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In this research work, a novel approach is proposed by introducing numerous scaling factors in the original equilibrium optimization technique which can be named as modified equilibrium optimization (MEO) algorithm and is utilized for the load frequency control (LFC) of two-area hybrid distributed power system. The introduced MEO meta-heuristic algorithm is compared with a standard EO algorithm and other meta-heuristic algorithms for different standard benchmark test functions. Furthermore, the genuine utilization of the MEO algorithm is tried by designing a multi-stage PID (MS-PID) controller for frequency regulation of the power system with distributed energy sources including renewable sources. The supremacy of the reinforced MEO methodology-based MS-PID controller for enhanced frequency regulation is presented and its outcomes are compared with the EO-tuned PID and MS-PID. From the performance comparison, it is recognized that the MEO-based MS-PID controller is more efficacious.

In this paper, a novel optimization algorithm is proposed by hybridizing firefly and whale optimization algorithms and it is applied to the problem of determining optimal design parameters of model predictive control. The developed hybrid algorithm is compared with firefly and whale optimization algorithms considering unimodal, multimodal, composite and CEC-C06 2019 benchmark optimization problems in terms of statistical analysis. Comparison results showed that hybrid algorithm has the best performance for approximately 67% of 39 benchmark functions in finding the minimum in an average of independent 100 experiments for each function. For the functions in which the proposed algorithm gives the best results, approximately 64% improvement is achieved compared to FA and 39% improvement compared to WOA. In terms of convergence speed, in average 2% of improvement is obtained. As an application to engineering problems, optimization of parameters of the model predictive control for inverted pendulum and distillation column is considered and the performance of the proposed algorithm is compared with the performances of firefly algorithm and whale optimization algorithm. For the considered applications, a novel objective function is selected. The selected objective function for hybrid firefly–whale optimization algorithm enables finding the optimal prediction horizon and control horizon as well as the Q and R matrices such that the system responses satisfy desired settling time and maximum overshoot criteria. Most of considered comparisons demonstrate that the proposed hybrid algorithm has better performance.

Differential Evolution (DE) is a powerful evolutionary algorithm for global optimization problems. Generally, appropriate mutation strategies and proper equilibrium between global exploration and local exploitation are significant to the performance of DE. From this consideration, in this paper, we present a novel DE variant, abbreviated to DMIE-DE, to further enhance the optimization capacity of DE by developing a dual mutations collaboration mechanism with elites guiding and inferiors eliminating techniques. More specifically, an explorative mutation strategy DE/current-to-embest with an elite individual serving as part of the difference vector and an exploitative mutation strategy DE/ebest-to-rand with selecting an elite individual as the base vector are employed simultaneously to achieve the balance between local and global performance of the whole population instead of only one mutation strategy in classical DE algorithm. The control parameters F and CR for above mutation strategies are updated adaptively to supplement the optimization ability of DMIE-DE based on a rational probability distribution model and the successful experience from the previous iterations. Moreover, an inferior solutions eliminating technique is embedded to enhance the convergence speed and compensate cost of the fitness evaluation times during the evaluation process. To evaluate the performance of DMIE-DE, experiments are conducted by comparing with five state-of-the-art DE variants on solving 29 test functions in CEC2017 benchmark set. The experimental results indicate that the performance of DMIE-DE is significantly better than, or at least comparable to the considered DE variants.

Jaya algorithm is an advanced optimization algorithm, which has been applied to many real-world optimization problems. Jaya algorithm has better performance in some optimization field. However, Jaya algorithm exploration capability is not better. In order to enhance exploration capability of the Jaya algorithm, a self-adaptively commensal learning-based Jaya algorithm with multi-populations (Jaya-SCLMP) is presented in this paper. In Jaya-SCLMP, a commensal learning strategy is used to increase the probability of finding the global optimum, in which the person history best and worst information is used to explore new solution area. Moreover, a multi-populations strategy based on Gaussian distribution scheme and learning dictionary is utilized to enhance the exploration capability, meanwhile every sub-population employed three Gaussian distributions at each generation, roulette wheel selection is employed to choose a scheme based on learning dictionary. The performance of Jaya-SCLMP is evaluated based on 28 CEC 2013 unconstrained benchmark problems. In addition, three reliability problems, i.e. complex (bridge) system, series system and series-parallel system are selected. Compared with several Jaya variants and several state-of-the-art other algorithms, the experimental results reveal that Jaya-SCLMP is effective.

To solve engineering problems with evolutionary algorithms, many expensive objective function evaluations (FEs) are required. To alleviate this difficulty, the surrogate-assisted evolutionary algorithm (SAEA) has attracted increasingly more attention in both academia and industry. The existing SAEAs depend on the quantity and quality of the original samples, and it is difficult for them to yield satisfactory solutions within the limited number of FEs. Moreover, these methods easily fall into local optima as the dimension increases. To address these problems, this paper proposes an adaptive surrogate-assisted particle swarm optimization (ASAPSO) algorithm. In the proposed algorithm, an adaptive surrogate selection method that depends on the comparison between the best existing solution and the latest obtained solution is suggested to ensure the effectiveness of the optimization operations and improve the computational efficiency. Additionally, a model output criterion based on the standard deviation is suggested to improve the robustness and stability of the ensemble model. To verify the performance of the proposed algorithm, 10 benchmark functions with different modalities from 10 to 50 dimensions are tested, and the results are compared with those of five state-of-the-art SAEAs. The experimental results indicate that the proposed algorithm performs well for most benchmark functions within the limited number of FEs. The performance of the proposed algorithm in solving engineering problems is verified by applying the algorithm to the PX oxidation process.

Balancing the convergence and the diversity is one of the crucial researches in solving multi-objective problems (MOPs). However, the optimization algorithms are inefficient and require massive iterations. The convergence accuracy and the distribution of the obtained non-dominated solutions are defective in solving complex MOPs. To solve these problems, a novel adaptive multi-objective particle swarm optimization using a three-stage strategy (tssAMOPSO) is proposed in this paper. Firstly, an adaptive flight parameter adjustment is proposed to manage the states of the algorithm, switching between the global exploration and the local exploitation. Then, the three-stage strategy, including adaptive optimization, decomposition, and Gaussian attenuation mutation, is conducted by population in each iteration. The three-stage strategy remarkably promotes the diversity and efficiency of the optimization process. Furthermore, the convergence analysis of three-stage strategy is provided in detail. Finally, particles are equipped with memory interval to improve the reliability of personal best selection. In the maintenance of external archive, the proposed fusion index can enhance the quality of non-dominated solutions directly. A series of benchmark instances, ZDT and DTLZ test suits, are used to verify the performance of tssAMOPSO. Several classical and state-of-the-art algorithms are employed for experimental comparisons. Experimental results show that tssAMOPSO outperforms the other algorithms and achieves admirable comprehensive performance.

