Adaptive Distributed Differential Evolution

The Importance of Being Constrained: Dealing with Infeasible Solutions in Differential Evolution and Beyond

We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple bound constraints. Currently, in the field of heuristic optimisation, such specification is rarely mentioned or investigated due to the assumed triviality or insignificance of this question. Here, we demonstrate that, at least in algorithms based on Differential Evolution, this choice induces notably different behaviours in terms of performance, disruptiveness, and population diversity. This is shown theoretically (where possible) for standard Differential Evolution in the absence of selection pressure and experimentally for the standard and state-of-the-art Differential Evolution variants, on a special test function and the BBOB benchmarking suite, respectively. Moreover, we demonstrate that the importance of this choice quickly grows with problem dimensionality. Differential Evolution is not at all special in this regard-there is no reason to presume that other heuristic optimisers are not equally affected by the aforementioned algorithmic choice. Thus, we urge the heuristic optimisation community to formalise and adopt the idea of a new algorithmic component in heuristic optimisers, which we refer to as the strategy of dealing with infeasible solutions. This component needs to be consistently: (a) specified in algorithmic descriptions to guarantee reproducibility of results, (b) studied to better understand its impact on an algorithm's performance in a wider sense (i.e., convergence time, robustness, etc.), and (c) included in the (automatic) design of algorithms. All of these should be done even for problems with bound constraints.

Transferable Adaptive Differential Evolution for Many-Task Optimization

The evolutionary multitask optimization (EMTO) algorithm is a promising approach to solve many-task optimization problems (MaTOPs), in which similarity measurement and knowledge transfer (KT) are two key issues. Many existing EMTO algorithms estimate the similarity of population distribution to select a set of similar tasks and then perform KT by simply mixing individuals among the selected tasks. However, these methods may be less effective when the global optima of the tasks greatly differ from each other. Therefore, this article proposes to consider a new kind of similarity, namely, shift invariance, between tasks. The shift invariance is defined that the two tasks are similar after linear shift transformation on both the search space and the objective space. To identify and utilize the shift invariance between tasks, a two-stage transferable adaptive differential evolution (TRADE) algorithm is proposed. In the first evolution stage, a task representation strategy is proposed to represent each task by a vector that embeds the evolution information. Then, a task grouping strategy is proposed to group the similar (i.e., shift invariant) tasks into the same group while the dissimilar tasks into different groups. In the second evolution stage, a novel successful evolution experience transfer method is proposed to adaptively utilize the suitable parameters by transferring successful parameters among similar tasks within the same group. Comprehensive experiments are carried out on two representative MaTOP benchmarks with a total of 16 instances and a real-world application. The comparative results show that the proposed TRADE is superior to some state-of-the-art EMTO algorithms and single-task optimization algorithms.

A Robust and Explainable Structure-Based Algorithm for Detecting the Organ Boundary From Ultrasound Multi-Datasets

Detecting the organ boundary in an ultrasound image is challenging because of the poor contrast of ultrasound images and the existence of imaging artifacts. In this study, we developed a coarse-to-refinement architecture for multi-organ ultrasound segmentation. First, we integrated the principal curve-based projection stage into an improved neutrosophic mean shift-based algorithm to acquire the data sequence, for which we utilized a limited amount of prior seed point information as the approximate initialization. Second, a distribution-based evolution technique was designed to aid in the identification of a suitable learning network. Then, utilizing the data sequence as the input of the learning network, we achieved the optimal learning network after learning network training. Finally, a scaled exponential linear unit-based interpretable mathematical model of the organ boundary was expressed via the parameters of a fraction-based learning network. The experimental outcomes indicated that our algorithm 1) achieved more satisfactory segmentation outcomes than state-of-the-art algorithms, with a Dice score coefficient value of 96.68 ± 2.2%, a Jaccard index value of 95.65 ± 2.16%, and an accuracy of 96.54 ± 1.82% and 2) discovered missing or blurry areas.

