An Improved Moth-Flame Optimization algorithm with hybrid search phase

Improved moth-flame algorithm based on cat chaotic and dynamic cosine factor

The moth-flame algorithm shows some shortcomings in solving the complex problem of optimization, such as insufficient population diversity and unbalanced search ability. In this paper, an IMFO (Improved Moth-Flame Optimization) algorithm is proposed to be applied in solving the optimization problem of function. First, cat chaotic mapping is used to generate the initial position of moth to improve the population diversity. Second, cosine inertia weight is introduced to balance the global and local search abilities of the algorithm. Third, the memory information in the particle swarm algorithm is introduced into the iterative process of the algorithm to speed up the convergence of the population. Finally, Gaussian mutation strategy is used in the current optimal solution to avoid the algorithm from falling into the local optimum. Simulation experiments are conducted on 11 benchmark test functions, compared with other improved MFO (Moth-Flame Optimization) algorithms and classical optimization algorithms. The results show that the IMFO has higher accuracy and stability in solving the above-mentioned test functions. The proposed algorithm is experimented and verified by optimizing the KELM (Kernel Extreme Learning Machine) in an engineering example and exhibits a better optimization performance.

Self-adaptive moth flame optimizer combined with crossover operator and Fibonacci search strategy for COVID-19 CT image segmentation

The COVID-19 is one of the most significant obstacles that humanity is now facing. The use of computed tomography (CT) images is one method that can be utilized to recognize COVID-19 in early stage. In this study, an upgraded variant of Moth flame optimization algorithm (Es-MFO) is presented by considering a nonlinear self-adaptive parameter and a mathematical principle based on the Fibonacci approach method to achieve a higher level of accuracy in the classification of COVID-19 CT images. The proposed Es-MFO algorithm is evaluated using nineteen different basic benchmark functions, thirty and fifty dimensional IEEE CEC'2017 test functions, and compared the proficiency with a variety of other fundamental optimization techniques as well as MFO variants. Moreover, the suggested Es-MFO algorithm's robustness and durability has been evaluated with tests including the Friedman rank test and the Wilcoxon rank test, as well as a convergence analysis and a diversity analysis. Furthermore, the proposed Es-MFO algorithm resolves three CEC2020 engineering design problems to examine the problem-solving ability of the proposed method. The proposed Es-MFO algorithm is then used to solve the COVID-19 CT image segmentation problem using multi-level thresholding with the help of Otsu's method. Comparison results of the suggested Es-MFO with basic and MFO variants proved the superiority of the newly developed algorithm.

MMKE: Multi-trial vector-based monkey king evolution algorithm and its applications for engineering optimization problems

Monkey king evolution (MKE) is a population-based differential evolutionary algorithm in which the single evolution strategy and the control parameter affect the convergence and the balance between exploration and exploitation. Since evolution strategies have a considerable impact on the performance of algorithms, collaborating multiple strategies can significantly enhance the abilities of algorithms. This is our motivation to propose a multi-trial vector-based monkey king evolution algorithm named MMKE. It introduces novel best-history trial vector producer (BTVP) and random trial vector producer (RTVP) that can effectively collaborate with canonical MKE (MKE-TVP) using a multi-trial vector approach to tackle various real-world optimization problems with diverse challenges. It is expected that the proposed MMKE can improve the global search capability, strike a balance between exploration and exploitation, and prevent the original MKE algorithm from converging prematurely during the optimization process. The performance of the MMKE was assessed using CEC 2018 test functions, and the results were compared with eight metaheuristic algorithms. As a result of the experiments, it is demonstrated that the MMKE algorithm is capable of producing competitive and superior results in terms of accuracy and convergence rate in comparison to comparative algorithms. Additionally, the Friedman test was used to examine the gained experimental results statistically, proving that MMKE is significantly superior to comparative algorithms. Furthermore, four real-world engineering design problems and the optimal power flow (OPF) problem for the IEEE 30-bus system are optimized to demonstrate MMKE's real applicability. The results showed that MMKE can effectively handle the difficulties associated with engineering problems and is able to solve single and multi-objective OPF problems with better solutions than comparative algorithms.