This study proposes an intelligent hybridization between the multi-level cross-entropy optimizer (MCEO) and moth-flame optimization (MFO) algorithms to keep a good compromise between exploration and exploitation. The proposed hybrid multi-level cross-entropy-based moth-flame (MCMF) algorithm uses MCEO as a global search engine during the first phase of the optimization process that allows for fast approximation of the global best position (BP). The boundaries of the search space are then adaptively confined within the effective region around the current BP by applying the proposed search space boundaries confining factor (SSBCF). The modified MFO with two different moth generation patterns is then employed as a local search engine to simultaneously probe for new and proper BPs within the confined and overall search space. This prevents MCMF from becoming trapped in local optima while maintaining a balance between exploration and exploitation. The hybridization between both algorithms allows MCMF to accelerate throughout the early steps of the search process using the high exploration ability of MCEO, whereas, in the later stages of optimization, promising solutions will possess a high probability to be exploited using the higher exploitation power of MFO in the confined space. The competence of the MCMF is compared with other well-known state-of-the-art algorithms on 15 unconstrained benchmark functions and 5 constrained engineering design problems having a wide range of dimensions and varied complexities. The statistical results on the benchmark functions and the solved engineering examples verify that the proposed algorithm can provide very competitive and promising results. The results demonstrate the comprehensive superiority of the hybrid MCMF compared to both MCEO and MFO in terms of fewer function calls, high escaping ability from local optima, and fast convergence speed.

Past present future (PPF) is a new stochastic optimization algorithm inspired by the phenomena of the way an individual learns from a successful person in society. PPF is based on the concept of “future improvement of a person’s life depending on his/her past experience and present work.” The influence of successful persons also affects the improvement of the future life of an individual. This work develops a mathematical model for PPF following the above facts. In this new algorithm, the population is divided into subpopulations and a switching mechanism is followed among the subpopulations to track the change in optimal positions of an individual thereby accelerating the convergence rate. In addition, this switching mechanism also prevents pre-mature convergence. PPF was found to possess low computational complexity with fast convergence characteristics. The proposed PPF is compared with 41 up-to-date meta-heuristic algorithms taking an extensive set of benchmark functions to verify the efficiency. In addition, five classical engineering design problems are simulated to estimate the efficacy of the PPF algorithm in optimizing engineering problems. The results confirm the superior performance of the proposed algorithm to get the optimal solution with less iteration and have shown the best competitive performance compared to all other algorithms.

Although the salient object detection method based on the fully convolutional neural network has achieved better performance, how to learn effective feature representations in complex scenes to obtain more accurate saliency maps is still a challenge. In order to cope with the above-mentioned challenges, an addition or cascade structure is generally used to fuse feature information between multiple levels. However, these methods are susceptible to the influence of messy background information. The network may regard non-salient objects with similar salient appearances as target predictions, and the prediction results may be incomplete due to different appearance areas of salient objects. We design a network composed of multiple attention mechanisms to selectively integrate deep and shallow feature information, and more effectively deal with the transfer and fusion of features. In this paper, we propose a multi-attention embedded network (MAENet), which introduces attention mechanisms to give different feature information with different weights for handling the transfer and aggregation of features at different levels. The multi-attention feature aggregation (MAFA) module is proposed, which uses the channel attention mechanism to give different weights to the features to be fused, and then uses the spatial attention mechanism to selectively aggregate shallow edge information and deep abstract semantic features to avoid excessive redundant information which affects the saliency mapping, as well as suppressing non-salient areas with “salient” appearance. In addition, The multi-scale feature extraction (MFE) module and the self-attention (SA) module are also proposed for obtaining sufficiently rich and useful multi-scale context information and enhancing the function of the top layer. Finally, the attentional residual refinement (ARR) module is utilized to refine the saliency map after each feature fusion and further improve the input function. MAENet can accurately segment salient objects and provide clear local details. Experimental results on five benchmark datasets show that the proposed method achieves the favorable performance against 14 state-of-the-art methods on popular evaluation metrics.

Grey wolf optimization (GWO) is a meta-heuristic inspired by the social hierarchy and the hunting behaviors observed in wolves. The GWO algorithm has been successfully applied in many fields, such as finance, engineering and industry. However, the GWO has the disadvantages that it is prone to stagnate in local solutions, and the convergence may be slower. In order to overcome these shortcomings, we re-analyzed the hunting behaviors of wolves and observed that there are very frequent communications between leaders and ω-type wolves during the hunting process. This process is called judging prey. Based on this observation, we propose an improved optimization algorithm, termed decision-making grey wolf optimization algorithm (DGWO). At variance with the original GWO, DGWO includes four steps, instead of three: searching for prey, judging prey, encircling prey and attacking prey. The algorithm is tested using 29 well-known benchmark functions and traveling salesman problem, and compared with the GWO algorithm, as well as to the existing improved algorithms random walk grey wolf optimization and modified grey wolf optimization. Results show that including the judging prey stage in DGWO results in a faster convergence and it effectively prevents the algorithm to stop in local optima.

In this paper, a hybrid sunflower-teaching learning-based optimization (SFO-TLBO) algorithm has been proposed, integrating two well-known algorithms, namely sunflower optimization, and teaching–learning-based optimization. The proposed hybrid SFO-TLBO algorithm has been incorporated based on the ratio of the fitness value of the search agent and the average fitness value of the population. The SFO has more tendency of global exploration but has a problem of slow convergence speed. On the other hand, the convergence of the TLBO algorithm is fast, but it may get stuck in local optima. In this work, we have hybridized SFO with TLBO to take advantage of both the algorithms and also to balance the trade-off between exploitation and exploration. The proposed hybrid SFO-TLBO has been first applied to nineteen test benchmark functions. The outcomes have been compared with twelve state-of-the-art algorithms. In seventeen benchmark test functions, better performance has been achieved by the proposed hybrid SFO-TLBO. Also, the proposed hybrid SFO-TLBO algorithm has been used to solve an Internet of Vehicles (IoV) optimization problem and performance has been compared with fifteen state-of-the-art algorithms. In solving the IoV problem, hybrid SFO-TLBO has been achieved better performance in comparison with all fifteen considered algorithms which showcases the applicability of hybrid SFO-TLBO algorithm in resolving large-scale, real-world problems. In addition, for feature selection problems, a binary version of hybrid SFO-TLBO has been proposed, in which a wrapper approach is used to decide an optimal subset of features with a k-nearest neighbor classifier. The proposed binary method also determines an optimal value of k for the k-nearest neighbor classifier. The binary hybrid SFO-TLBO algorithm has been applied to the QSAR biodegradation dataset for classification, and for evidencing its efficiency, its performance has been compared with the other state-of-the-art algorithms. The results of the proposed approach are quite encouraging, and an average accuracy of 89.10% has been achieved.