Surrogate-Assisted Hybrid-Model Estimation of Distribution Algorithm for Mixed-Variable Hyperparameters Optimization in Convolutional Neural Networks

The performance of a convolutional neural network (CNN) heavily depends on its hyperparameters. However, finding a suitable hyperparameters configuration is difficult, challenging, and computationally expensive due to three issues, which are 1) the mixed-variable problem of different types of hyperparameters; 2) the large-scale search space of finding optimal hyperparameters; and 3) the expensive computational cost for evaluating candidate hyperparameters configuration. Therefore, this article focuses on these three issues and proposes a novel estimation of distribution algorithm (EDA) for efficient hyperparameters optimization, with three major contributions in the algorithm design. First, a hybrid-model EDA is proposed to efficiently deal with the mixed-variable difficulty. The proposed algorithm uses a mixed-variable encoding scheme to encode the mixed-variable hyperparameters and adopts an adaptive hybrid-model learning (AHL) strategy to efficiently optimize the mixed-variables. Second, an orthogonal initialization (OI) strategy is proposed to efficiently deal with the challenge of large-scale search space. Third, a surrogate-assisted multi-level evaluation (SME) method is proposed to reduce the expensive computational cost. Based on the above, the proposed algorithm is named s urrogate-assisted hybrid-model EDA (SHEDA). For experimental studies, the proposed SHEDA is verified on widely used classification benchmark problems, and is compared with various state-of-the-art methods. Moreover, a case study on aortic dissection (AD) diagnosis is carried out to evaluate its performance. Experimental results show that the proposed SHEDA is very effective and efficient for hyperparameters optimization, which can find a satisfactory hyperparameters configuration for the CIFAR10, CIFAR100, and AD diagnosis with only 0.58, 0.97, and 1.18 GPU days, respectively.

Distributed Differential Evolution With Adaptive Resource Allocation

Distributed differential evolution (DDE) is an efficient paradigm that adopts multiple populations for cooperatively solving complex optimization problems. However, how to allocate fitness evaluation (FE) budget resources among the distributed multiple populations can greatly influence the optimization ability of DDE. Therefore, this article proposes a novel three-layer DDE framework with adaptive resource allocation (DDE-ARA), including the algorithm layer for evolving various differential evolution (DE) populations, the dispatch layer for dispatching the individuals in the DE populations to different distributed machines, and the machine layer for accommodating distributed computers. In the DDE-ARA framework, three novel methods are further proposed. First, a general performance indicator (GPI) method is proposed to measure the performance of different DEs. Second, based on the GPI, a FE allocation (FEA) method is proposed to adaptively allocate the FE budget resources from poorly performing DEs to well-performing DEs for better search efficiency. This way, the GPI and FEA methods achieve the ARA in the algorithm layer. Third, a load balance strategy is proposed in the dispatch layer to balance the FE burden of different computers in the machine layer for improving load balance and algorithm speedup. Moreover, theoretical analyses are provided to show why the proposed DDE-ARA framework can be effective and to discuss the lower bound of its optimization error. Extensive experiments are conducted on all the 30 functions of CEC 2014 competitions at 10, 30, 50, and 100 dimensions, and some state-of-the-art DDE algorithms are adopted for comparisons. The results show the great effectiveness and efficiency of the proposed framework and the three novel methods.

Optimizing Niche Center for Multimodal Optimization Problems

Many real-world optimization problems require searching for multiple optimal solutions simultaneously, which are called multimodal optimization problems (MMOPs). For MMOPs, the algorithm is required both to enlarge population diversity for locating more global optima and to enhance refine ability for increasing the accuracy of the obtained solutions. Thus, numerous niching techniques have been proposed to divide the population into different niches, and each niche is responsible for searching on one or more peaks. However, it is often a challenge to distinguish proper individuals as niche centers in existing niching approaches, which has become a key issue for efficiently solving MMOPs. In this article, the niche center distinguish (NCD) problem is treated as an optimization problem and an NCD-based differential evolution (NCD-DE) algorithm is proposed. In NCD-DE, the niches are formed by using an internal genetic algorithm (GA) to online solve the NCD optimization problem. In the internal GA, a fitness-entropy measurement objective function is designed to evaluate whether a group of niche centers (i.e., encoded by a chromosome in the internal GA) is promising. Moreover, to enhance the exploration and exploitation abilities of NCD-DE in solving the MMOPs, a niching and global cooperative mutation strategy that uses both niche and population information is proposed to generate new individuals. The proposed NCD-DE is compared with some state-of-the-art and recent well-performing algorithms. The experimental results show that NCD-DE achieves better or competitive performance on both the accuracy and completeness of the solutions than the compared algorithms.

