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Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.

Environmental protection is the major concern of any form of manufacturing industry today. As focus has shifted towards sustainable cooling strategies, minimum quantity lubrication (MQL) has proven its usefulness. The current survey intends to make the MQL strategy more effective while improving its performance. A Ranque–Hilsch vortex tube (RHVT) was implemented into the MQL process in order to enhance the performance of the manufacturing process. The RHVT is a device that allows for separating the hot and cold air within the compressed air flows that come tangentially into the vortex chamber through the inlet nozzles. Turning tests with a unique combination of cooling technique were performed on titanium (Grade 2), where the effectiveness of the RHVT was evaluated. The surface quality measurements, forces values, and tool wear were carefully investigated. A combination of analysis of variance (ANOVA) and evolutionary techniques (particle swarm optimization (PSO), bacteria foraging optimization (BFO), and teaching learning-based optimization (TLBO)) was brought into use in order to analyze the influence of the process parameters. In the end, an appropriate correlation between PSO, BFO, and TLBO was investigated. It was shown that RHVT improved the results by nearly 15% for all of the responses, while the TLBO technique was found to be the best optimization technique, with an average time of 1.09 s and a success rate of 90%.

A genetic algorithm (GA) is an evolutionary algorithm inspired by the natural selection and biological processes of reproduction of the fittest individual. GA is one of the most popular optimization algorithms that is currently employed in a wide range of real applications. Initially, the GA fills the population with random candidate solutions and develops the optimal solution from one generation to the next. The GA applies a set of genetic operators during the search process: selection, crossover, and mutation. This article aims to review and summarize the recent contributions to the GA research field. In addition, the definitions of the GA essential concepts are reviewed. Furthermore, the article surveys the real-life applications and roles of GA. Finally, future directions are provided to develop the field.

Multiobjective reliability-based design optimization (RBDO) is a research area, which has not been investigated in the literatures comparing with single-objective RBDO. This work conducts an exhaustive study of fifteen new and popular metaheuristic multiobjective RBDO algorithms, including non-dominated sorting genetic algorithm II, differential evolution for multiobjective optimization, multiobjective evolutionary algorithm based on decomposition, multiobjective particle swarm optimization, multiobjective flower pollination algorithm, multiobjective bat algorithm, multiobjective gray wolf optimizer, multiobjective multiverse optimization, multiobjective water cycle optimizer, success history-based adaptive multiobjective differential evolution, success history-based adaptive multiobjective differential evolution with whale optimization, multiobjective salp swarm algorithm, real-code population-based incremental learning and differential evolution, unrestricted population size evolutionary multiobjective optimization algorithm, and multiobjective jellyfish search optimizer. In addition, the adaptive chaos control method is employed for the above-mentioned algorithms to estimate the probabilistic constraints effectively. This comparative analysis reveals the critical technologies and enormous challenges in the RBDO field. It also offers new insight into simultaneously dealing with the multiple conflicting design objectives and probabilistic constraints. Also, this study presents the advantage and future development trends or incurs the increased challenge of researchers to put forward an effective multiobjective RBDO algorithm that assists the complex engineering system design.

The learning process of artificial neural networks is considered as one of the most difficult challenges in machine learning and has attracted many researchers recently. The main difficulty of training a neural network is the nonlinear nature and the unknown best set of main controlling parameters (weights and biases). The main disadvantages of the conventional training algorithms are local optima stagnation and slow convergence speed. This makes stochastic optimization algorithm reliable alternative to alleviate these drawbacks. This work proposes a new training algorithm based on the recently proposed whale optimization algorithm (WOA). It has been proved that this algorithm is able to solve a wide range of optimization problems and outperform the current algorithms. This motivated our attempts to benchmark its performance in training feedforward neural networks. For the first time in the literature, a set of 20 datasets with different levels of difficulty are chosen to test the proposed WOA-based trainer. The results are verified by comparisons with back-propagation algorithm and six evolutionary techniques. The qualitative and quantitative results prove that the proposed trainer is able to outperform the current algorithms on the majority of datasets in terms of both local optima avoidance and convergence speed.

Differential evolution (DE) is a simple yet powerful evolutionary algorithm for numerical optimization. However, the performance of DE significantly relies on its mutation operator and control parameters (scaling factor and crossover rate). In this paper, we propose a novel DE variant by introducing a series of combined strategies into DE, called CSDE. Specifically, in CSDE, to obtain a proper balance between global exploration ability and local exploitation ability, we adopt two mutation operators with different characteristics to produce the mutant vector, and provide a mechanism based on their own historical success rate to coordinate the two adopted mutation operators. Moreover, we combine a periodic function based on one modulo operation, an individual-independence macro-control function and an individual-dependence function based on individual’s fitness value information to adaptively produce scaling factor and crossover rate. To verify the effectiveness of the proposed CSDE, comparison experiments contained seven other state-of-the-art DE variants are tested on a suite of 30 benchmark functions and four real-world problems. The simulation results demonstrate that CSDE achieves the best overall performance among the eight DE variants.