Since real-world problems are quite complex, developing more effective methods to optimize them is taken into consideration at the present age. One of the most popular strategies to solve such problems is nature-inspired metaheuristic algorithms which have presented promising solutions in different fields. The JAYA algorithm is an innovative and promising technique for solving a wide range of optimization problems. Hence, this investigation provides a new hybrid algorithm based on JAYA and crow search algorithm (CSA), known as HJCSA, to enhance its performance. In other words, the mechanism of updating position in CSA is integrated with JAYA algorithm to reinforce the convergence and search capabilities of JAYA algorithm. The proposed hybrid algorithm is evaluated through solving 20 well-known benchmark functions, and obtained results are compared with various up-to-date algorithms, including CSA, JAYA, particle swarm optimization (PSO), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), moth-flame optimization (MFO), and sine–cosine algorithm (SCA). In addition, a real-world engineering problem is optimized by the proposed optimization approach and compared with other published works. The results showed that the suggested optimization algorithm is much more vigorous in escaping from local minima, possessing better convergence, and discovering more accurate solutions.

This study’s primary purpose is to improve the original krill herd (KH) optimization algorithm by using chaos theory and propose a novel chaotic krill herd (CKH) optimization algorithm. Fourteen different chaotic map functions have been added to the several steps of the KH and CKH optimization algorithms already existing in the literature to improve their performances. Six different well-known benchmark functions have been used to test the performances of the developed algorithm. The proposed algorithm has better performance to reach the global optimum of the objective function which has many local minimums. The proposed algorithm improved the KH and CKH optimization algorithms' performances which already exist in the literature. Proposed novel CKH has been applied to rubber bushing stiffness optimization which is a real automotive industry problem. Obtained results have been compared with KH, CKH, genetic algorithm (GA), differential evaluation algorithm (DE) and particle swarm optimization (PSO). The proposed algorithm has better performance to reach the global optimum of the objective function. The performance and validity of the algorithm have been proved not only by using six different benchmark functions but also by using finite element analysis of rubber bushing. The study is also a unique optimization activity that uses the KH algorithm to optimize rubber bushing by using nonlinear finite element analysis.

The knapsack problem arises in several real-world applications, like manufacturing systems, transportation, cutting and packing, and hydrological studies. In this paper, we investigate the use of an iterative rounding strategy-based algorithm for tackling a special knapsack problem: the set-union knapsack problem. First, the approach builds a series of starting partial solutions by using the principle of fractional values related to a series of linear relaxations of the (sub)instance at hand. Second, each step of the rounding procedure is coupled with an enhanced local search procedure, where its goal is to search around a local partial solution by applying the so-called critical element tailored for the problem studied. Third, both degrading and re-optimization strategies are introduced in order to extend the diversified search space. Finally, all strategies are embedded into an iterative search in order to augmenting the quality of the solutions. The performance of the proposed method is evaluated on benchmark instances of the literature and new large-scale instances; its provided results are compared to those reached by the Cplex solver and the best methods available in the literature. The method seems competitive, where it is able to achieve new (lower) bounds and matches the rest of the bounds.

As a relatively new model, the Artificial Bee Colony Algorithm (ABC) has shown impressive success in solving optimization problems. Nevertheless, its efficiency is still not satisfactory for some complex optimization problems. This paper has modified ABC and its other recent variants to improve its performance by modify the scout phase. This modification enhances its exploitation ability by intensifying the regions in the search space, which probably includes reasonable solutions. The experiments were performed on the CEC2014 benchmark suite, CEC2015 benchmark functions, and three real-life problems: pressure vessel design problem, tension and compression spring design problem, and Frequency-Modulated (FM) problem. And the proposed modification was applied to basic ABC, Gbest-Guided ABC, Depth First Search ABC, and Teaching Learning Based ABC, and they were compared with their modified counterparts. The results have shown that our modification can successfully increase the performance of the original versions. Moreover, the proposed modified algorithm was compared with the state-of-the-art optimization algorithms, and it produced competitive results.

The PQ index is an integrated grouting process parameter that represents the relationship between grouting pressure and grout flow. By tracking the variation in the PQ index, operators can understand and control the grouting process. Therefore, accurate and reliable PQ index prediction is important for grouting process guidance. However, because the original grouting process parameter time series has chaotic characteristics and noise interference, traditional point prediction suffers from inevitable prediction errors and cannot quantify the uncertainties associated with the prediction. In this study, to cope with these deficiencies, a hybrid interval prediction model for the PQ index based on an improved extreme learning machine with a lower upper bound estimation method is proposed. In this model, the lower upper bound estimation method is used to construct an advanced extreme learning machine with interval prediction ability to perceive the uncertainties of the prediction. The improved grey wolf optimizer algorithm is applied to optimize the parameters of the extreme learning machine. Moreover, to enhance the prediction ability, cooperating with the hybrid data preprocessing method based on a noise reduction and decomposition strategy, a feature selection method is developed to identify the chaotic characteristics of the PQ index time series and determine the optimal input form of the interval prediction model. The proposed model is applied to predict the PQ value in the grouting process at a hydropower project in China. The results reveal that the proposed model can construct high-quality prediction intervals, which is superior to the performance of other benchmark models and has high potential for practical applications in grouting projects.

The beetle antennae search algorithm was recently proposed and investigated for solving global optimization problems. Although the performance of the algorithm and its variants were shown to be better than some existing meta-heuristic algorithms, there is still a lack of convergence analysis. In this paper, we provide theoretical analysis on the convergence of the beetle antennae search algorithm. We test the performance of the BAS algorithm via some representative benchmark functions. Meanwhile, some applications of the BAS algorithm are also presented.

The cuckoo search (CS) algorithm is an effective optimization algorithm, but it is prone to stagnation in suboptimality because of some limitations in its exploration mechanisms. This paper introduces a variation of CS called exploratory CS (ECS), which incorporates three modifications to the original CS algorithm to enhance its exploration capabilities. First, ECS uses a special type of opposition-based learning called refraction learning to improve the ability of CS to jump out of suboptimality. Second, ECS uses the Gaussian perturbation to optimize the worst candidate solutions in the population before the discard step in CS. Third, in addition to the Levy flight mutation method used in CS, ECS employs two mutation methods, namely highly disruptive polynomial mutation and Jaya mutation, to generate new improved candidate solutions. A set of 14 widely used benchmark functions was used to evaluate and compare ECS to three variations of CS:CS with Levy flight (CS), CS with highly disruptive polynomial mutation (CS10) and CS with pitch adjustment mutation (CS11). The overall experimental and statistical results indicate that ECS exhibits better performance than all of the tested CS variations. Besides, the single-objective IEEE CEC 2014 functions were used to evaluate and compare the performance of ECS to six well-known swarm optimization algorithms: CS with Levy flight, Grey wolf optimizer (GWO), distributed Grey wolf optimizer (DGWO), distributed adaptive differential evolution with linear population size reduction evolution (L-SHADE), memory-based hybrid Dragonfly algorithm and Fireworks algorithm with differential mutation. Interestingly, the results indicate that ECS provides competitive performance compared to the tested six well-known swarm optimization algorithms.

