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Unconstrained continuous large-scale global optimization (LSGO) is still a challenging task for a wide range of modern metaheuristic approaches. A cooperative coevolution approach is a good tool for increasing the performance of an evolutionary algorithm in solving high-dimensional optimization problems. However, the performance of cooperative coevolution approaches for LSGO depends significantly on the problem decomposition, namely, on the number of subcomponents and on how variables are grouped in these subcomponents. Also, the choice of the population size is still an open question for population-based algorithms. This paper discusses a method for selecting the number of subcomponents and the population size during the optimization process ("on fly") from a predefined pool of parameters. The selection of the parameters is based on their performance in the previous optimization steps. The main goal of the study is the improvement of coevolutionary decomposition-based algorithms for solving LSGO problems. In this paper, we propose a novel self-adapt evolutionary algorithm for solving continuous LSGO problems. We have tested this algorithm on 15 optimization problems from the IEEE LSGO CEC'2013 benchmark suite. The proposed approach, on average, outperforms cooperative coevolution algorithms with a static number of subcomponents and a static number of individuals. [ABSTRACT FROM AUTHOR]

In this paper, a new stochastic optimization algorithm is introduced, called Driving Training-Based Optimization (DTBO), which mimics the human activity of driving training. The fundamental inspiration behind the DTBO design is the learning process to drive in the driving school and the training of the driving instructor. DTBO is mathematically modeled in three phases: (1) training by the driving instructor, (2) patterning of students from instructor skills, and (3) practice. The performance of DTBO in optimization is evaluated on a set of 53 standard objective functions of unimodal, high-dimensional multimodal, fixed-dimensional multimodal, and IEEE CEC2017 test functions types. The optimization results show that DTBO has been able to provide appropriate solutions to optimization problems by maintaining a proper balance between exploration and exploitation. The performance quality of DTBO is compared with the results of 11 well-known algorithms. The simulation results show that DTBO performs better compared to 11 competitor algorithms and is more efficient in optimization applications. [ABSTRACT FROM AUTHOR]

Golden jackal optimization (GJO) is an effective metaheuristic algorithm that imitates the cooperative hunting behavior of the golden jackal. However, since the update of the prey's position often depends on the male golden jackal and there is insufficient diversity of golden jackals in some cases, it is prone to falling into a local optimal optimum. In order to address these drawbacks of GJO, this paper proposes an improved algorithm, called a hybrid GJO and golden sine (S) algorithm (Gold-SA) with dynamic lens-imaging (L) learning (LSGJO). First, this paper proposes novel dual golden spiral update rules inspired by Gold-SA. These rules give GJO the ability to think like a human (Gold-SA), making the golden jackal more intelligent in the process of preying, and improving the ability and efficiency of optimization. Second, a novel nonlinear dynamic decreasing scaling factor is introduced into the lens-imaging learning operator to maintain the population diversity. The performance of LSGJO is verified through 23 classical benchmark functions and 3 complex design problems in real scenarios. The experimental results show that LSGJO converges faster and more accurately than 11 state-of-the-art optimization algorithms, the global and local search ability has improved significantly, and the proposed algorithm has shown superior performance in solving constrained problems. [ABSTRACT FROM AUTHOR]

Classification is used to categorize data and produce decisions for several domains. To improve the accuracy of classification, researchers have tended to hybridize the neural network with other metaheuristic algorithms in order to better exploit and explore the search space and thereby solve many different classification problems in an effective manner. The hybridization of algorithms is now commonplace and has resulted in the creation of novel methods that are more effective in comparison with those that employ a sole algorithm. Therefore, in this paper, a hybridization approach is employed to utilize the African buffalo optimization (ABO) algorithm as an optimizer to adjust the weights of the probabilistic neural network (PNN). The effectiveness of the proposed (ABO-PNN) method is investigated by applying it to several different classification problems. The efficiency of the ABO algorithm is assessed based on the PNN training results produced and its performance is compared with that of different types of optimization algorithm. The performance of the proposed algorithm in terms of classification accuracy is tested on 11 benchmark datasets. The results show that the ABO is better than the firefly algorithm (FA) in terms of both classification accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