Many-Objective Job-Shop Scheduling: A Multiple Populations for Multiple Objectives-Based Genetic Algorithm Approach

The job-shop scheduling problem (JSSP) is a challenging scheduling and optimization problem in the industry and engineering, which relates to the work efficiency and operational costs of factories. The completion time of all jobs is the most commonly considered optimization objective in the existing work. However, factories focus on both time and cost objectives, including completion time, total tardiness, advance time, production cost, and machine loss. Therefore, this article first time proposes a many-objective JSSP that considers all these five objectives to make the model more practical to reflect the various demands of factories. To optimize these five objectives simultaneously, a novel multiple populations for multiple objectives (MPMO) framework-based genetic algorithm (GA) approach, called MPMOGA, is proposed. First, MPMOGA employs five populations to optimize the five objectives, respectively. Second, to avoid each population only focusing on its corresponding single objective, an archive sharing technique (AST) is proposed to store the elite solutions collected from the five populations so that the populations can obtain optimization information about the other objectives from the archive. This way, MPMOGA can approximate different parts of the entire Pareto front (PF). Third, an archive update strategy (AUS) is proposed to further improve the quality of the solutions in the archive. The test instances in the widely used test sets are adopted to evaluate the performance of MPMOGA. The experimental results show that MPMOGA outperforms the compared state-of-the-art algorithms on most of the test instances.

Developing Nonlinear Customer Preferences Models for Product Design Using Opining Mining and Multiobjective PSO-Based ANFIS Approach

Online customer reviews can clearly show the customer experience, and the improvement suggestions based on the experience, which are helpful to product optimization and design. However, the research on establishing a customer preference model based on online customer reviews is not ideal, and the following research problems are found in previous studies. Firstly, the product attribute is not involved in the modelling if the corresponding setting cannot be found in the product description. Secondly, the fuzziness of customers' emotions in online reviews and nonlinearity in the models were not appropriately considered. Thirdly, the adaptive neuro-fuzzy inference system (ANFIS) is an effective way to model customer preferences. However, if the number of inputs is large, the modelling process will be failed due to the complex structure and long computational time. To solve the above-given problems, this paper proposed multiobjective particle swarm optimization (PSO) based ANFIS and opinion mining, to build customer preference model by analyzing the content of online customer reviews. In the process of online review analysis, the opinion mining technology is used to conduct comprehensive analysis on customer preference and product information. According to the analysis of information, a new method for establishing customer preference model is proposed, that is, a multiobjective PSO based ANFIS. The results show that the introducing of multiobjective PSO method into ANFIS can effectively solve the defects of ANFIS itself. Taking hair dryer as a case study, it is found that the proposed approach performs better than fuzzy regression, fuzzy least-squares regression, and genetic programming based fuzzy regression in modelling customer preference.

Forecasting oil consumption with attention-based IndRNN optimized by adaptive differential evolution

Accurate prediction of oil consumption plays a dominant role in oil supply chain management. However, because of the effects of the coronavirus disease 2019 (COVID-19) pandemic, oil consumption has exhibited an uncertain and volatile trend, which leads to a huge challenge to accurate predictions. The rapid development of the Internet provides countless online information (e.g., online news) that can benefit predict oil consumption. This study adopts a novel news-based oil consumption prediction methodology-convolutional neural network (CNN) to fetch online news information automatically, thereby illustrating the contribution of text features for oil consumption prediction. This study also proposes a new approach called attention-based JADE-IndRNN that combines adaptive differential evolution (adaptive differential evolution with optional external archive, JADE) with an attention-based independent recurrent neural network (IndRNN) to forecast monthly oil consumption. Experimental results further indicate that the proposed news-based oil consumption prediction methodology improves on the traditional techniques without online oil news significantly, as the news might contain some explanations of the relevant confinement or reopen policies during the COVID-19 period.