Label-specific features learning can effectively exploit the unique features of each label, which alleviates the high dimensionality and improves the classification performance of multi-label. However, most existing label-specific features learning algorithms assume that label space is complete, ignoring the effect of missing labels on the classification accuracy. Some methods try to recover the missing labels first and then learn the mapping between the completed label matrix and the feature matrix. However, early intervention in the recovery of missing labels may affect the distribution of original labels to a certain extent. In this paper, feature-label dual-mapping for missing label-specific features learning is proposed. According to the information that the label depends on the feature, the dual-mapping weight of the complete feature space and the missing label space is jointly learned. Therefore, the proposed algorithm is to conduct latent missing labels recovery by feature-label dual-mapping to directly obtain target weight in this paper, avoiding the negative influence of early label recovery intervention. Compared with several state-of-the-art methods in 10 benchmark multi-label data sets, the results show that the proposed algorithm is reasonable and effective.

The gaining sharing knowledge based optimization algorithm (GSK) is recently developed metaheuristic algorithm, which is based on how humans acquire and share knowledge during their life-time. This paper investigates a modified version of the GSK algorithm to find the best feature subsets. Firstly, it represents a binary variant of GSK algorithm by employing a probability estimation operator (Bi-GSK) on the two main pillars of GSK algorithm. And then, the chaotic maps are used to enhance the performance of the proposed algorithm. Ten different types of chaotic maps are considered to adapt the parameters of the GSK algorithm that make a proper balance between exploration and exploitation and save the algorithm from premature convergence. To check the performance of proposed approaches of GSK algorithm, twenty-one benchmark datasets are taken from the UCI repository for feature selection. The performance is measured by calculating different type of measures, and several metaheuristic algorithms are adopted to compare the obtained results. The results indicate that Chebyshev chaotic map shows the best result among all chaotic maps which improve the performance accuracy and convergence rate of the original algorithm. Moreover, it outperforms the other metaheuristic algorithms in terms of efficiency, fitness value and the minimum number of selected features.

Recent developments designate the quick growing of optimization meta-heuristics in the domain of optimization. Sine–cosine optimizer is a stochastic technique that generates various preliminary random research agents global optimal solutions and involves them to fluctuate toward or outwards the superior global optima solution utilizing a mathematical model based on sine and cosine trigonometry functions. Nevertheless, standard SCA provides insufficient global optima results on complex dimension functions illustrating poor convergence rate. The search process of the SCA method holds various shortcomings such as slow convergence, weak balance amid exploration and exploitation, and inefficiency in convergence. To overcome these shortcomings in this work, we are trying to present a new heuristic approach based on merging the features of SCA (sine–cosine approach) with a HS (harmony search approach) known as HSCAHS algorithm. The existing approach integrates the merits of the sine–cosine algorithm and HS algorithm to reduce demerits, like the trapping in local optima and unbalanced exploitation. The new approach presents own work performance in two different stages; firstly, the sine–cosine algorithm starts the explore procedure to augment exploration capability. Secondly, harmony search part starts its search from SCA finds so far to augment the exploitation tendencies. Hence, hybrid approach can find best possible solution in which least time improves the exploitation and exploration. Hence, the newly existing hybrid approach can be quickly convergent, statistically sound and more robust. The capability of the hybrid approach is verified by applying it on eighteen tested benchmark, economic dispatch, three-bar truss design, rolling element bearing design, multiple disc clutch brake design, speed reducer design and planetary gear train design problems. The experimental solutions reveal that the hybrid approach is able to finding the superior quality of optimal goal (or solution) of the optimize functions in most cases in comparison with others.

The constrained optimization problem is widely used in real-world applications and always hard to handle when the objective function is multimodal or the constraints are too stringent. In this manuscript, an improved differential evolution algorithm is proposed by using a novel individual evaluation scheme as well as a designed constraint handling technique. Firstly, the constrained optimization problem is converted into a biobjective optimization model in which all constraints are taken as an integrated function and further optimized just like the original objective. Then, based on the present individuals, both a reference point and a dynamic line are generated. The distances from any individual to the reference point as well as the dynamic line are adopted to evaluate the individual, and used to categorize individuals for evolving into groups. In addition, in order to improve the feasibility of individuals, a novel constraint handling technique is presented by utilizing the locations of some infeasible points. Finally, the proposed algorithm is executed on some recent benchmark functions as well as the system reliability redundancy allocation problems, and the computation results show the effectiveness of these presented techniques.

This paper proposes a novel metaheuristic-based optimization technique called search space reduction (SSR) optimization algorithm. This algorithm attempts to solve the common pitfalls in the existing algorithms in the literature by randomly generating the search agents in every iteration instead of following the best solution. This new algorithm is simple, computationally efficient, which is based on the concept of reducing the search space. The performance of this algorithm is tested over classical test functions and CEC’17 benchmark test functions. The results are compared with well-established algorithms in the literature. The test results show that the proposed algorithm exhibits good exploration and exploitation capabilities. Further, this algorithm also outperforms other algorithms in solving multimodal optimization problems. In addition to this, the computational complexity of this algorithm is also presented according to CEC’17 guidelines. The proposed algorithm is also employed to solve three engineering design problems and a more complex re-entry trajectory optimization problem to show its effectiveness.

Meta-heuristic algorithms have shown promising results in solving various optimization problems. The crow search algorithm (CSA) is a new and effective meta-heuristic algorithm that emulates crows’ intelligent group behavior in nature. However, it suffers from several problems, such as trapping into local optimum and premature convergence. This paper proposes an improved crow search algorithm (ICSA), which has been tested and evaluated by a set of well-known benchmark functions. A new update mechanism that uses the merits of the global best position to move toward the best position is proposed. This mechanism increases the convergence of the algorithm and improves its local search-ability. Twenty benchmark functions are used to evaluate the performance of the proposed ICSA. Moreover, the ICSA algorithm is compared with the conventional CSA and other meta-heuristic algorithms such as particle swarm optimization (PSO), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), gray wolf optimizer (GWO), moth-flame optimization (MFO), and sine-cosine algorithm (SCA). The experimental result shows that the proposed ICSA algorithm has produced promising results and outperformed conventional CSA and other meta-heuristic algorithms. Also, the proposed ICSA has a more robust convergence for optimizing objective functions in terms of solution accuracy and efficiency.