The metaheuristic optimization algorithms are relatively new optimization algorithms introduced to solve optimization problems in recent years. For example, the firefly algorithm (FA) is one of the metaheuristic algorithms inspired by the fireflies' flashing behavior. However, its weakness in terms of exploration and early convergence has been pointed out. In this paper, two approaches were proposed to improve the FA. In the first proposed approach, a new improved opposition-based learning FA (IOFA) method was presented to accelerate the convergence and improve the FA's exploration capability. In the second proposed approach, a symbiotic organisms search (SOS) algorithm improved the exploration and exploitation of the first approach; two new parameters set these two goals, and the second approach was named IOFASOS. The purpose of the second method is that in the process of the SOS algorithm, the whole population is effective in the IOFA method to find solutions in the early stages of implementation, and with each iteration, fewer solutions are affected in the population. The experiments on 24 standard benchmark functions were conducted, and the first proposed approach showed a better performance in the small and medium dimensions and exhibited a relatively moderate performance in the higher dimensions. In contrast, the second proposed approach was better in increasing dimensions. In general, the empirical results showed that the two new approaches outperform other algorithms in most mathematical benchmarking functions. Thus, The IOFASOS model has more efficient solutions. [ABSTRACT FROM AUTHOR]

The introduction of cloud computing has brought about significant developments in information technology. Users can benefit from the multitude of cloud technology services only by connecting to the internet. In cloud computing, load balancing is the fundamental issue that has challenged experts in this research area. Load balancing helps increase user satisfaction and enhance systems' productivity through efficient and fair work assignments between computing resources. Besides, maintaining a load balancing among resources would be difficult because the resources are usually distributed in a heterogeneous way. Many load-balancing methods try to solve this problem by the metaheuristics algorithm, and each of them attempted to enhance the operation and efficiency of systems. In this paper, Grey wolf optimization (GWO) algorithm has been used based on the resource reliability capability to maintain proper load balancing. In this method, first, the GWO algorithm tries to find the unemployed or busy nodes and, after discovering this node, try to calculate each node's threshold and fitness function. The results of simulation in CloudSim showed that the costs and response time in the proposed method are less than the other methods, and the obtained solutions are ideal. [ABSTRACT FROM AUTHOR]

One of the useful knowledge representation tools, which can describe the joint probability distribution between some random variables with a graphical model and can be trained by a dataset, is the Bayesian network (BN). A BN is composed of a network structure and a conditional probability distribution table for each node. Discovering an optimal BN structure is an NP‐hard optimization problem that various meta‐heuristic algorithms are applied to solve this problem by researchers. The genetic algorithms, ant colony optimization, evolutionary programming, artificial bee colony, and bacterial foraging optimization are some of the meta‐heuristic methods to solve this problem using a dataset. Most of these methods are applying a scoring metric to generate the best network structure from a set of candidates. A Fixed Structure Learning Automata‐Based (FSLA‐B) algorithm is presented in this paper to solve the structure learning problem of BNs. There is a fixed structure learning automaton for each pair of vertices in the BN's graph structure in the proposed algorithm. The action of this automaton determines the presence and direction of an edge between the vertices. The proposed algorithm performs a guided search procedure using the FSLA and escapes from local optimums. Several datasets are utilised in this paper to evaluate the performance of the proposed algorithm. By performing various experiments, multiple meta‐heuristic algorithms are compared with the introduced new one. The obtained results represented that the proposed algorithm could produce competitive results and find the near‐optimal solution for the BN structure learning problem. [ABSTRACT FROM AUTHOR]

