The accurate classification of plant growth stages from image sequences is a challenging problem due to the gradual and continuous nature of plant development. Significant variability exists within the same category of growth, and temporal boundaries between successive categories often exhibit visual similarities, complicating the classification task. Whereas the existing approaches are limited and rely on the analysis of single frames, they do not take temporal information embedded in sequential data, reducing robustness and accuracy. They also show vulnerability to intra-category variability among the images and also to inter-class overlap at the temporal boundaries. To address these challenges, we propose a novel approach, PSO-SqueezeTempVote, for plant temporal state categorisation that combines PSO for hyperparameter optimisation of the SqueezeNet architecture with Temporal Image Sequence Fusion (TISF) for temporal ensemble learning. The PSO part effectively optimises some critical hyperparameters, hence improving the performance of the model on individual frames. Meanwhile, the component of TISF exploits temporal continuity using a sequence of images’ aggregation through majority voting. This enables classifying the segment of an image much more precisely than the previously done approaches. Results on our datasets confirm that the PSOSqueezeTempVot has improved the state-of-the-art techniques by almost 13%, out of which approximately 6% was contributed by TISF itself.

Image processing is a fundamental field in computer science with applications across various real-life areas. Image enhancement in the preprocessing stage is crucial for tasks in computer vision. Contrast enhancement in images aims to improve visual quality by increasing contrast and highlighting significant details. Although classical contrast enhancement techniques are widely used, they often suffer from issues such as over-enhancement due to the lack of mechanisms to control this improvement. To improve the contrast, transformation functions assign new intensities to each pixel in the image. One of the main drawbacks of the transformation functions is tuning their parameters. On the other hand, most contrast-enhancement techniques are typically used to improve the contrast in color images. In this regard, this study examines the effectiveness of three color spaces-HSV, HSI, and CIELAB-in enhancing contrast, with the goal of identifying the most effective space for this purpose. Additionally, the performance of a widely used metaheuristic is evaluated in tuning the parameters of the transformation function. The model is evaluated using standard quality indicators on a public image dataset. Preliminary findings suggest that the HSI color space is better suited for optimization using metaheuristics and effectively improves image contrast.

Training artificial neural networks is a fundamental step in developing machine learning models, as it determines their ability to learn and generalise from data. While gradient-based methods such as stochastic gradient descent and its variants dominate training approaches, they are susceptible to issues like sensitivity to initialisation and convergence to local optima. To address these challenges, gradient-free metaheuristic algorithms, such as differential evolution (DE), are promising alternatives due to their ability to effectively explore complex optimisation landscapes. In this paper, we propose a novel DE-based algorithm, PruneClust-DE, for training multilayer neural networks. Our approach introduces two key strategies: (1) clustering-based interpolation, which partitions the population into clusters, identifies centroids, and generates new candidate solutions by interpolating between cluster centroids to balance exploration and exploitation, and (2) fitness-based pruning, a mechanism that retains only the fittest individuals after introducing new candidates, ensuring a constant yet high-quality population. We validate our proposed algorithm across diverse datasets and compare its performance with other state-of-the-art methods, demonstrating its superiority in achieving robust results.

Determining optimal weights and biases for neural networks is a critical task. While gradient-based methods are widely used for training, they are sensitive to initialisation and susceptible to local optima. Population-based metaheuristics, such as differential evolution (DE), can offer a reliable alternative. Recently, clustering-based DE approaches have been proposed to further improve this process. However, they suffer from increased complexity, particularly with growing network sizes, leading to longer computation times. In this paper, we introduce strategies to reduce the time complexity of clustering-based DE, including clustering in the objective space, a two-tier clustering period, and one-step k-means clustering. We select one of the recent training algorithms, C2L-DE, as a representative method to incorporate our proposed strategies, leading to a lightweight version, C2L-DE-Lite. We show that C2L-DE-Lite decreases the complexity from $O\left. {\left({\sqrt {{N_{pop}}} \cdot{N_{pop}}\cdot} \right.d\cdot I}\right)$, where Npopis the population size, d is the dimensionality, and I is the number of iterations, to $O\left({\frac{{{N_{pop}}\cdot\sqrt {{N_{pop}}} }}{{CP}}}\right)$, where CP is the clustering period. This means that the complexity remains constant for increasing sizes of networks. Extensive experiments demonstrate that while significantly reducing time complexity, C2L-DE-Lite maintains similar performance levels.