Hybridizing slime mould algorithm with simulated annealing algorithm: a hybridized statistical approach for numerical and engineering design problems

The existing slime mould algorithm clones the uniqueness of the phase of oscillation of slime mould conduct and exhibits slow convergence in local search space due to poor exploitation phase. This research work exhibits to discover the best solution for objective function by commingling slime mould algorithm and simulated annealing algorithm for better variation of parameters and named as hybridized slime mould algorithm-simulated annealing algorithm. The simulated annealing algorithm improves and accelerates the effectiveness of slime mould technique as well as assists to take off from the local optimum. To corroborate the worth and usefulness of the introduced strategy, nonconvex, nonlinear, and typical engineering design difficulties were analyzed for standard benchmarks and interdisciplinary engineering design concerns. The proposed technique version is used to evaluate six, five, five unimodal, multimodal and fixed-dimension benchmark functions, respectively, also including 11 kinds of interdisciplinary engineering design difficulties. The technique's outcomes were compared to the results of other on-hand optimization methods, and the experimental results show that the suggested approach outperforms the other optimization techniques.

A new imperialist competitive algorithm with spiral rising mechanism for solving path optimization problems

Intelligent optimization algorithms have now become important means for solving global optimization problems. The imperialist competitive algorithm (ICA) is a nature-inspired meta-heuristic algorithm that imitates social behavior. ICA has been widely used in optimization problems, however, ICA tends to fall into a local optimal solution because of its fast convergence speed, which may lead to premature convergence when solving optimization problems. To solve these problems, a new improved ICA algorithm is proposed. Based on the original ICA algorithm, the theory of spiral rising is introduced to enlarge the search space and enhance the global search ability of the algorithm based on ensuring the necessary speed of convergence. In this paper, the improved optimization algorithm is applied to 19 classical benchmark functions, and the improved ICA is applied to the robot path optimization problems to solve the optimal path. The improved ICA algorithm improves the optimization ability and algorithm stability.

Moth Flame Optimization: Theory, Modifications, Hybridizations, and Applications

The Moth flame optimization (MFO) algorithm belongs to the swarm intelligence family and is applied to solve complex real-world optimization problems in numerous domains. MFO and its variants are easy to understand and simple to operate. However, these algorithms have successfully solved optimization problems in different areas such as power and energy systems, engineering design, economic dispatch, image processing, and medical applications. A comprehensive review of MFO variants is presented in this context, including the classic version, binary types, modified versions, hybrid versions, multi-objective versions, and application part of the MFO algorithm in various sectors. Finally, the evaluation of the MFO algorithm is presented to measure its performance compared to other algorithms. The main focus of this literature is to present a survey and review the MFO and its applications. Also, the concluding remark section discusses some possible future research directions of the MFO algorithm and its variants.

A Computational Intelligence Hybrid Algorithm Based on Population Evolutionary and Neural Network Learning for the Crude Oil Spot Price Prediction

This research attempts to reinforce the cultivating expression of radial basis function neural network (RBFnet) through computational intelligence (CI) and swarm intelligence (SI) learning methods. Consequently, the artificial immune system (AIS) and ant colony optimization (ACO) approaches are utilized to cultivate RBFnet for function approximation issue. The proposed hybridization of AIS and ACO approaches optimization (HIAO) algorithm combines the complementarity of exploitation and exploration to realize problem solving. It allows the solution domain having the advantages of intensification and diversification, which further avoids the situation of immature convergence. In addition, the empirical achievements have confirmed that the HIAO algorithm not only obtained the best accurate function approximation for theoretically standard nonlinear problems, it can be further applied on the instance solving for practical crude oil spot price prediction.

Optimal Scheduling of Regional Combined Heat and Power System Based on Improved MFO Algorithm

Due to the inflexibility of cogeneration power plants and the uncertainty of wind power production, the excess power of the distribution network brings challenges to the power grid operation. This paper introduced an improved moth-flame optimization algorithm to meet the challenge of energy complementary dispatching. The proposed algorithm adopts three effective strategies, namely inertia weight, unified initialization, and the spiral position update strategy, which maintains a strong global search ability and a potent compromise between global and local search. The effectiveness of the proposed method was evaluated by benchmark functions. Furthermore, the proposed method was applied to combine heat and power system operation problems and economic dispatch in light load and wind power unpredictability. In order to verify the robustness of the algorithm and solve the complex constraints of power systems under extreme conditions, three different cases had been discussed. The experimental findings indicate that the proposed algorithm shows better performances in terms of convergence speed, ability to escape from a local optimum solution, and population diversity maintenance under different complexity conditions of engineering problems.