Surrogate-assisted meta-heuristic algorithms have shown good performance to solve the computationally expensive problems within a limited computational resource. Compared to the method that only one surrogate model is utilized, the surrogate ensembles have shown more efficiency to get a good optimal solution. In this paper, we propose a bi-stage surrogate-assisted hybrid algorithm to solve the expensive optimization problems. The framework of the proposed method is composed of two stages. In the first stage, a number of global searches will be conducted in sequence to explore different sub-spaces of the decision space, and the solution with the maximum uncertainty in the final generation of each global search will be evaluated using the exact expensive problems to improve the accuracy of the approximation on corresponding sub-space. In the second stage, the local search is added to exploit the sub-space, where the best position found so far locates, to find a better solution for real expensive evaluation. Furthermore, the local and global searches in the second stage take turns to be conducted to balance the trade-off of the exploration and exploitation. Two different meta-heuristic algorithms are, respectively, utilized for the global and local search. To evaluate the performance of our proposed method, we conduct the experiments on seven benchmark problems, the Lennard–Jones potential problem and a constrained test problem, respectively, and compare with five state-of-the-art methods proposed for solving expensive problems. The experimental results show that our proposed method can obtain better results, especially on high-dimensional problems. [ABSTRACT FROM AUTHOR]

The difficulty and complexity of the real-world numerical optimization problems has grown manifold, which demands efficient optimization methods. To date, various metaheuristic approaches have been introduced, but only a few have earned recognition in research community. In this paper, a new metaheuristic algorithm called Archimedes optimization algorithm (AOA) is introduced to solve the optimization problems. AOA is devised with inspirations from an interesting law of physics Archimedes' Principle. It imitates the principle of buoyant force exerted upward on an object, partially or fully immersed in fluid, is proportional to weight of the displaced fluid. To evaluate performance, the proposed AOA algorithm is tested on CEC'17 test suite and four engineering design problems. The solutions obtained with AOA have outperformed well-known state-of-the-art and recently introduced metaheuristic algorithms such genetic algorithms (GA), particle swarm optimization (PSO), differential evolution variants L-SHADE and LSHADE-EpSin, whale optimization algorithm (WOA), sine-cosine algorithm (SCA), Harris' hawk optimization (HHO), and equilibrium optimizer (EO). The experimental results suggest that AOA is a high-performance optimization tool with respect to convergence speed and exploration-exploitation balance, as it is effectively applicable for solving complex problems. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/79822-archimedes-optimization-algorithm [ABSTRACT FROM AUTHOR]

Tree-Seed Algorithm is a kind of swarm intelligence optimization algorithm. It is used to solve various problems widely, but it still has some shortcomings need to be overcame, such as imbalance between exploration and exploitation, local stagnation, premature convergence, and so on. In this study, an enhanced meta-heuristic optimization algorithm, called Migration Tree-Seed Algorithm (MTSA), is proposed inspiring by Grey Wolf Optimizer (GWO). The hierarchical gravity learning and random-based migration mechanisms are introduced to overcome the intrinsic defects of the basic TSA. Firstly, hierarchy mechanism ensures the tree migration to guide the seed generation avoiding the local stagnation. Secondly, random-based migration mechanism increases the seed diversity to improve the exploration ability. Finally, the coordinated update of the two mechanisms actuate a suitable trade-off between exploration ans exploitation. We use IEEE CEC 2014 benchmark functions to compare MTSA with basic TSA, the TSA variants (STSA, EST-TSA, fb_TSA), GWO, ABC, SCA, BOA, JAYA and RSA. MTSA is subsequently applied to three classical engineering design problems reported in the specialized literature. Both results show that the MTSA is very competitive and effective compared with other well-known meta-heuristics, proving its excellent applicability in real-world challenging problems with unknown search spaces. • A modified MTSA is proposed based on the hierarchy mechanism of the GWO and random-based migration mechanism. • Procedure of updating seeds positions allows obtaining neighbouring solutions in terms of α , β , and δ trees for mostly promoting exploitation. • The proposed enhanced MTSA is evaluated using 30 benchmark functions in IEEE CEC 2014 and applying in three engineering problems. • The experimental results were superior to some well-known or variant algorithms in continuous optimization domain. [ABSTRACT FROM AUTHOR]