Abstract The widely applied JPEG standard has undergone recent efforts using population-based metaheuristic (PBMH) algorithms to optimise quantisation tables (QTs) for specific images. However, user preferences, like an Android developer’s preference for small-size images, are often overlooked, leading to high-quality images with large file sizes. Another limitation is the lack of comprehensive coverage in current QTs, failing to accommodate all possible combinations of file size and quality. Therefore, this paper aims to propose three distinct contributions. First, to include the user’s opinion in the compression process, the file size of the output image can be controlled by a user in advance. To this end, we propose a novel objective function for population-based JPEG image compression. Second, we suggest a novel representation to tackle the lack of comprehensive coverage. Our proposed representation can not only provide more comprehensive coverage but also find the proper value for the quality factor for a specific image without any background knowledge. Both representation and objective function changes are independent of the search strategies and can be used with any population-based metaheuristic (PBMH) algorithm. Therefore, as the third contribution, we also provide a comprehensive benchmark on 22 state-of-the-art and recently-introduced PBMH algorithms on our new formulation of JPEG image compression. Our extensive experiments on different benchmark images and in terms of different criteria show that our novel formulation for JPEG image compression can work effectively.

Energy consumption is a fundamental concern in mobile application development, bearing substantial significance for both developers and end-users. Main objective of this research is to propose a novel neural network-based framework, enhanced by a metaheuristic approach, to achieve robust energy prediction in the context of mobile app development. The metaheuristic approach here aims to achieve two goals: 1) identifying suitable learning algorithms and their corresponding hyperparameters, and 2) determining the optimal number of layers and neurons within each layer. Moreover, due to limitations in accessing certain aspects of a mobile phone, there might be missing data in the data set, and the proposed framework can handle this. In addition, we conducted an optimal algorithm selection strategy, employing 13 base and advanced metaheuristic algorithms, to identify the best algorithm based on accuracy and resistance to missing values. The representation in our proposed metaheuristic algorithm is variable-size, meaning that the length of the candidate solutions changes over time. We compared the algorithms based on the architecture found by each algorithm at different levels of missing values, accuracy, F-measure, and stability analysis. Additionally, we conducted a Wilcoxon signed-rank test for statistical comparison of the results. The extensive experiments show that our proposed approach significantly improves energy consumption prediction. Particularly, the JADE algorithm, a variant of differential evolution (DE), DE, and the covariance matrix adaptation evolution strategy deliver superior results under various conditions and across different missing value levels.

The efficient management of agricultural resources requires a deep understanding of plant growth dynamics. This research focuses on Sweden's forestry sector and explicitly addresses the crucial early stages of pine tree development. The main difficulty in categorising plant growth over time is that instances within a given category are not identical, while instances from different categories may have similarities. In this context, we present a novel measurement system that integrates the capa-bilities of evolutionary computation and deep transfer learning using image data. The image acquisition system includes a tray of plates that moves through a nursery, generating a dataset captured over 44 days of plant growth. Our newly proposed algorithm, EvoSqueezeNet, employs various search strategies for SqueezeNet deep transfer learning to find proper hyper-parameters. We opted for SqueezeNet based on our preliminary studies, revealing its superior performance compared to other pre-trained models in our case study. Given that our approach is independent of any specific evolutionary algorithm, we utilised five distinct search strategies. These include Differential Evolution (DE), Particle Swarm Optimisation (PSO), Covariance Ma-trix Adaptation Evolution Strategy (CMA-ES), Comprehensive Learning PSO (CLPSO), and Linear Population Size Reduction Success-History Adaptation DE (LSHADE). Consequently, we proposed five EvoSqueezeNet schemes for temporal plant growth categorisation. One characteristic of our proposed model is that it uses a limited computation budget for search strategies, en-hancing its applicability in real-world applications. The proposed EvoSqueezeNet methodology demonstrates an error reduction of more than 40%, showcasing its superior performance compared to competing methods.