An Improved Wild Horse Optimizer for Solving Optimization Problems

Wild horse optimizer (WHO) is a recently proposed metaheuristic algorithm that simulates the social behavior of wild horses in nature. Although WHO shows competitive performance compared to some algorithms, it suffers from low exploitation capability and stagnation in local optima. This paper presents an improved wild horse optimizer (IWHO), which incorporates three improvements to enhance optimizing capability. The main innovation of this paper is to put forward the random running strategy (RRS) and the competition for waterhole mechanism (CWHM). The random running strategy is employed to balance exploration and exploitation, and the competition for waterhole mechanism is proposed to boost exploitation behavior. Moreover, the dynamic inertia weight strategy (DIWS) is utilized to optimize the global solution. The proposed IWHO is evaluated using twenty-three classical benchmark functions, ten CEC 2021 test functions, and five real-world optimization problems. High-dimensional cases (D = 200, 500, 1000) are also tested. Comparing nine well-known algorithms, the experimental results of test functions demonstrate that the IWHO is very competitive in terms of convergence speed, precision, accuracy, and stability. Further, the practical capability of the proposed method is verified by the results of engineering design problems.

A boosted chimp optimizer for numerical and engineering design optimization challenges

Chimp optimization algorithm (ChoA) has a wholesome attitude roused by chimp's amazing thinking and hunting ability with a sensual movement for finding the optimal solution in the global search space. Classical Chimps optimizer algorithm has poor convergence and has problem to stuck into local minima for high-dimensional problems. This research focuses on the improved variants of the chimp optimizer algorithm and named as Boosted chimp optimizer algorithms. In one of the proposed variants, the existing chimp optimizer algorithm has been combined with SHO algorithm to improve the exploration phase of the existing chimp optimizer and named as IChoA-SHO and other variant is proposed to improve the exploitation search capability of the existing ChoA. The testing and validation of the proposed optimizer has been done for various standard benchmarks and Non-convex, Non-linear, and typical engineering design problems. The proposed variants have been evaluated for seven standard uni-modal benchmark functions, six standard multi-modal benchmark functions, ten standard fixed-dimension benchmark functions, and 11 types of multidisciplinary engineering design problems. The outcomes of this method have been compared with other existing optimization methods considering convergence speed as well as for searching local and global optimal solutions. The testing results show the better performance of the proposed methods excel than the other existing optimization methods.

An improved arithmetic optimization algorithm with forced switching mechanism for global optimization problems

Arithmetic optimization algorithm (AOA) is a newly proposed meta-heuristic method which is inspired by the arithmetic operators in mathematics. However, the AOA has the weaknesses of insufficient exploration capability and is likely to fall into local optima. To improve the searching quality of original AOA, this paper presents an improved AOA (IAOA) integrated with proposed forced switching mechanism (FSM). The enhanced algorithm uses the random math optimizer probability (RMOP) to increase the population diversity for better global search. And then the forced switching mechanism is introduced into the AOA to help the search agents jump out of the local optima. When the search agents cannot find better positions within a certain number of iterations, the proposed FSM will make them conduct the exploratory behavior. Thus the cases of being trapped into local optima can be avoided effectively. The proposed IAOA is extensively tested by twenty-three classical benchmark functions and ten CEC2020 test functions and compared with the AOA and other well-known optimization algorithms. The experimental results show that the proposed algorithm is superior to other comparative algorithms on most of the test functions. Furthermore, the test results of two training problems of multi-layer perceptron (MLP) and three classical engineering design problems also indicate that the proposed IAOA is highly effective when dealing with real-world problems.