In this paper, improved salp swarm algorithm is proposed. The algorithm integrates (1) random opposition-based learning (2) multiple leadership and (3) simulated annealing in swarm intelligence-based metaheuristic salp swarm algorithm. This integration increases the exploration and exploitation of the original salp swarm algorithm. Hence, the effectiveness of the proposed algorithm is better for complex multi-modal problems. The algorithm is tested on several standard numerical benchmark functions and CEC-2015 benchmarks. Results are compared with some well-known metaheuristics. The results represent the merit of the proposed algorithm with respect to other algorithms. The improved salp swarm algorithm is applied for feed-forward neural network training. Performance is compared with other metaheuristic-based feedforward neural network trainers for different data sets. The results show the efficiency and effectiveness of proposed algorithm in solving complex multi-modal problems.

The purpose of multi-objective optimization is to simultaneously optimize several objective functions that are usually in conflict with each other. An acceptable solution is one that can strike a trade-off between the results of these functions. Although, multi-objective evolutionary algorithms have a good history in solving multi-objective problems, how to find more accurate and diverse solutions set at an acceptable time is still a challenge. In this study, a quantum-inspired multi-objective harmony search algorithm is proposed to solve multi-objective optimization problems. In this algorithm, a new quantum mutation strategy is proposed, which is a combination of harmony improvisation operators and a quantum adaptive rotation gate. While the use of the rotation gate leads to the move to further solutions and complete coverage of the problem space, the improvisation operators (PAR and BW) trigger tiny impulses and mutate into neighbor solutions. The advantage of such an algorithm is to strengthen the balance between the exploration and exploitation processes. Also, the crowding distance metric of the elitism strategy ensures the production of solutions with maximum variety in the problem space. The results of the implementation of this algorithm on multi-objective benchmark functions indicate significant improvement in criteria such as the distance to Pareto optimal, the scattering, and the convergence rate compared to the state-of-the-art methods.

The major purpose of this article is to enhance the performance of GOA algorithm by integrating a new mutation operator to the standard GOA algorithm. A series of six different variants of enhanced GOA is proposed by integrating GOA with six different variants of the mutation operator. The new enhanced metaheuristic optimization method is called EGOAs. EGOA aims to address the problems of slow convergence and trapping into local optima, by achieving a good balance between exploration and exploitation, using a special mutation operator that enhances the diversity of the standard GOA, to find the best solution for global optimization problems. The implementation process for enhancing the GOA algorithm is presented and the effectiveness of the enhanced algorithm is evaluated against 60 of the optimization benchmark functions, and compared to that of the standard GOA, as well as to other metaheuristic optimization algorithms. The performance of EGOAs was compared with the other improved methods based on GOA. Experimental results show that EGOAs is clearly superior to the standard GOA algorithm, as well as to other well-known algorithms, in terms of achieving the best optimal value, convergence speed, and avoiding local minima, which makes EGOAs a promising addition to the arsenal of metaheuristic algorithms.

We consider polyhedral separation of sets as a possible tool in supervised classification. In particular, we focus on the optimization model introduced by Astorino and Gaudioso (J Optim Theory Appl 112(2):265–293, 2002) and adopt its reformulation in difference of convex (DC) form. We tackle the problem by adapting the algorithm for DC programming known as DCA. We present the results of the implementation of DCA on a number of benchmark classification datasets.

In this paper, a cooperative bat searching algorithm (CBA) is proposed by using a communication topology to share information among all the bats in bat algorithm (BA). Inspired by the cooperation mechanism in the distributed control theory, a cooperative term is added to the original BA to accelerate the searching process. The convergence issue is rigorously studied for CBA by using the Jury’s test. Moreover, numerical evaluation is conducted to compare CBA with other variants of BA by solving fifteen benchmark functions from IEEE congress on evolutionary computation. The results are provided to demonstrate the effectiveness of the proposed CBA. As an application, CBA and binary CBA are equipped as the real-time optimizers in a networked model predictive control strategy to solve a balanced coordination problem. The proposed CBA showed competitive performance.

Novel metaheuristic algorithms are now considered an appealing collection of methods for solving complex optimization problems, in which the challenging objective is to find a better solution in a shorter computation time. Focusing on the same objective, this paper proposes a novel metaheuristic optimization algorithm inspired by heat transfer relationships based on the second law of thermodynamics. Imitating the heat transfer behavior of solid objects, the proposed method is called the heat transfer relation-based optimization algorithm (HTOA). This behavior was modeled on a heat transfer function used to measure temperature differences between the selected solutions and the best solution. This function was employed to determine and add the heat capacity transferred between those solutions. Finally, all the solutions were heat-exchanged with the best solution to select the fittest solution and exclude the rest. This procedure continued until the best solution or solutions were found. The proposed method is challenged by many famous benchmark problems in two categories as well as two real-world problems (PID controller and linear regression). The HTOA was then compared with a number of well-known and state-of-the-art optimization algorithms. Selecting better solutions and requiring shorter computation time, the proposed HTOA outperformed the other algorithms.

Big data (BD) approach has significantly impacted on the development and expansion of supply chain network management and design. The available problems in the supply chain network (SCN) include production, distribution, transportation, ordering, and inventory holding problems. These problems under the BD environment are challenging and considerably affect the efficiency of the SCN. The drastic environmental and regulatory changes around the world and the rising concerns about carbon emissions have increased the awareness of customers regarding the carbon footprint of the products they are consuming. This has enforced supply chain managers to change strategies to reframe carbon emissions.. The decisions such as an optimization of the suitable network of the proper lot sizes can play a crucial role in minimizing the whole carbon emissions in the SCN. In this paper, a new integrated production–transportation–ordering–inventory holding problem for SCN is developed. In this regard, a mixed-integer nonlinear programming (MINLP) model in the multi-product, multi-level, and multi-period SCN is formulated based on the minimization of the total costs and the related cost of carbon emissions. The research also uses a chance-constrained programming approach. The proposed model needs a range of real-time parameters from capacities, carbon caps, and costs. These parameters along with the various sizes of BD, namely velocity, variety, and volume, have been illustrated. A lot-sizing policy along with carbon emissions is also provided in the proposed model. One of the important contributions of this paper is the three various carbon regulation policies that include carbon capacity-and-trade, the strict capacity on emission, and the carbon tax on emissions in order to assess the carbon emissions. As there is no benchmark available in the literature, this study contributes toward this aspect by proposing two hybrid novel meta-heuristics (H-1) and (H-2) to optimize the large-scale problems with the complex structure containing BD. Hence, a generated random dataset possessing the necessary parameters of BD, namely velocity, variety, and volume, is provided to validate and solve the suggested model. The parameters of the proposed algorithms are calibrated and controlled using the Taguchi approach. In order to evaluate hybrid algorithms and find optimal solutions, the study uses 15 randomly generated data examples having necessary features of BD and T test significance. Finally, the effectiveness and performance of the presented model are analyzed by a set of sensitivity analyses. The outcome of our study shows that H-2 is of higher efficiency.