Abstract Integrating machine learning techniques into medical diagnostic systems holds great promise for enhancing disease identification and treatment. Among the various options for training such systems, the extreme learning machine (ELM) stands out due to its rapid learning capability and computational efficiency. However, the random selection of input weights and hidden neuron biases in the ELM can lead to suboptimal performance. To address this issue, our study introduces a novel approach called modified Harris hawks optimizer (MHHO) to optimize these parameters in ELM for medical classification tasks. By applying the MHHO‐based method to seven medical datasets, our experimental results demonstrate its superiority over seven other evolutionary‐based ELM trainer models. The findings strongly suggest that the MHHO approach can serve as a valuable tool for enhancing the performance of ELM in medical diagnosis.

Summary This paper presents an extended version of Deeper, a search‐based simulation‐integrated test solution that generates failure‐revealing test scenarios for testing a deep neural network‐based lane‐keeping system. In the newly proposed version, we utilize a new set of bio‐inspired search algorithms, genetic algorithm (GA), and evolution strategies (ES), and particle swarm optimization (PSO), that leverage a quality population seed and domain‐specific crossover and mutation operations tailored for the presentation model used for modeling the test scenarios. In order to demonstrate the capabilities of the new test generators within Deeper, we carry out an empirical evaluation and comparison with regard to the results of five participating tools in the cyber‐physical systems testing competition at SBST 2021. Our evaluation shows the newly proposed test generators in Deeper not only represent a considerable improvement on the previous version but also prove to be effective and efficient in provoking a considerable number of diverse failure‐revealing test scenarios for testing an ML‐driven lane‐keeping system. They can trigger several failures while promoting test scenario diversity, under a limited test time budget, high target failure severity, and strict speed limit constraints.

Particle Swarm Optimization (PSO) has efficiently solved several real-world applications and optimization problems. However, it has shortcomings, such as premature convergence and stagnation at local minima. Inertia weight is a parameter of this algorithm that controls the global and local exploration and exploitation capability by determining the influence of the previous velocity on its current motion. Therefore, this article proposes a PSO with a Diversity-aware Inertia and Velocity Control (PSOIVC) algorithm to improve the PSO performance. The PSOIVC employs a novel diversity-aware inertia weight and velocity control approach to tune the parameters to produce a trade-off between exploration and exploitation of the algorithm using the dimension-wise diversity. The PSOIVC algorithm is compared with eight algorithms, including variants of the PSO, on a set of 30 benchmark functions for a single objective real parameter in 30 and 50 dimensions. Based on the results, the proposal presents significant outcomes according to the average values obtained for both comparisons; because it performed similarly or better than the other algorithms in 23/30 and 16/30 for 30 and 50 dimensions, respectively.

Particle swarm optimization (PSO) is essential to evolutionary computation algorithms (ECA). The PSO has some drawbacks as premature convergence and stagnation at local minima. Inertia weight is a parameter that controls the global and local exploration and exploitation capability in the PSO by determining the influence of the previous velocity on its current motion. This article proposes using a stagnation counter that verifies the times the PSO is stuck in the same fitness value. In the proposed fuzzy controlled PSO with stagnation coefficient (FCPSO), a fuzzy controller is designed to tune the inertia weight based on the population's diversity and the search's stagnation. This modification allows the PSO to escape from suboptimal values enhancing its search capabilities. The FCPSO is tested over 28 benchmark functions in 50 dimensions. Besides, it has been compared with nine optimization algorithms from the state-of-the-art. The experiments and comparisons suggest that the FCPSO is an interesting tool for solving complex optimization problems.