• A Brief Review of Multi-Objective Optimization with Algorithms and Trends. • A new multi-objective algorithm inspired by lightning and Lichtenberg Figures. • The first hybrid multi-objective meta-heuristic: trajectory and population - based. • Lichtenberg patterns presents advantageous convergence-coverage balance. • Tested on complex functions-problems and compared with renowned MO meta-heuristics. With the advancement of computing and inspired by optimal phenomena found in nature, several algorithms capable of solving complex engineering problems have been developed. This work details the development of the Multi-objective Lichtenberg Algorithm, the version capable of dealing with more than one objective of a newly created meta-heuristic inspired by the propagation of radial intra-cloud lightning and Lichtenberg figures. The algorithm considers in its optimization routine a hybrid system based on both the population and the trajectory, demonstrating a great capacity for exploration and exploitation since it distributes points to be evaluated in the objective function through a Lichtenberg figure that is shot in sizes and different rotations at each iteration. The Multi-objective Lichtenberg Algorithm (MOLA) is the first hybrid multi-objective meta-heuristic and was tested against traditional and recent meta-heuristics using famous and complex test function groups and also constrained complex engineering problems. Regarding important metrics for convergence and coverage assessment, the Multi-objective Lichtenberg Algorithm proved to be a promising multi-objective algorithm surpassing others traditional and recent algorithms such as NSGA-II, MOPSO, MOEA/D, MOGOA and MOGWO with expressive values of convergence and maximum spread. [ABSTRACT FROM AUTHOR]

In this paper, a new compact algorithm is proposed. Two sinusoidal formulas are used to automatically adjust the crossover rate and the mutation scaling factor in the compact Differential Evolution (cDE) metaheuristic. The proposed algorithm, called Compound Sinusoidal cDE, CScDE, is compared to seven state-of-the-art compact algorithms on the well-known BBOB test-bed, the CEC-2014 test suite for continuous optimisation, as well as five real-world optimisation problems chosen from the CEC-2011 benchmarks. The CScDE algorithm outperformed its competitors for most problem categories and over most dimensions. It is also compared to some well-established population-based metaheuristics. • A compact compound sinusoidal differential evolution, CScDE, is proposed. • CScDE uses sinusoidal formulas to adjust the parameters of compact DE. • Both binomial and exponential crossover are tested. • CScDE is applied on 89 reference problems with several dimensions. • CScDE outperformed state-of-the-art compact algorithms. [ABSTRACT FROM AUTHOR]

Metaheuristic optimization methods have been implemented for solving several problems. However, when it is required to implement those algorithms in hardware to run online, there is not enough information. This paper describes how could be programmed and implemented those optimization algorithms. Moreover, a complete evaluation is shown as well as a comparative study regarding the most important metaheuristic optimization algorithms. Thus, this paper presents a comparison between five optimization algorithms implemented into a cRIO field-programmable gate array (LabVIEW FPGA) NI-9030 of National Instruments T M (NI). The algorithms implemented were particle swarm optimization (PSO), bat algorithm (BA), grey wolf optimizer (GWO), earthquake algorithm (EA), and Nelder–Mead algorithm (NM). To analyze hardware device utilization and execution time by each algorithm, synthesis results were presented. In addition, a set of ten benchmark functions was selected to compare performance between algorithms. Results show the feasibility of this approach for NI FPGA hardware. From device utilization results, GWO presents the lowest placed usage (29%) while NM shows the fastest execution time (0.683 ms). Nevertheless, PSO, GWO and EA show better performance between benchmark functions due their exploration characteristics which make possible to find a better solution. [Display omitted] • Information about optimization implementation in hardware to run online is not enough • A hardware implementation of five optimization algorithms is described. • Five optimization algorithms were implemented into a cRIO LabVIEW FPGA. • Complete and comparative studies of those optimization algorithms are presented. • EA and GWO optimization algorithms are first time implemented into a FPGA. [ABSTRACT FROM AUTHOR]