This paper presents a novel bio-inspired optimization algorithm called Coronavirus Optimization Algorithm (COVIDOA). COVIDOA is an evolutionary search strategy that mimics the mechanism of coronavirus when hijacking human cells. COVIDOA is inspired by the frameshifting technique used by the coronavirus for replication. The proposed algorithm is tested using 20 standard benchmark optimization functions with different parameter values. Besides, we utilized five IEEE Congress of Evolutionary Computation (CEC) benchmark test functions (CECC06, 2019 Competition) and five CEC 2011 real-world problems to prove the proposed algorithm's efficiency. The proposed algorithm is compared to eight of the most popular and recent metaheuristic algorithms from the state-of-the-art in terms of best cost, average cost (AVG), corresponding standard deviation (STD), and convergence speed. The results demonstrate that COVIDOA is superior to most existing metaheuristics.

Motivated by biological evolution, this paper explains the rationality of Vision Transformer by analogy with the proven practical evolutionary algorithm (EA) and derives that both have consistent mathematical formulation. Then inspired by effective EA variants, we propose a novel pyramid EATFormer backbone that only contains the proposed EA-based transformer (EAT) block, which consists of three residual parts, i.e., Multi-scale region aggregation, global and local interaction, and feed-forward network modules, to model multi-scale, interactive, and individual information separately. Moreover, we design a task-related head docked with transformer backbone to complete final information fusion more flexibly and improve a modulated deformable MSA to dynamically model irregular locations. Massive quantitative and quantitative experiments on image classification, downstream tasks, and explanatory experiments demonstrate the effectiveness and superiority of our approach over state-of-the-art methods. E.g., our Mobile (1.8 M), Tiny (6.1 M), Small (24.3 M), and Base (49.0 M) models achieve 69.4, 78.4, 83.1, and 83.9 Top-1 only trained on ImageNet-1K with naive training recipe; EATFormer-Tiny/Small/Base armed Mask-R-CNN obtain 45.4/47.4/49.0 box AP and 41.4/42.9/44.2 mask AP on COCO detection, surpassing contemporary MPViT-T, Swin-T, and Swin-S by 0.6/1.4/0.5 box AP and 0.4/1.3/0.9 mask AP separately with less FLOPs; Our EATFormer-Small/Base achieve 47.3/49.3 mIoU on ADE20K by Upernet that exceeds Swin-T/S by 2.8/1.7. Code is available at https://github.com/zhangzjn/EATFormer.

Scheduling is an important tool for a manufacturing system, where it can have a major impact on the productivity of a production process. In order to find an optimal solution to scheduling problems it gives rise to complex combinatorial optimization problems. Unfortunately, most of them fall into the class of NP-hard combinatorial problems. In this paper, we focus on the design of multiobjective evolutionary algorithms (MOEAs) to solve a variety of scheduling problems. Firstly, we introduce fitness assignment mechanism and performance measures for solving multiple objective optimization problems, and introduce evolutionary representations and hybrid evolutionary operations especially for the scheduling problems. Then we apply these EAs to the different types of scheduling problems, included job shop scheduling problem (JSP), flexible JSP, Automatic Guided Vehicle (AGV) dispatching in flexible manufacturing system (FMS), and integrated process planning and scheduling (IPPS). Through a variety of numerical experiments, we demonstrate the effectiveness of these Hybrid EAs (HEAs) in the widely applications of manufacturing scheduling problems. This paper also summarizes a classification of scheduling problems, and illustrates the design way of EAs for the different types of scheduling problems. It is useful to guide how to design an effective EA for the practical manufacturing scheduling problems. As known, these practical scheduling problems are very complex, and almost is a combination of different typical scheduling problems.

This paper proposes the Love Evolution Algorithm (LEA), a novel evolutionary algorithm inspired by the stimulus–value–role theory. The optimization process of the LEA includes three phases: stimulus, value, and role. Both partners evolve through these phases and benefit from them regardless of the outcome of the relationship. This inspiration is abstracted into mathematical models for global optimization. The efficiency of the LEA is validated through numerical experiments with CEC2017 benchmark functions, outperforming seven metaheuristic algorithms as evidenced by the Wilcoxon signed-rank test and the Friedman test. Further tests using the CEC2022 benchmark functions confirm the competitiveness of the LEA compared to seven state-of-the-art metaheuristics. Lastly, the study extends to real-world problems, demonstrating the performance of the LEA across eight diverse engineering problems. Source codes of the LEA are publicly available at  https://ww2.mathworks.cn/matlabcentral/fileexchange/159101-love-evolution-algorithm .