Plagiarism detection is a challenging task, aiming to identify similar items in two documents. In this paper, we present a novel approach to automatic plagiarism detection that combines BERT (bidirectional encoder representations from transformers) word embedding, attention mechanism-based long short-term memory (LSTM) networks, and an improved differential evolution (DE) algorithm for weight initialisation. BERT is used to pretrain deep bidirectional representations in all layers, while the pre-trained BERT model can be fine-tuned with only one extra output layer without significant changes in architecture. Deep learning algorithms often use the random weighting method for initialisation, followed by gradient-based optimisation algorithms such as back-propagation for training, making them susceptible to getting trapped in local optima. To address this, population- based metaheuristic algorithms such as DE can be used. We propose an improved DE algorithm with a clustering-based mutation operator, where first a winning cluster of candidate solutions is identified and a new updating strategy is then applied to include new candidate solutions in the current population. The proposed DE algorithm is used in LSTM, attention mechanism, and feed- forward neural networks to yield the initial seeds for subsequent gradient-based optimisation. We compare our proposed model with conventional and population-based approaches on three datasets (SNLI, MSRP and SemEval2014) and demonstrate it to give superior plagiarism detection performance.

The performance of feed-forward neural networks (FFNN) is directly dependant on the training algorithm. Conventional training algorithms such as gradient-based approaches are so popular for FFNN training, but they are susceptible to get stuck in local optimum. To overcome this, population-based metaheuristic algorithms such as differential evolution (DE) are a reliable alternative. In this paper, we propose a novel training algorithm, Reg-IDE, based on an improved DE algorithm. Weight regularisation in conventional algorithms is an approach to reduce the likelihood of over-fitting and enhance generalisation. However, to the best of our knowledge, the current DE-based trainers do not employ regularisation. This paper, first, proposes a regularisation-based objective function to improve the generalisation of the algorithm by adding a new term to the objective function. Then, a region-based strategy determines some regions in search space using a clustering algorithm and updates the population based on the information available in each region. In addition, quasi opposition-based learning enhances the exploration of the algorithm. The best candidate solution found by improved DE is then used as the initial network weights for the Levenberg-Marquardt (LM) algorithm, as a local refinement. Experimental results on different benchmarks and in comparison with 26 conventional and population-based approaches apparently demonstrate the excellent performance of Reg-IDE.

The balance between exploration and exploitation is an important feature in Evolutionary Algorithms (EA). The use of different operators permits to explore the search space and exploit the most prominent regions. This article introduces a dynamic operator selection method that considers different criteria at the same time. The proposed approach uses a dynamic decision matrix (DyDM) to identify which operators must be used at each iteration based on how the algorithm behaves. The DyDM considers specific information as the diversity of the algorithm to avoid stagnation, the actual iteration to work accordingly, and the fitness to direct the search. The proposed approach is called Dynamic Decision Matrix Optimizer (DyDMO) and it has been compared with different well-known algorithms tested on the CEC 2017 benchmark functions. The comparative analysis and non-parametric statistical tests validate how DyDMO im-proves the quality of the solutions and is more stable than its comnetitors.

Autonomous unmanned aerial vehicles (UAVs) are essential for detecting and tracking specific events, such as automatic navigation. The intelligent monitoring of people’s social distances in crowds is one of the most significant events caused by the coronavirus. The virus is spreading more quickly among the crowds, and the disease cycle continues in congested areas. Due to the error that occurs when humans monitor their activity, an automated model is required to alert to social distance violations in crowds. As a result, this article proposes a two-step framework based on autonomous UAV videos, including human tracking and deep learning-based recognition of the crowd’s social distance. The deep architecture is a modified-fast and lightweight ShuffleNet learning structure. First, the Kalman filter is used to determine the positions of individuals, and then the modified ShuffleNet is used to refine the bounding boxes obtained and determine the social distance. The social distance is calculated using the initial refinement of the bounding box obtained during the tracking step and the scale in frames of the human body. The observed average accuracy, average processing time (APT), and processed frame per second (FPS) for three congestion datasets were 97.5%, 84 milliseconds, and 11.5 FPS, respectively. Real-time decision-making was achieved by reducing the size and resolution of the frames. Additionally, the frames were re-labeled to reduce the computational complexity associated with detecting social distancing. The experimental results demonstrated that the proposed method could operate more quickly and accurately on various resolution frames of UAV videos with difficult conditions.