Underwater image classification is a challenging task because of challenging underwater environment and lighting conditions. We propose a novel learning classifier system (LCS), which can classify large-size underwater images with promising accuracy, and acquire knowledge in interpretable format, by using a novel classification convolution autoencoder (CCAE). In proposed system, CCAE is designed as a hybrid network, which combines benefits of classification and autoencoder, to extract compressed non-trivial features. It is also used to decompress LCS generated rules to original input space. In order to evaluate effectiveness of proposed solution, experiments are conducted on selected underwater synsets of benchmark ImageNet dataset. Results are compared with famous CNN methods based on parameters such as accuracy, precision, recall and F-measure. Experiments show that proposed system can accurately classify large-size underwater images with promising accuracy and outperforms well-known deep CNN methods. It has also been observed that LCS generated rules are well generalized, accurate and interpretable.

Aiming at the shortcomings of quantum-behaved particle swarm optimization algorithm (QPSO), an improved quantum-behaved particle swarm optimization algorithm (IQPSO) is put forward, and the improved algorithm is applied in solving a kind of fuzzy portfolio selection problems. Firstly, a kind of portfolio models with fuzzy return rates and background risk is established followed by some necessary preparations of fuzzy theory. Then, in the improved algorithm, hybrid probability distribution strategy and contraction–expansion coefficient with nonlinear structure are chosen to enhance particle’s exploration ability, and premature prevention mechanism is used to maintain population diversity. Furthermore, the experimental results on 16 benchmark functions show that IQPSO has better convergence and robustness than PSO with inertia weight, QPSO and QPSO with a hybrid probability distribution in most cases. Finally, when solving a fuzzy portfolio model, IQPSO provides comparable and superior results compared with the other metaheuristics.

This article presents an improved version of the coyote optimization algorithm (COA) that is more compatible with nature. In the proposed algorithm, fitness-distance balance (FDB) and Levy flight were used to determine the social tendency of coyote packs and to develop a more effective model imitating the birth of new coyotes. The balanced search performance, global exploration capability, and local exploitation ability of the COA algorithm were enhanced, and the premature convergence problem resolved using these two methods. The performance of the proposed Levy roulette FDB-COA (LRFDBCOA) was compared with 28 other meta-heuristic search (MHS) algorithms to verify its effectiveness on 90 benchmark test functions in different dimensions. The proposed LRFDBCOA and the COA ranked, respectively, the first and the ninth, according to nonparametric statistical results. The proposed algorithm was applied to solve the AC optimal power flow (ACOPF) problem incorporating thermal, wind, and combined solar-small hydro powered energy systems. This problem is described as a constrained, nonconvex, and complex power system optimization problem. The simulation results showed that the proposed algorithm exhibited a definite superiority over both the constrained and highly complex real-world engineering ACOPF problem and the unconstrained convex/nonconvex benchmark problems. WOS:000625039600003 2-s2.0-85102027544

Small sample size (SSS) problems pose a tremendous challenge in modeling tasks due to insufficient training samples, especially in process industry where thousands of useless samples overwhelm very limited valuable samples, leading to deterioration on the prediction ability of trained models for key variables. In this study, the prediction ability to forecast models is enhanced by generating virtual samples. Considering the integrated effects of attributes, a new data augment approach, called ITNN-VSG, which integrates virtual sample generation (VSG) with input-training neural network (ITNN), was put forward to enlarge training datasets for improving the performance of forecasting models. In the absence of any available domain-specific knowledge about target models, a query-driven interpolation process was first developed to explore the overall tendency of data distribution in both sparse regions and dense regions. Second, an ITNN with fixed weights was used to calculate the input corresponding to the virtual output generated by the interpolation process. To validate the effectiveness of the proposed approach, several in silico experiments were carried out on a benchmark dataset from sinc(x) function, followed by a real-world application to purified terephthalic acid (PTA) solvent system. The experimental results demonstrated that the proposed approach outperformed other existing approaches such as mega-trend-diffusion and tree-based-trend-diffusion.

Due to its effective search mechanism, gravitational search algorithm (GSA) has become a very popular and robust tool for the global optimization in a very short span of time. The search mechanism of GSA is based on its two features, namely $$K_\mathrm{best}$$ archive and gravitational constant G. The $$K_\mathrm{best}$$ archive stores the best agents (solutions) at any evolutionary state and hence helps GSA for global search. Each agent interacts with exactly same agents of $$K_\mathrm{best}$$ archive without considering its current impact on the search process, which results a rapid loss of diversity, premature convergence and the high time complexity in GSA model. On the other hand, the exponentially decreasing behavior of G scales the step size of the agent. However, this scaling is same for all agents which may cause inappropriate step size for their next move, and therefore leads the swarm towards stagnation or sometimes skipping the true optima. To address these problems, an improved version of GSA called ‘A novel neighborhood archives embedded gravitational constant in GSA (NAGGSA)’ is proposed in this paper. In NAGGSA, we first propose two novel neighborhood archives for each agent which helps in increased diversified search with less time complexity. Secondly, a novel gravitational constant is proposed for each agent according to the distance-fitness based scaling mechanism. The performance of the proposed variant is tested over different suites of well-known benchmark test functions. Experimental results and statistical analyses reveal that NAGGSA remarkably outperforms the compared algorithms.

This paper describes a novel implicit fourth-order approximation for solving the 2D quasilinear elliptic partial differential equations on an irrational domain. In this technique, we use 9-grid points compact cell with half-step unequal mesh discretization in both x- and y-coordinates. We also study fourth-order explicit approximations for the solution of normal derivatives on an irrational domain. The proposed method has been extended to solve quasilinear elliptic equations in vector form. Stability analysis is discussed in order to verify the convergence of the proposed computational method. On applications, we solve several benchmark nonlinear elliptic problems including steady-state Burgers’ and Navier–Stokes equations. The outcome of numerical results is shown the reliability, accuracy and the stability character of the method even for high values of Re.

Redheaded Agama lizards attack their prey in a well-organized manner. This work models the dynamic foraging behaviour of Agama lizards and their effective way of capturing prey into a mathematical model named as artificial lizard search optimization (ALSO) algorithm. The idea is based on a recent study in which the researchers reported that the lizards control the swing of their tails in a measured manner to redirect angular momentum from their bodies to their tails, stabilizing body attitude in the sagittal plane. A balanced lumping (between body and tail angles) plays a significant role in capturing the prey in a shot. In formulating the optimization problem, a swarm of lizard are considered that are hunting for the prey. To study the performance of the proposed ALSO, it has been simulated. A comparative study is done with some well-known nature-inspired optimization techniques on classical unimodal, multimodal and other benchmark functions. Further, the algorithm is also tested on an object detection application. The result proves the effectiveness of the proposed ALSO algorithm over other nature-inspired state of the art.