Migration-Based Moth-Flame Optimization Algorithm

Moth–flame optimization (MFO) is a prominent swarm intelligence algorithm that demonstrates sufficient efficiency in tackling various optimization tasks. However, MFO cannot provide competitive results for complex optimization problems. The algorithm sinks into the local optimum due to the rapid dropping of population diversity and poor exploration. Hence, in this article, a migration-based moth–flame optimization (M-MFO) algorithm is proposed to address the mentioned issues. In M-MFO, the main focus is on improving the position of unlucky moths by migrating them stochastically in the early iterations using a random migration (RM) operator, maintaining the solution diversification by storing new qualified solutions separately in a guiding archive, and, finally, exploiting around the positions saved in the guiding archive using a guided migration (GM) operator. The dimensionally aware switch between these two operators guarantees the convergence of the population toward the promising zones. The proposed M-MFO was evaluated on the CEC 2018 benchmark suite on dimension 30 and compared against seven well-known variants of MFO, including LMFO, WCMFO, CMFO, CLSGMFO, LGCMFO, SMFO, and ODSFMFO. Then, the top four latest high-performing variants were considered for the main experiments with different dimensions, 30, 50, and 100. The experimental evaluations proved that the M-MFO provides sufficient exploration ability and population diversity maintenance by employing migration strategy and guiding archive. In addition, the statistical results analyzed by the Friedman test proved that the M-MFO demonstrates competitive performance compared to the contender algorithms used in the experiments.

An Improved Moth-Flame Optimization Algorithm with Adaptation Mechanism to Solve Numerical and Mechanical Engineering Problems

Moth-flame optimization (MFO) algorithm inspired by the transverse orientation of moths toward the light source is an effective approach to solve global optimization problems. However, the MFO algorithm suffers from issues such as premature convergence, low population diversity, local optima entrapment, and imbalance between exploration and exploitation. In this study, therefore, an improved moth-flame optimization (I-MFO) algorithm is proposed to cope with canonical MFO's issues by locating trapped moths in local optimum via defining memory for each moth. The trapped moths tend to escape from the local optima by taking advantage of the adapted wandering around search (AWAS) strategy. The efficiency of the proposed I-MFO is evaluated by CEC 2018 benchmark functions and compared against other well-known metaheuristic algorithms. Moreover, the obtained results are statistically analyzed by the Friedman test on 30, 50, and 100 dimensions. Finally, the ability of the I-MFO algorithm to find the best optimal solutions for mechanical engineering problems is evaluated with three problems from the latest test-suite CEC 2020. The experimental and statistical results demonstrate that the proposed I-MFO is significantly superior to the contender algorithms and it successfully upgrades the shortcomings of the canonical MFO.

DMFO-CD: A Discrete Moth-Flame Optimization Algorithm for Community Detection

In this paper, a discrete moth–flame optimization algorithm for community detection (DMFO-CD) is proposed. The representation of solution vectors, initialization, and movement strategy of the continuous moth–flame optimization are purposely adapted in DMFO-CD such that it can solve the discrete community detection. In this adaptation, locus-based adjacency representation is used to represent the position of moths and flames, and the initialization process is performed by considering the community structure and the relation between nodes without the need of any knowledge about the number of communities. Solution vectors are updated by the adapted movement strategy using a single-point crossover to distance imitating, a two-point crossover to calculate the movement, and a single-point neighbor-based mutation that can enhance the exploration and balance exploration and exploitation. The fitness function is also defined based on modularity. The performance of DMFO-CD was evaluated on eleven real-world networks, and the obtained results were compared with five well-known algorithms in community detection, including GA-Net, DPSO-PDM, GACD, EGACD, and DECS in terms of modularity, NMI, and the number of detected communities. Additionally, the obtained results were statistically analyzed by the Wilcoxon signed-rank and Friedman tests. In the comparison with other comparative algorithms, the results show that the proposed DMFO-CD is competitive to detect the correct number of communities with high modularity.

B-MFO: A Binary Moth-Flame Optimization for Feature Selection from Medical Datasets

Advancements in medical technology have created numerous large datasets including many features. Usually, all captured features are not necessary, and there are redundant and irrelevant features, which reduce the performance of algorithms. To tackle this challenge, many metaheuristic algorithms are used to select effective features. However, most of them are not effective and scalable enough to select effective features from large medical datasets as well as small ones. Therefore, in this paper, a binary moth-flame optimization (B-MFO) is proposed to select effective features from small and large medical datasets. Three categories of B-MFO were developed using S-shaped, V-shaped, and U-shaped transfer functions to convert the canonical MFO from continuous to binary. These categories of B-MFO were evaluated on seven medical datasets and the results were compared with four well-known binary metaheuristic optimization algorithms: BPSO, bGWO, BDA, and BSSA. In addition, the convergence behavior of the B-MFO and comparative algorithms were assessed, and the results were statistically analyzed using the Friedman test. The experimental results demonstrate a superior performance of B-MFO in solving the feature selection problem for different medical datasets compared to other comparative algorithms.