Differential evolution and its variants have already proven their worth in the field of evolutionary optimization techniques. This study further enhances the success history-based adaptive differential evolution (SHADE) by hybridizing it with a modified Whale optimization algorithm (WOA). In the new algorithm, the two algorithms, SHADE and modified WOA, carry out the search process independently and share information like the global best solution and whole population and thus guides both the algorithms to explore and exploit new promising areas in the search space. It also reduces the chance of being trapped in local optima and stagnation. The proposed algorithm (SHADE–WOA) is tested, evaluating CEC 2017 functions using dimensions 30, 50, and 100. The results are compared with modified DE algorithms, namely SaDE, SHADE, LSHADE, LSHADE-SPACMA, and LSHADE-cnEpSin, also with modified WOA algorithms, namely ACWOA, AWOA, IWOA, HIWOA, and MCSWOA. The new algorithm's efficiency in solving real-world problems is examined by solving two unconstrained and four constrained engineering design problems. The performance is verified statistically using non-parametric statistical tests like Friedman's test and Wilcoxon's test. Analysis of numerical results, convergence analysis, diversity analysis, and statistical analysis ensures the enhanced performance of the proposed SHADE–WOA. • Introduced hybrid SHADE–WOA algorithm using SHADE and modified WOA. • A new phase "co-operative hunting strategy" is used on WOA. • A new parameter α is introduced in WOA for balancing exploration and exploitation. • Population information is shared among the algorithms to guide the search processes. • Compared with latest DE and WOA variants using CEC 2017 function set. [ABSTRACT FROM AUTHOR]

The optimal power flow (OPF) is a vital tool for optimizing the control parameters of a power system by considering the desired objective functions subject to system constraints. Metaheuristic algorithms have been proven to be well-suited for solving complex optimization problems. The whale optimization algorithm (WOA) is one of the well-regarded metaheuristics that is widely used to solve different optimization problems. Despite the use of WOA in different fields of application as OPF, its effectiveness is decreased as the dimension size of the test system is increased. Therefore, in this paper, an effective whale optimization algorithm for solving optimal power flow problems (EWOA-OPF) is proposed. The main goal of this enhancement is to improve the exploration ability and maintain a proper balance between the exploration and exploitation of the canonical WOA. In the proposed algorithm, the movement strategy of whales is enhanced by introducing two new movement strategies: (1) encircling the prey using Levy motion and (2) searching for prey using Brownian motion that cooperate with canonical bubble-net attacking. To validate the proposed EWOA-OPF algorithm, a comparison among six well-known optimization algorithms is established to solve the OPF problem. All algorithms are used to optimize single- and multi-objective functions of the OPF under the system constraints. Standard IEEE 6-bus, IEEE 14-bus, IEEE 30-bus, and IEEE 118-bus test systems are used to evaluate the proposed EWOA-OPF and comparative algorithms for solving the OPF problem in diverse power system scale sizes. The comparison of results proves that the EWOA-OPF is able to solve single- and multi-objective OPF problems with better solutions than other comparative algorithms. [ABSTRACT FROM AUTHOR]