The radio frequency identification (RFID) technology is widely used for object identification and tracking applications, which brings the most challenging RFID network planning (RNP) problem. However, existing RNP methods have some defects, such as the number of readers is uncertain and objectives conflict each other. In this paper, we propose a hybrid particle swarm optimization algorithm with K-means clustering and virtual forces for RNP, which is named as HPSO-RNP. HPSO-RNP can search the number of readers automatically and initialize the coordinates of readers through the K-means algorithms. Virtual force is integrated into the random movement to adjust the location of readers during the search process of PSO. Moreover, we consider four objective functions in a hierarchical manner. To compare HPSO-RNP with the existing method, extensive experiments are conducted on eight RNP benchmark datasets and the results validate that the performance of the proposed method is superior for planning RFID networks in terms of the number of readers, interference, power and load balance.

This paper considers a passive target localization problem based on the noisy time of arrival measurements obtained from multiple receivers and a single transmitter. The maximum likelihood (ML) estimator for this localization problem is formulated as a highly nonlinear and non-convex optimization problem, where conventional optimization methods are not suitable for solving such a problem. Consequently, this paper proposes an improved adaptive hybrid firefly differential evolution (AHFADE) algorithm, based on hybridization of firefly algorithm (FA) and differential evolution (DE) algorithm to estimate the unknown position of the target. The proposed AHFADE algorithm dynamically adjusts the control parameters, thus maintaining high population diversity during the evolution process. This paper aims to improve the accuracy of the global optimal solution by incorporating evolutionary operators of the DE in different searching stages of the FA. In this regard, an adaptive parameter is employed to select an appropriate mutation operator for achieving a proper balance between global exploration and local exploitation. In order to efficiently solve the ML estimation problem, this paper proposes the well-known semidefinite programming (SDP) method to convert the non-convex problem into a convex one. The simulation results obtained from the proposed AHFADE algorithm and well-known algorithms, such as SDP, DE and FA, are compared against Cramer–Rao lower bound (CRLB). The statistical analysis has been performed to compare the performance of the proposed AHFADE algorithm with several well-known algorithms on CEC2014 benchmark problems. The obtained simulation results show that the proposed AHFADE algorithm is more robust in high-noise environments compared to existing algorithms.

Genetic algorithm (GA) is used to solve a variety of optimization problems. Mutation operator also is responsible in GA for maintaining a desired level of diversity in the population. Here, a directional mutation operator is proposed for real-coded genetic algorithm (RGA) along with a directional crossover (DX) operator to improve its performance. These evolutionary operators use directional information to guide the search process in the most promising area of the variable space. The performance of an RGA with the proposed mutation operator and directional crossover (DX) is tested on six benchmark optimization problems of different complexities, and the results are compared to that of the RGAs with five other mutation schemes. The proposed IRGA is found to outperform other RGAs in terms of accuracy in the solutions, convergence rate, and computational time, which is established firmly through statistical analysis. Furthermore, the performance of the proposed IRGA is compared to that of a few recently proposed optimization algorithms. The proposed IRGA is seen to yield the superior results compared to that of the said techniques. It is also applied to solve five constrained engineering optimization problems, where again, it has proved its supremacy. The proposed mutation scheme using directional information leads to an efficient search, and consequently, a superior performance is obtained.

The selection of the mutation strategy for differential evolution (DE) algorithm plays an important role in the optimization performance, such as exploration ability, convergence accuracy and convergence speed. To improve these performances, an improved differential evolution algorithm with neighborhood mutation operators and opposition-based learning, namely NBOLDE, is developed in this paper. In the proposed NBOLDE, the new evaluation parameters and weight factors are introduced into the neighborhood model to propose a new neighborhood strategy. On this basis, a new neighborhood mutation strategy based on DE/current-to-best/1, namely DE/neighbor-to-neighbor/1, is designed in order to replace large-scale global mutation by local neighborhood mutation with high search efficiency. Then, a generalized opposition-based learning is employed to optimize the initial population and select the better solution between the current solution and reverse solution in order to approximate global optimal solution, which can amend the convergence direction, accelerate convergence, improve efficiency, enhance the stability and avoid premature convergence. Finally, the proposed NBOLDE is compared with four state-of-the-art DE variants by 12 benchmark functions with low-dimension and high-dimension. The experiment results indicate that the proposed NBOLDE has a faster convergence speed, higher convergence accuracy, and better optimization capabilities in solving high-dimensional complex functions.

The pattern of the object movement is periodic, but there occur few uncertainty issues during tracking and locating the movable object. Moreover, discovering the hidden periodic pattern from the historical moving object is a challenging task which may lead to an eventual periodic pattern. Therefore, a spatiotemporal database regarding probability is introduced to investigate the processing and also to detect probabilities concerning uncertainties. In this proposed approach, a periodic pattern tree miner is employed to find all eventual periodic patterns. In addition to this, a novel global pollination artificial fish swarm approach which is the integration of global flower pollination algorithm and artificial fish swarm algorithm is employed in the clustering process to obtain the best dense cluster. On the other hand, the novel global pollination artificial fish swarm approach provides a dynamic, high quality and an exact number of better clusters. We also presented the experimental analysis to obtain eventual periodic pattern mining by means of a modified frequent pattern tree, and the testing is done by utilizing the trucks and bus datasets. Then the comparative analysis is done with a sub-pattern tree to prove the memory usage and time consumption. The simulation results describe that the performances of global pollination artificial fish swarm approach provide better numerical efficiency on various 13 benchmark functions.

In this paper, a new population-based stochastic optimization algorithm called Hybrid Self-Adaptive Differential Evolution (HSADE) is proposed. The algorithm addresses unconstrained global optimization problems, exploring and combining the best features of some Differential Evolution (DE), obtaining a good balance between exploration and exploitation. These approaches are important for increasing the accuracy and efficiency of a population-based stochastic algorithm and for adapting the control parameter values during the optimization process. Further, they are crucial for increasing the convergence speed and reducing the risk of search stagnation. To verify the performance of the HSADE, 25 benchmark functions were tested presenting an optimal performance when compared to some state-of-the-art DEs algorithms. Furthermore, an experimental problem in an automotive sector, related to automatic internal combustion engine calibration, was used adjusting 300 decision variables. The HSADE achieved a reliable calibration, reducing the time required to perform approximately 90% when comparing to other optimization algorithms.

