novelties of these new algorithms to inspirations from either biology, human behaviors, physics, or other phenomena. In addition, these new algorithms, compared against basic versions of other metaheuristics using classical benchmark problems without shift/rotation, show competitive performances. In this study, we exhaustively tabulate more than 500 metaheuristics. To comparatively evaluate the performance of the recent competitive variants and newly proposed metaheuristics, 11 newly proposed metaheuristics and 4 variants of established metaheuristics are comprehensively compared on the CEC2017 benchmark suite. In addition, whether these algorithms have a search bias to the center of the search space is investigated. The results show that the performance of the newly proposed EBCM (effective butterfly optimizer with covariance matrix adaptation) algorithm performs comparably to the 4 well performing variants of the established metaheuristics and possesses similar properties and behaviors, such as convergence, diversity, exploration and exploitation trade-offs, in many aspects. The performance of all 15 of the algorithms is likely to deteriorate due to certain transformations, while the 4 state-of-the-art metaheuristics are less affected by transformations such as the shifting of the global optimal point away from the center of the search space. It should be noted that, except EBCM, the other 10 new algorithms proposed mostly during 2019-2020 are inferior to the well performing 2017 variants of differential evolution and evolution strategy in terms of convergence speed and global search ability on CEC 2017 functions.

Neural networks have been successfully employed in various domains such as classification, regression and clustering, etc. Generally, the back propagation (BP) based iterative approaches are used to train the neural networks, however, it results in the issues of local minima, sensitivity to learning rate and slow convergence. To overcome these issues, randomization based neural networks such as random vector functional link (RVFL) network have been proposed. RVFL model has several characteristics such as fast training speed, direct links, simple architecture, and universal approximation capability, that make it a viable randomized neural network. This article presents the first comprehensive review of the evolution of RVFL model, which can serve as the extensive summary for the beginners as well as practitioners. We discuss the shallow RVFLs, ensemble RVFLs, deep RVFLs and ensemble deep RVFL models. The variations, improvements and applications of RVFL models are discussed in detail. Moreover, we discuss the different hyperparameter optimization techniques followed in the literature to improve the generalization performance of the RVFL model. Finally, we give potential future research directions/opportunities that can inspire the researchers to improve the RVFL's architecture and learning algorithm further.

Transfer Optimization has gained a remarkable attention from the Swarm and Evolutionary Computation community in the recent years. It is undeniable that the concepts underlying Transfer Optimization are formulated on solid grounds. However, evidences observed in recent contributions confirm that there are critical aspects that are not properly addressed to date. This short communication aims to engage the readership around a reflection on these issues, and to provide rationale why they remain unsolved. Specifically, we emphasize on three critical points of Evolutionary Multitasking Optimization: i) the plausibility and practical applicability of this paradigm; ii) the novelty of some proposed multitasking methods; and iii) the methodologies used for evaluating newly proposed multitasking algorithms. As a result of this research, we conclude that some important efforts should be directed by the community in order to keep the future of this promising field on the right track. Our ultimate purpose is to unveil gaps in the current literature, so that prospective works can attempt to fix these gaps, avoiding to stumble on the same stones and eventually achieve valuable advances in the area., Comment: 17 pages, 3 figures. This papers has been accepted and published in Swarm and Evolutionary Computation under this DOI: 10.1016/j.swevo.2022.101203

The advent of Internet of Things (IoT) has bring a new era in communication technology by expanding the current inter-networking services and enabling the machine-to-machine communication. IoT massive deployments will create the problem of optimal power allocation. The objective of the optimization problem is to obtain a feasible solution that minimizes the total power consumption of the WSN, when the error probability at the fusion center meets certain criteria. This work studies the optimization of a wireless sensor network (WNS) at higher dimensions by focusing to the power allocation of decentralized detection. More specifically, we apply and compare four algorithms designed to tackle Large scale global optimization (LGSO) problems. These are the memetic linear population size reduction and semi-parameter adaptation (MLSHADE-SPA), the contribution-based cooperative coevolution recursive differential grouping (CBCC-RDG3), the differential grouping with spectral clustering-differential evolution cooperative coevolution (DGSC-DECC), and the enhanced adaptive differential evolution (EADE). To the best of the authors knowledge, this is the first time that LGSO algorithms are applied to the optimal power allocation problem in IoT networks. We evaluate the algorithms performance in several different cases by applying them in cases with 300, 600 and 800 dimensions.

Extreme learning machine (ELM), which can be viewed as a variant of Random Vector Functional Link (RVFL) network without the input-output direct connections, has been extensively used to create multi-layer (deep) neural networks. Such networks employ randomization based autoencoders (AE) for unsupervised feature extraction followed by an ELM classifier for final decision making. Each randomization based AE acts as an independent feature extractor and a deep network is obtained by stacking several such AEs. Inspired by the better performance of RVFL over ELM, in this paper, we propose several deep RVFL variants by utilizing the framework of stacked autoencoders. Specifically, we introduce direct connections (feature reuse) from preceding layers to the fore layers of the network as in the original RVFL network. Such connections help to regularize the randomization and also reduce the model complexity. Furthermore, we also introduce denoising criterion, recovering clean inputs from their corrupted versions, in the autoencoders to achieve better higher level representations than the ordinary autoencoders. Extensive experiments on several classification datasets show that our proposed deep networks achieve overall better and faster generalization than the other relevant state-of-the-art deep neural networks., Comment: 29 pages, 17 figures

Many-objective evolutionary algorithms (MOEAs), especially the decomposition-based MOEAs, have attracted wide attention in recent years. Recent studies show that a well designed combination of the decomposition method and the domination method can improve the performance ,i.e., convergence and diversity, of a MOEA. In this paper, a novel way of combining the decomposition method and the domination method is proposed. More precisely, a set of weight vectors is employed to decompose a given many-objective optimization problem(MaOP), and a hybrid method of the penalty-based boundary intersection function and dominance is proposed to compare local solutions within a subpopulation defined by a weight vector. A MOEA based on the hybrid method is implemented and tested on problems chosen from two famous test suites, i.e., DTLZ and WFG. The experimental results show that our algorithm is very competitive in dealing with MaOPs. Subsequently, our algorithm is extended to solve constraint MaOPs, and the constrained version of our algorithm also shows good performance in terms of convergence and diversity. These reveals that using dominance locally and combining it with the decomposition method can effectively improve the performance of a MOEA., Comment: arXiv admin note: substantial text overlap with arXiv:1803.06282, arXiv:1806.10950