This manuscript proposes a new metaheuristic optimization algorithm for solving the problems related to constraint optimization. The proposed algorithm is based on a nature-inspired algorithm like a lightning search algorithm and differential evolution algorithm. The proposed algorithm consists of two stages. In the first/exploitation/local stage, the fitness values are calculated by using a lightning search algorithm, the inclusion of weight factor in the lightning search algorithm, and differential evolution algorithm using the same population. In the second/global/exploration stage, the minimum value of fitness for each row population by the implementation of the above three algorithms is updated with the population. The first and second stage continues until certain criteria are achieved. The final minimum value is the optimized result. Validation of the proposed methodology is performed by using 60 benchmark functions. The proposed methodology is compared with seven other well-known algorithms namely the lightning search algorithm, differential evolution algorithm cuckoo search algorithm, particle swarm optimization algorithm, seagull optimization algorithm, chimp optimization algorithm, and mayfly algorithm by computing mean, standard deviation, best and worst value for 60 benchmark functions. The proposed methodology is also validated by implementing it in seven real-time constraint optimized problems. Furthermore, the efficiency of the proposed technique has been validated statistically for unimodal and multimodal test functions. The results show a better performance of the proposed optimized algorithm compared to other algorithms. [ABSTRACT FROM AUTHOR]

• An innovation on the algorithm has been proposed to improve the performance of TSA. • The proposed method is based on the roulette wheel selection method of the GA. • Experiments of the performance of R-TSA on test functions have been carried out. • A superior performance of the proposed approaches is proved in the experiments. The Tree seed algorithm (TSA) is a metaheuristic algorithm inspired by the relationship between trees and seeds. It has been proposed for very low-dimensional optimization problems and achieved promising results compared to other optimization algorithms. However, it has been determined that the performance of the TSA is lower than other algorithms for high-dimensional problems. This is due to the fact that TSA cannot scan the local optimum and search space effectively. A new TSA based on the roulette wheel strategy (R-TSA) has been proposed in this study to eliminate this disadvantage and solve high-dimensional problems. With this strategy, the trees selected at the seed production phase of TSA were diversified and the locations of the seeds were updated to prevent it from being stuck in local minima, with the aim of scanning the search space more effectively. The R-TSA was applied to high-dimensional (20, 50 and 100) benchmark functions and both convergence and box-plot graphs were obtained by using the results of these functions. Moreover, current algorithms in published literature were applied to these functions and the results obtained were compared with the R-TSA. It was observed from the analysis results that the performance of the R-TSA was higher than that of TSA. [ABSTRACT FROM AUTHOR]

In recent years, new metaheuristic algorithms have been developed taking as reference the inspiration on biological and natural phenomena. This nature-inspired approach for algorithm development has been widely used by many researchers in solving optimization problems. These algorithms have been compared with the traditional ones and have demonstrated to be superior in many complex problems. This paper attempts to describe the algorithms based on nature, which are used in optimizing fuzzy clustering in real-world applications. We briefly describe the optimization methods, the most cited ones, nature-inspired algorithms that have been published in recent years, authors, networks and relationship of the works, etc. We believe the paper can serve as a basis for analysis of the new area of nature and bio-inspired optimization of fuzzy clustering. [ABSTRACT FROM AUTHOR]

Several population-based metaheuristic optimization algorithms have been proposed in the last decades, none of which are able either to outperform all existing algorithms or to solve all optimization problems according to the No Free Lunch (NFL) theorem. Many of these algorithms behave effectively, under a correct setting of the control parameter(s), when solving different engineering problems. The optimization behavior of these algorithms is boosted by applying various strategies, which include the hybridization technique and the use of chaotic maps instead of the pseudo-random number generators (PRNGs). The hybrid algorithms are suitable for a large number of engineering applications in which they behave more effectively than the thoroughbred optimization algorithms. However, they increase the difficulty of correctly setting control parameters, and sometimes they are designed to solve particular problems. This paper presents three hybridizations dubbed HYBPOP, HYBSUBPOP, and HYBIND of up to seven algorithms free of control parameters. Each hybrid proposal uses a different strategy to switch the algorithm charged with generating each new individual. These algorithms are Jaya, sine cosine algorithm (SCA), Rao's algorithms, teaching-learning-based optimization (TLBO), and chaotic Jaya. The experimental results show that the proposed algorithms perform better than the original algorithms, which implies the optimal use of these algorithms according to the problem to be solved. One more advantage of the hybrid algorithms is that no prior process of control parameter tuning is needed. [ABSTRACT FROM AUTHOR]