A Multiobjective Framework for Many-Objective Optimization

It is known that many-objective optimization problems (MaOPs) often face the difficulty of maintaining good diversity and convergence in the search process due to the high-dimensional objective space. To address this issue, this article proposes a novel multiobjective framework for many-objective optimization (Mo4Ma), which transforms the many-objective space into multiobjective space. First, the many objectives are transformed into two indicative objectives of convergence and diversity. Second, a clustering-based sequential selection strategy is put forward in the transformed multiobjective space to guide the evolutionary search process. Specifically, the selection is circularly performed on the clustered subpopulations to maintain population diversity. In each round of selection, solutions with good performance in the transformed multiobjective space will be chosen to improve the overall convergence. The Mo4Ma is a generic framework that any type of evolutionary computation algorithm can incorporate compatibly. In this article, the differential evolution (DE) is adopted as the optimizer in the Mo4Ma framework, thus resulting in an Mo4Ma-DE algorithm. Experimental results show that the Mo4Ma-DE algorithm can obtain well-converged and widely distributed Pareto solutions along with the many-objective Pareto sets of the original MaOPs. Compared with seven state-of-the-art MaOP algorithms, the proposed Mo4Ma-DE algorithm shows strong competitiveness and general better performance.

Multisurrogate-Assisted Ant Colony Optimization for Expensive Optimization Problems With Continuous and Categorical Variables

As an effective optimization tool for expensive optimization problems (EOPs), surrogate-assisted evolutionary algorithms (SAEAs) have been widely studied in recent years. However, most current SAEAs are designed for continuous/ combinatorial EOPs, which are not suitable for mixed-variable EOPs. This article focuses on one kind of mixed-variable EOP: EOPs with continuous and categorical variables (EOPCCVs). A multisurrogate-assisted ant colony optimization algorithm (MiSACO) is proposed to solve EOPCCVs. MiSACO contains two main strategies: 1) multisurrogate-assisted selection and 2) surrogate-assisted local search. In the former, the radial basis function (RBF) and least-squares boosting tree (LSBT) are employed as the surrogate models. Afterward, three selection operators (i.e., RBF-based selection, LSBT-based selection, and random selection) are devised to select three solutions from the offspring solutions generated by ACO, with the aim of coping with different types of EOPCCVs robustly and preventing the algorithm from being misled by inaccurate surrogate models. In the latter, sequence quadratic optimization, coupled with RBF, is utilized to refine the continuous variables of the best solution found so far. By combining these two strategies, MiSACO can solve EOPCCVs with limited function evaluations. Three sets of test problems and two real-world cases are used to verify the effectiveness of MiSACO. The results demonstrate that MiSACO performs well in solving EOPCCVs.

A Penalty-Based Differential Evolution for Multimodal Optimization

It is very difficult to locate multiple global optimal solutions (GOSs) of multimodal optimization problems (MMOPs). To deal with this issue, a penalty-based multimodal optimization differential evolution (DE), called PMODE, is developed in this article. In PMODE, a penalty strategy with a dynamic penalty radius is constructed to solve MMOPs. An elite selection mechanism is designed to identify and select elite solutions. The neighboring areas of these elite solutions are penalized. PMODE uses a popular DE variant-JADE as its search engine. The proposed PMODE is compared with several other state-of-the-art multimodal optimization algorithms on 20 MMOPs used in the IEEE CEC2013 special session. The experimental results show that PMODE performs better than other state-of-the-art methods.