Training multi-layer neural networks (MLNNs), a challenging task, involves finding appropriate weights and biases. MLNN training is important since the performance of MLNNs is mainly dependent on these network parameters. However, conventional algorithms such as gradient-based methods, while extensively used for MLNN training, suffer from drawbacks such as a tendency to getting stuck in local optima. Population-based metaheuristic algorithms can be used to overcome these problems. In this paper, we propose a novel MLNN training algorithm, CenDE-DOBL, that is based on differential evolution (DE), a centroid-based strategy (Cen-S), and dynamic opposition-based learning (DOBL). The Cen-S approach employs the centroid of the best individuals as a member of population, while other members are updated using standard crossover and mutation operators. This improves exploitation since the new member is obtained based on the best individuals, while the employed DOBL strategy, which uses the opposite of an individual, leads to enhanced exploration. Our extensive experiments compare CenDE-DOBL to 26 conventional and population-based algorithms and confirm it to provide excellent MLNN training performance.

Differential evolution (DE) is an effective population-based metaheuristic algorithm for solving complex optimisation problems. However, the performance of DE is sensitive to the mutation operator. In this paper, we propose a novel DE algorithm, Clu-DE, that improves the efficacy of DE using a novel clustering-based mutation operator. First, we find, using a clustering algorithm, a winner cluster in search space and select the best candidate solution in this cluster as the base vector in the mutation operator. Then, an updating scheme is introduced to include new candidate solutions in the current population. Experimental results on CEC-2017 benchmark functions with dimensionalities of 30, 50 and 100 confirm that Clu-DE yields improved performance compared to DE.

Differential Evolution (DE) algorithm has been shown notable performance in solving complex optimization problems. In recent years, some variants of the DE algorithm have been proposed based on the concept of center-based sampling strategy. To the best of our knowledge, the related papers employed center-based sampling for population initialization or as the base vector in mutation operator. In fact, they were operation-level approaches applied during the optimization process, and none of them was about proposing a population-level approach to utilize center-based sampling to accelerate convergence rate of algorithms. This paper proposes a novel center-based sampling scheme for the DE algorithm that utilizes center-based sampling as a member of the population. In our scheme, one candidate solution is the center of the best candidate solutions, while other individuals in the population behave similarly to the standard DE algorithm. The center-based candidate solution is not updated using standard operators and is set to the center in each iteration. To validate our scheme, we benchmark our algorithm on CEC-2017 benchmark functions with three dimensions of 30, 50, and 100. Also, we design some experiments to analyze the behavior of the proposed center-based scheme. Our experiments demonstrate a significant improvement of the proposed algorithm on the majority of benchmark functions.

Image thresholding is a crucial image processing task. Most of the time, it plays a pivotal role in an image processing chain, therefore, any error in image thresholding can propagate to other steps such as edge detection, area/volume estimation, or object recognition. Multi-level image thresholding is a popular method for image segmentation, dividing an image into homogeneous regions. Conventional algorithms are timeconsuming due to utilising an exhaustive search, especially when the number of threshold levels increases. On the other hand, population-based metaheuristic algorithms have been successfully applied to this problem. In this paper, we propose a center-based differential evolution (DE) algorithm for high-dimensional multilevel image thresholding (many-level image thresholding). While DE has been shown to yield satisfactory performance for various real-world optimisation problems, in our algorithm, DE is further boosted with a center-based sampling strategy. We evaluate our algorithm on a set of benchmark images on high-dimensional search spaces and with regards to an entropy-based objective function and peak signal-to-noise ratio (PSNR). The obtained results demonstrate that the proposed algorithm can improve upon the performance of other metaheuristic image thresholding techniques.