Opposition-based learning (OBL) is an effective strategy to enhance many optimization methods among which opposition-based differential evolution (ODE) is one of the successful variants. However, ODE is a strict point-to-point algorithm, which may cause those opposite solutions to be ignored who are close to, however, have a gap to more promising solutions in the neighborhood. It usually provides a relatively narrow search channel for the candidate solutions and cannot maintain well population diversity. Hence, it is necessary to broaden the search neighborhood of the opposite solutions to increase the possibility of seeking out an even better solution. Thus, a new approach, GODE, is proposed to implement a Gaussian perturbation operation around the opposite point to expand its search neighborhood. Three different self-adaptive standard deviation models are then proposed and compared in the Gaussian perturbation strategy. Subsequently, a multi-stage perturbation strategy with different sized neighborhood is adopted to balance exploration and exploitation during different evolutionary stages. GODE is firstly compared with DE and ODE on CEC2014 benchmark suite with dimension of 30, 50 and 100. Many recent state-of-the-art algorithms using OBL strategy are further conducted comparison with GODE. The experimental results and statistical comparison analysis demonstrated that GODE has better or equal competitive performance against the classical and recent competitors.

Handwritten word recognition is undoubtedly a challenging task due to various writing styles of individuals. So, lots of efforts are put to recognize handwritten words using efficient classifiers based on extracted features that rely on the visual appearance of the handwritten text. Due to numerous real-time applications, handwritten word recognition is an important research area which is seeking a lot of attention from researchers for the last 10 years. In this article, the authors have proposed a holistic approach and eXtreme Gradient Boosting (XGBoost) technique to recognize offline handwritten Gurumukhi words. In this direction, four state-of-the-art features like zoning, diagonal, intersection & open-end points and peak extent features have been considered to extract discriminant features from the handwritten word digital images. The proposed approach is evaluated on a public benchmark dataset of Gurumukhi script that comprises 40,000 samples of handwritten words. Based on extracted features, the words are classified into one of the 100 classes based on XGBoost technique. Effectiveness of the system is assessed based on several evaluation parameters like CPU elapsed time, accuracy, precision, recall, F1-score and area under curve (AUC). XGBoost technique attained the best results of accuracy (91.66%), recall (91.66%), precision (91.39%), F1-score (91.14%) and AUC (95.66%) using zoning features based on 90% data as the training set and remaining 10% data as the testing set. The comparison of the proposed approach with the existing approaches has also been done which reveals the significance of the XGBoost technique comparatively.

Due to advances in information technology, data collection is becoming much easier. Clustering is an important technique for exploring data structures used in many fields, such as customer segmentation, image recognition, social science, and so on. However, in real-world applications, there are a lot of noises or outliers which will seriously influence the clustering performance in the dataset. Besides, the clustering results are susceptible to the initial centroids and algorithm parameters. To overcome the influence of outliers on clustering results, this study combines the advantages of probability c-means and fuzzy c-ordered means to propose a fuzzy possibilistic c-ordered means (FPCOM) algorithm. In order to solve the problem of parameters and initial centroids determination, this study employs a sine cosine algorithm (SCA) combined with FPCOM to improve the clustering results. The proposed algorithm is named SCA-FPCOM algorithm. Ten benchmark datasets collected from the UCI machine repository were used to validate the proposed algorithm in terms of adjusted rand index and the Silhouette coefficient. According to the experimental results, the SCA-FPCOM algorithm can obtain better results than other algorithms.

Monarch butterfly optimization (MBO), which is a simple and widely used algorithm, has some limitations, such as utilizing the obtained experiential knowledge about the search space inefficiently, the lack of exploration, and being rotational variance. This paper proposes a new variation of MBO, which is called knowledge-based MBO (KMBO), to address these limitations. KMBO is proposed by introducing new operators that are linearized and can utilize the population's experimental knowledge. Furthermore, KMBO adopts the re-initialization operator to enhance the exploration ability and increase the diversity of the population. To verify KMBO’s performance, it is tested on 23 well-known optimization benchmark functions and compared with MBO and five other state-of-the-art evolutionary algorithms. Experimental results confirm the superior performance of our proposed algorithm compared with MBO in terms of solution accuracy and convergence speed. Also, results demonstrate that KMBO performs better than or provides competitive performance with the other six algorithms. In addition, the real-world application of KMBO on clustering optimization is presented. The results prove that KMBO is applicable to solve real-world problems and achieve superior results.

To improve ant colony optimization (ACO) for traveling salesman problem (TSP), its two main strategies which are tour construction and pheromone updating have been modified, and one modified ACO (MACO) has been proposed. For the first strategy (tour construction strategy), one new method to construct tours by combining paths of two meeting ants has been applied. And for second strategy (pheromone updating strategy), one new method to polarize pheromone density of all paths has been proposed. Based on the applications for 40 standard benchmark TSP instances (datasets) ranging from 29 to 13,509 cities, the good performance of the MACO is verified. To verify the MACO deeply, based on the applications for some standard TSP instances, the computing results of MACO are compared with three typical state-of-the-art algorithms based on ACO methods. Moreover, based on the applications for some standard TSP instances, the computing results of MACO are compared with 10 state-of-the-art metaheuristic algorithms. The comparison studies show that the MACO can attain the optimal solution with higher accuracy, no matter how complicated the TSPs are. And its performance is the best, comparing to all state-of-the-art algorithms. At last, two new strategies used in MACO have been analyzed comprehensively by the applications for 25 TSPs. The results show that the first strategy is mainly used to improve the computing efficiency, and the second one is mainly used to improve the computing effect.

Extreme learning machine (ELM) is an emerging machine learning algorithm for training single-hidden-layer feedforward networks (SLFNs). The salient features of ELM are that its hidden layer parameters can be generated randomly, and only the corresponding output weights are determined analytically through the least-square manner, so it is easier to be implemented with faster learning speed and better generalization performance. As the online version of ELM, online sequential ELM (OS-ELM) can deal with the sequentially coming data one by one or chunk by chunk with fixed or varying chunk size. However, OS-ELM cannot function well in dealing with dynamic modeling problems due to the data saturation problem. In order to tackle this issue, in this paper, we propose a novel OS-ELM, named adaptive OS-ELM (AOS-ELM), for enhancing the generalization performance and dynamic tracking capability of OS-ELM for modeling problems in nonstationary environments. The proposed AOS-ELM can efficiently reduce the negative effects of the data saturation problem, in which approximate linear dependence (ALD) and a modified hybrid forgetting mechanism (HFM) are adopted to filter the useless new data and alleviate the impacts of the outdated data, respectively. The performance of AOS-ELM is verified using selected benchmark datasets and a real-world application, i.e., device-free localization (DFL), by comparing it with classic ELM, OS-ELM, FOS-ELM, and DU-OS-ELM. Experimental results demonstrate that AOS-ELM can achieve better performance.