Adaptive Estimation Distribution Distributed Differential Evolution for Multimodal Optimization Problems

Multimodal optimization problems (MMOPs) require algorithms to locate multiple optima simultaneously. When using evolutionary algorithms (EAs) to deal with MMOPs, an intuitive idea is to divide the population into several small "niches," where different niches focus on locating different optima. These population partition strategies are called "niching" techniques, which have been frequently used for MMOPs. The algorithms for simultaneously locating multiple optima of MMOPs are called multimodal algorithms. However, many multimodal algorithms still face the difficulty of population partition since most of the niching techniques involve the sensitive niching parameters. Considering this issue, in this article, we propose a parameter-free niching method based on adaptive estimation distribution (AED) and develop a distributed differential evolution (DDE) algorithm, which is called AED-DDE, for solving MMOPs. In AED-DDE, each individual finds its own appropriate niche size to form a niche and acts as an independent unit to find a global optimum. Therefore, we can avoid the difficulty of population partition and the sensitivity of niching parameters. Different niches are co-evolved by using the master-slave multiniche distributed model. The multiniche co-evolution mechanism can improve the population diversity for fully exploring the search space and finding more global optima. Moreover, the AED-DDE algorithm is further enhanced by a probabilistic local search (PLS) to refine the solution accuracy. Compared with other multimodal algorithms, even the winner of CEC2015 multimodal competition, the comparison results fully demonstrate the superiority of AED-DDE.

Assessment of Ship-Overtaking Situation Based on Swarm Intelligence Improved KDE

This paper proposes a data-driven risk assessment model for ship overtaking based on the particle swarm optimization (PSO) improved kernel density estimation (KDE). By minimizing the mean square error between the real probability distribution of the ship overtaking point and the kernel density estimation probability distribution calculated by the current kernel density bandwidth, the longitude and latitude of the ship overtaking point are displayed by the color corresponding to the probability as the cost objective function of the search bandwidth of the algorithm. This can better show the distribution of the overtaking points of channel propagation traffic flow. A probability-based ship-overtaking risk evaluation model is developed through the bandwidth and density analysis optimized by an intelligent algorithm. In order to speed up searching the optimal variable width of the kernel density estimator for ship encountering positions, an improved adaptive variable-width kernel density estimator is proposed. The latter reduces the risk of too smooth probability density estimation phenomenon. Its convergence is proved. Finally, the model can efficiently evaluate the risk status of ship overtaking and provide navigational auxiliary decision support for pilots.

Tool for Predicting College Student Career Decisions: An Enhanced Support Vector Machine Framework

The goal of this research is to offer an effective intelligent model for forecasting college students’ career decisions in order to give a useful reference for career decisions and policy formation by relevant departments. The suggested prediction model is mainly based on a support vector machine (SVM) that has been modified using an enhanced butterfly optimization approach with a communication mechanism and Gaussian bare-bones mechanism (CBBOA). To get a better set of parameters and feature subsets, first, we added a communication mechanism to BOA to improve its global search capability and balance exploration and exploitation trends. Then, Gaussian bare-bones was added to increase the population diversity of BOA and its ability to jump out of the local optimum. The optimal SVM model (CBBOA-SVM) was then developed to predict the career decisions of college students based on the obtained parameters and feature subsets that are already optimized by CBBOA. In order to verify the effectiveness of CBBOA, we compared it with some advanced algorithms on all benchmark functions of CEC2014. Simulation results demonstrated that the performance of CBBOA is indeed more comprehensive. Meanwhile, comparisons between CBBOA-SVM and other machine learning approaches for career decision prediction were carried out, and the findings demonstrate that the provided CBBOA-SVM has better classification and more stable performance. As a result, it is plausible to conclude that the CBBOA-SVM is capable of being an effective tool for predicting college student career decisions.