Population-based metaheuristic algorithms are problem-independent approaches to solve global optimisation problems. The human mental search (HMS) algorithm is a powerful population-based metaheuristic algorithm that has been shown to yield competitive performance for a variety of optimisation problems. HMS comprises three main operators, mental search, grouping, and movement. Mental search explores the neighbourhood of candidate solutions based on a Levy flight distribution to allow for simultaneous exploration and exploitation. Grouping is used to cluster the current population in order to find a promising area in search space, while during movement, candidate solutions move towards the identified promising area. In this paper, we propose an improved HMS algorithm-HMS-IS-OSK - that introduces an adaptive selection of the number of mental processes to improve the exploitation ability of HMS, and a one-step k-means algorithm for grouping to decrease the computational complexity. To evaluate the proposed algorithm, we perform a set of experiments on the CEC 2017 bench-mark functions with dimensionalities of 30, 50, and 100. The obtained results show that HMS-IS-OSK outperforms standard HMS as well as other population-based metaheuristic algorithms including covariance matrix adaptation evolution strategy (CMAES), particle swarm optimisation (PSO), artificial bee colony algorithm (ABC), whale optimisation algorithm (WOA), grey wolf optimiser (GWO), and moth-flame optimisation (MFO).

Multi-layer feed-forward neural networks have been used to tackle many complex practical applications. Their performance is closely related to the success of training algorithms which adapt the weights in the network. Although conventional algorithms such as back-propagation are widely used, they suffer from drawbacks such as a tendency to get trapped in local optima. Stochastic optimisation algorithms, and in particular population-based metaheuristics, represent a useful alternative in this context. In this paper, we have proposed an effective hybrid algorithm, CLPSO-LM, which is based on particle swarm optimisation (PSO), a population-based metaheuristic algorithm, the Levenberg- Marquardt (LM) algorithm as a local search algorithm, and a comprehensive learning (CL) strategy. The CL strategy in our algorithm is responsible for improving the exploration ability of the algorithm and preventing premature convergence using neighbour candidate solutions in PSO. The best position found by comprehensive learning PSO is then used as the initial network weights for the LM algorithm. An extensive set of experiments on different classification benchmark datasets and comparison to various conventional and population-based algorithms shows CLPSO-LM to yield very competitive performance.

Particle swarm optimization (PSO) has demonstrated a promising performance for solving challenging optimization problems, but its performance in solving large-scale optimization problems (LSGO) has drastically decreased. In the canonical PSO, velocity has a significant effect on the performance of PSO, which is updated based on cognitive and social factors. It can help particles to share information effectively. In this paper, a center-based velocity is proposed in which a new component, named opening "center of gravity factor", is added to velocity update rule to propose the center-based PSO (CenPSO). Center of gravity factor benefits from center-based sampling strategy, a new direction in population-based metaheuristics, especially to tackle LSGOs. The proposed method is evaluated on two benchmark functions, namely, CEC2010 and CEC2017, with dimensions 100 and 1000. The experimental results verify that CenPSO is significantly better than PSO over the majority of benchmark functions.

Differential Evolution (DE) algorithm is an efficient metaheuristic algorithm in solving complex real-world optimization problems. DE algorithm benefits from two populations for updating individuals, while it might cause memory problems in practice during solving large-scale optimization problems; especially when they are used in an embedded system. One strategy to tackle this problem is utilizing a one-array scheme which benefits from only one population, leading to a half-space memory. This paper proposes a novel DE algorithm based on one-array DE and a random replacement strategy; it adds an additional competition to the selection operator to make better use of the new individual that it might be potentially noteworthy. The positive feature of the introduced replacement strategy is that it does not need any extra computational budget. Also, due to employing one-array strategy, the proposed scheme has a lower memory complexity. Our experiments on CEC-2017 benchmark function with dimensions 30, 50, and 100 clearly illustrate the effectiveness of the proposed DE algorithm.

Colour quantisation is a common image processing technique to reduce the number of distinct colours in an image which are then represented by a colour palette. Selection of appropriate entries in this palette is challenging since the quality of the quantised image is directly dictated by the palette colours. In this paper, we propose a novel colour quantisation algorithm based on the human mental search (HMS) algorithm and subsequent refinement of the colour palette using k-means. HMS is a recent population-based metaheuristic algorithm that has been shown to yield good performance on a variety of optimisation problems. In the first stage, we use HMS to find a high-quality initial colour palette. In the second stage, this palette is refined using k-means to converge towards a local optimum and thus to further improve the quality of the quantised image. We evaluate our algorithm on a set of benchmark images and compare it to several conventional and soft computing-based colour quantisation algorithms to demonstrate excellent image quality, outperforming the other methods.