Adaptive Differential Evolution Algorithm Based on Fitness Landscape Characteristic

Differential evolution (DE) is a simple, effective, and robust algorithm, which has demonstrated excellent performance in dealing with global optimization problems. However, different search strategies are designed for different fitness landscape conditions to find the optimal solution, and there is not a single strategy that can be suitable for all fitness landscapes. As a result, developing a strategy to adaptively steer population evolution based on fitness landscape is critical. Motivated by this fact, in this paper, a novel adaptive DE based on fitness landscape (FL-ADE) is proposed, which utilizes the local fitness landscape characteristics in each generation population to (1) adjust the population size adaptively; (2) generate DE/current-to-pcbest mutation strategy. The adaptive mechanism is based on local fitness landscape characteristics of the population and enables to decrease or increase the population size during the search. Due to the adaptive adjustment of population size for different fitness landscapes and evolutionary processes, computational resources can be rationally assigned at different evolutionary stages to satisfy diverse requirements of different fitness landscapes. Besides, the DE/current-to-pcbest mutation strategy, which randomly chooses one of the top p% individuals from the archive cbest of local optimal individuals to be the pcbest, is also an adaptive strategy based on fitness landscape characteristic. Using the individuals that are approximated as local optimums increases the algorithm’s ability to explore complex multimodal functions and avoids stagnation due to the use of individuals with good fitness values. Experiments are conducted on CEC2014 benchmark test suit to demonstrate the performance of the proposed FL-ADE algorithm, and the results show that the proposed FL-ADE algorithm performs better than the other seven highly performing state-of-art DE variants, even the winner of the CEC2014 and CEC2017. In addition, the effectiveness of the adaptive population mechanism and DE/current-to-pcbest mutation strategy based on landscape fitness proposed in this paper are respectively verified.

Performance optimization of support vector machine with oppositional grasshopper optimization for acute appendicitis diagnosis

Preoperative differentiation of complicated and uncomplicated appendicitis is challenging. The research goal was to construct a new intelligent diagnostic rule that is accurate, fast, noninvasive, and cost-effective, distinguishing between complicated and uncomplicated appendicitis. Overall, 298 patients with acute appendicitis from the Wenzhou Central Hospital were recruited, and information on their demographic characteristics, clinical findings, and laboratory data was retrospectively reviewed and applied in this study. First, the most significant variables, including C-reactive protein (CRP), heart rate, body temperature, and neutrophils discriminating complicated from uncomplicated appendicitis, were identified using random forest analysis. Second, an improved grasshopper optimization algorithm-based support vector machine was used to construct the diagnostic model to discriminate complicated appendicitis (CAP) from uncomplicated appendicitis (UAP). The resultant optimal model can produce an average of 83.56% accuracy, 81.71% sensitivity, 85.33% specificity, and 0.6732 Matthews correlation coefficients. Based on existing routinely available markers, the proposed intelligent diagnosis model is highly reliable. Thus, the model can potentially be used to assist doctors in making correct clinical decisions.

Multi-objective multi-criteria evolutionary algorithm for multi-objective multi-task optimization

Evolutionary multi-objective multi-task optimization is an emerging paradigm for solving multi-objective multi-task optimization problem (MO-MTOP) using evolutionary computation. However, most existing methods tend to directly treat the multiple multi-objective tasks as different problems and optimize them by different populations, which face the difficulty in designing good knowledge transferring strategy among the tasks/populations. Different from existing methods that suffer from the difficult knowledge transfer, this paper proposes to treat the MO-MTOP as a multi-objective multi-criteria optimization problem (MO-MCOP), so that the knowledge of all the tasks can be inherited in a same population to be fully utilized for solving the MO-MTOP more efficiently. To be specific, the fitness evaluation function of each task in the MO-MTOP is treated as an evaluation criterion in the corresponding MO-MCOP, and therefore, the MO-MCOP has multiple relevant evaluation criteria to help the individual selection and evolution in different evolutionary stages. Furthermore, a probability-based criterion selection strategy and an adaptive parameter learning method are also proposed to better select the fitness evaluation function as the criterion. By doing so, the algorithm can use suitable evaluation criteria from different tasks at different evolutionary stages to guide the individual selection and population evolution, so as to find out the Pareto optimal solutions of all tasks. By integrating the above, this paper develops a multi-objective multi-criteria evolutionary algorithm framework for solving MO-MTOP. To investigate the proposed algorithm, extensive experiments are conducted on widely used MO-MTOPs to compare with some state-of-the-art and well-performing algorithms, which have verified the great effectiveness and efficiency of the proposed algorithm. Therefore, treating MO-MTOP as MO-MCOP is a potential and promising direction for solving MO-MTOP.

Evolutionary Computation for Expensive Optimization: A Survey

Expensive optimization problem (EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for the algorithm to find a satisfactory solution. Moreover, due to the fast-growing application demands in the economy and society, such as the emergence of the smart cities, the internet of things, and the big data era, solving EOP more efficiently has become increasingly essential in various fields, which poses great challenges on the problem-solving ability of optimization approach for EOP. Among various optimization approaches, evolutionary computation (EC) is a promising global optimization tool widely used for solving EOP efficiently in the past decades. Given the fruitful advancements of EC for EOP, it is essential to review these advancements in order to synthesize and give previous research experiences and references to aid the development of relevant research fields and real-world applications. Motivated by this, this paper aims to provide a comprehensive survey to show why and how EC can solve EOP efficiently. For this aim, this paper firstly analyzes the total optimization cost of EC in solving EOP. Then, based on the analysis, three promising research directions are pointed out for solving EOP, which are problem approximation and substitution, algorithm design and enhancement, and parallel and distributed computation. Note that, to the best of our knowledge, this paper is the first that outlines the possible directions for efficiently solving EOP by analyzing the total expensive cost. Based on this, existing works are reviewed comprehensively via a taxonomy with four parts, including the above three research directions and the real-world application part. Moreover, some future research directions are also discussed in this paper. It is believed that such a survey can attract attention, encourage discussions, and stimulate new EC research ideas for solving EOP and related real-world applications more efficiently.

Differential evolution-assisted salp swarm algorithm with chaotic structure for real-world problems

There is a new nature-inspired algorithm called salp swarm algorithm (SSA), due to its simple framework, it has been widely used in many fields. But when handling some complicated optimization problems, especially the multimodal and high-dimensional optimization problems, SSA will probably have difficulties in convergence performance or dropping into the local optimum. To mitigate these problems, this paper presents a chaotic SSA with differential evolution (CDESSA). In the proposed framework, chaotic initialization and differential evolution are introduced to enrich the convergence speed and accuracy of SSA. Chaotic initialization is utilized to produce a better initial population aim at locating a better global optimal. At the same time, differential evolution is used to build up the search capability of each agent and improve the sense of balance of global search and intensification of SSA. These mechanisms collaborate to boost SSA in accelerating convergence activity. Finally, a series of experiments are carried out to test the performance of CDESSA. Firstly, IEEE CEC2014 competition fuctions are adopted to evaluate the ability of CDESSA in working out the real-parameter optimization problems. The proposed CDESSA is adopted to deal with feature selection (FS) problems, then five constrained engineering optimization problems are also adopted to evaluate the property of CDESSA in dealing with real engineering scenarios. Experimental results reveal that the proposed CDESSA method performs significantly better than the original SSA and other compared methods.

Horizontal and vertical search artificial bee colony for image segmentation of COVID-19 X-ray images

The artificial bee colony algorithm (ABC) has been successfully applied to various optimization problems, but the algorithm still suffers from slow convergence and poor quality of optimal solutions in the optimization process. Therefore, in this paper, an improved ABC (CCABC) based on a horizontal search mechanism and a vertical search mechanism is proposed to improve the algorithm's performance. In addition, this paper also presents a multilevel thresholding image segmentation (MTIS) method based on CCABC to enhance the effectiveness of the multilevel thresholding image segmentation method. To verify the performance of the proposed CCABC algorithm and the performance of the improved image segmentation method. First, this paper demonstrates the performance of the CCABC algorithm itself by comparing CCABC with 15 algorithms of the same type using 30 benchmark functions. Then, this paper uses the improved multi-threshold segmentation method for the segmentation of COVID-19 X-ray images and compares it with other similar plans in detail. Finally, this paper confirms that the incorporation of CCABC in MTIS is very effective by analyzing appropriate evaluation criteria and affirms that the new MTIS method has a strong segmentation performance.