Many real-world problems are categorized as large-scale problems, and metaheuristic algorithms as an alternative method to solve large-scale problem; they need the evaluation of many candidate solutions to tackle them prior to their convergence, which is not affordable for practical applications since the most of them are computationally expensive. In other words, these problems are not only large-scale but also computationally expensive, that makes them very difficult to solve. There is no efficient surrogate model to support large-scale expensive global optimization (LSEGO) problems. As a result, the algorithms should address LSEGO problems using a limited computational budget to be applicable in real-world applications. Coordinate Descent (CD) algorithm is an optimization strategy based on the decomposition of a n-dimensional problem into n one-dimensional problem. To the best our knowledge, there is no significant study to assess benchmark functions with various dimensions and landscape properties to investigate CD algorithm and compare with other metaheuristic algorithms. In this paper, we propose a modified Coordinate Descent algorithm (MCD) to tackle LSEGO problems with a limited computational budget. Our proposed algorithm benefits from two leading steps, namely, finding the region of interest and then shrinkage of the search space by folding it into the half with exponential speed. One of the main advantages of the proposed algorithm is being free of any control parameters, which makes it far from the intricacies of the tuning process. The proposed algorithm is compared with cooperative co-evolution with delta grouping on 20 benchmark functions with dimension 1000. Also, we conducted some experiments on CEC-2017, D = 10,30,50, and 100, to investigate the behavior of MCD algorithm in lower dimensions. The results show that MCD is beneficial not only in large-scale problems, but also in low-scale optimization problems.

Multi-level image thresholding is a popular approach for image segmentation where the image is divided into several non-overlapping regions based on the image histogram. Conventional algorithms for multi-level image thresholding are time-consuming. This is in particular so when the number of thresholds increases due to the curse of dimensionality where the search space expands exponentially as the number of parameters (thresholds) increases. One approach to address this problem is to employ population-based metaheuristic algorithms. Since various such optimisation algorithms have been presented in the literature, in this paper, we benchmark the performance of 13 population-based algorithms in the high-dimensional search spaces of the multi-level image thresholding problem. The algorithms we assess include the whale optimisation algorithm (WOA), grey wolf optimiser (GWO), cuckoo optimisation algorithm (COA), biogeography-based optimisation (BBO), teaching-learning-based optimisation (TLBO), gravitational search algorithm (GSA), imperialist competitive algorithm (ICA), cuckoo search (CS), firefly algorithm (FA), bat algorithm (BA), differential evolution (DE), particle swarm optimisation (PSO), and genetic algorithm (GA). We evaluate these on different images with regards to objective function value as well as peak signal-to-noise ratio (PSNR) and also employ a non-parametric statistical test, the Wilcoxon signed rank test, to compare the algorithms and to draw conclusions about their performance for multi-level image thresholding.

Human mental search (HMS) is a recent population-based metaheuristic inspired by the exploration manner in the bid space of online auctions. It has three main operators: (1) mental search which explores the vicinity of each candidate solution based on Levy flight, (2) grouping which is performed using a clustering algorithm to find a promising area, and (3) moving towards the promising area. HMS has shown competitive performance in solving various optimisation problems.In this paper, an improved HMS algorithm, Global-Best Human Mental Search with Random Clustering Strategy (GHMS-RCS) is proposed as a variant of HMS for global optimisation. GHMS-RCS benefits from the information of global best solutions to improve the exploitation of the HMS algorithm. Also, to reduce the time complexity and enhance exploration and exploitation, a new strategy named random clustering is introduced to improve the grouping operator in HMS. Experimental results show that GHMS-RCS outperforms standard HMS as well as other population-based algorithms including particle swarm optimisation (PSO), shuffled frog-leaping algorithm (SFLA), and biogeography-based optimisation (BBO).