A Two-Phase Learning-Based Swarm Optimizer for Large-Scale Optimization

In this article, a simple yet effective method, called a two-phase learning-based swarm optimizer (TPLSO), is proposed for large-scale optimization. Inspired by the cooperative learning behavior in human society, mass learning and elite learning are involved in TPLSO. In the mass learning phase, TPLSO randomly selects three particles to form a study group and then adopts a competitive mechanism to update the members of the study group. Then, we sort all of the particles in the swarm and pick out the elite particles that have better fitness values. In the elite learning phase, the elite particles learn from each other to further search for more promising areas. The theoretical analysis of TPLSO exploration and exploitation abilities is performed and compared with several popular particle swarm optimizers. Comparative experiments on two widely used large-scale benchmark datasets demonstrate that the proposed TPLSO achieves better performance on diverse large-scale problems than several state-of-the-art algorithms.

Generation-Level Parallelism for Evolutionary Computation: A Pipeline-Based Parallel Particle Swarm Optimization

Due to the population-based and iterative-based characteristics of evolutionary computation (EC) algorithms, parallel techniques have been widely used to speed up the EC algorithms. However, the parallelism usually performs in the population level where multiple populations (or subpopulations) run in parallel or in the individual level where the individuals are distributed to multiple resources. That is, different populations or different individuals can be executed simultaneously to reduce running time. However, the research into generation-level parallelism for EC algorithms has seldom been reported. In this article, we propose a new paradigm of the parallel EC algorithm by making the first attempt to parallelize the algorithm in the generation level. This idea is inspired by the industrial pipeline technique. Specifically, a kind of EC algorithm called local version particle swarm optimization (PSO) is adopted to implement a pipeline-based parallel PSO (PPPSO, i.e., P³SO). Due to the generation-level parallelism in P³SO, when some particles still perform their evolutionary operations in the current generation, some other particles can simultaneously go to the next generation to carry out the new evolutionary operations, or even go to further next generation(s). The experimental results show that the problem-solving ability of P³SO is not affected while the evolutionary speed has been substantially accelerated in a significant fashion. Therefore, generation-level parallelism is possible in EC algorithms and may have significant potential applications in time-consumption optimization problems.

A survey on evolutionary computation for complex continuous optimization

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.

Adaptive Granularity Learning Distributed Particle Swarm Optimization for Large-Scale Optimization

Large-scale optimization has become a significant and challenging research topic in the evolutionary computation (EC) community. Although many improved EC algorithms have been proposed for large-scale optimization, the slow convergence in the huge search space and the trap into local optima among massive suboptima are still the challenges. Targeted to these two issues, this article proposes an adaptive granularity learning distributed particle swarm optimization (AGLDPSO) with the help of machine-learning techniques, including clustering analysis based on locality-sensitive hashing (LSH) and adaptive granularity control based on logistic regression (LR). In AGLDPSO, a master-slave multisubpopulation distributed model is adopted, where the entire population is divided into multiple subpopulations, and these subpopulations are co-evolved. Compared with other large-scale optimization algorithms with single population evolution or centralized mechanism, the multisubpopulation distributed co-evolution mechanism will fully exchange the evolutionary information among different subpopulations to further enhance the population diversity. Furthermore, we propose an adaptive granularity learning strategy (AGLS) based on LSH and LR. The AGLS is helpful to determine an appropriate subpopulation size to control the learning granularity of the distributed subpopulations in different evolutionary states to balance the exploration ability for escaping from massive suboptima and the exploitation ability for converging in the huge search space. The experimental results show that AGLDPSO performs better than or at least comparable with some other state-of-the-art large-scale optimization algorithms, even the winner of the competition on large-scale optimization, on all the 35 benchmark functions from both IEEE Congress on Evolutionary Computation (IEEE CEC2010) and IEEE CEC2013 large-scale optimization test suites.