Deep Ensemble of Slime Mold Algorithm and Arithmetic Optimization Algorithm for Global Optimization

In this paper, a new hybrid algorithm based on two meta-heuristic algorithms is presented to improve the optimization capability of original algorithms. This hybrid algorithm is realized by the deep ensemble of two new proposed meta-heuristic methods, i.e., slime mold algorithm (SMA) and arithmetic optimization algorithm (AOA), called DESMAOA. To be specific, a preliminary hybrid method was applied to obtain the improved SMA, called SMAOA. Then, two strategies that were extracted from the SMA and AOA, respectively, were embedded into SMAOA to boost the optimizing speed and accuracy of the solution. The optimization performance of the proposed DESMAOA was analyzed by using 23 classical benchmark functions. Firstly, the impacts of different components are discussed. Then, the exploitation and exploration capabilities, convergence behaviors, and performances are evaluated in detail. Cases at different dimensions also were investigated. Compared with the SMA, AOA, and another five well-known optimization algorithms, the results showed that the proposed method can outperform other optimization algorithms with high superiority. Finally, three classical engineering design problems were employed to illustrate the capability of the proposed algorithm for solving the practical problems. The results also indicate that the DESMAOA has very promising performance when solving these problems.

An Optimized Method for Skin Cancer Diagnosis Using Modified Thermal Exchange Optimization Algorithm

Skin cancer is the most common cancer of the body. It is estimated that more than one million people worldwide develop skin cancer each year. Early detection of this cancer has a high effect on the disease treatment. In this paper, a new optimal and automatic pipeline approach has been proposed for the diagnosis of this disease from dermoscopy images. The proposed method includes a noise reduction process before processing for eliminating the noises. Then, the Otsu method as one of the widely used thresholding method is used to characterize the region of interest. Afterward, 20 different features are extracted from the image. To reduce the method complexity, a new modified version of the Thermal Exchange Optimization Algorithm is performed to the features. This improves the method precision and consistency. To validate the proposed method's efficiency, it is implemented to the American Cancer Society database, its results are compared with some state-of-the-art methods, and the final results showed the superiority of the proposed method against the others.

Binary Spring Search Algorithm for Solving Various Optimization Problems

One of the most powerful tools for solving optimization problems is optimization algorithms (inspired by nature) based on populations. These algorithms provide a solution to a problem by randomly searching in the search space. The design’s central idea is derived from various natural phenomena, the behavior and living conditions of living organisms, laws of physics, etc. A new population-based optimization algorithm called the Binary Spring Search Algorithm (BSSA) is introduced to solve optimization problems. BSSA is an algorithm based on a simulation of the famous Hooke’s law (physics) for the traditional weights and springs system. In this proposal, the population comprises weights that are connected by unique springs. The mathematical modeling of the proposed algorithm is presented to be used to achieve solutions to optimization problems. The results were thoroughly validated in different unimodal and multimodal functions; additionally, the BSSA was compared with high-performance algorithms: binary grasshopper optimization algorithm, binary dragonfly algorithm, binary bat algorithm, binary gravitational search algorithm, binary particle swarm optimization, and binary genetic algorithm. The results show the superiority of the BSSA. The results of the Friedman test corroborate that the BSSA is more competitive.

A Combination Strategy of Feature Selection Based on an Integrated Optimization Algorithm and Weighted K-Nearest Neighbor to Improve the Performance of Network Intrusion Detection

With the widespread use of the Internet, network security issues have attracted more and more attention, and network intrusion detection has become one of the main security technologies. As for network intrusion detection, the original data source always has a high dimension and a large amount of data, which greatly influence the efficiency and the accuracy. Thus, both feature selection and the classifier then play a significant role in raising the performance of network intrusion detection. This paper takes the results of classification optimization of weighted K-nearest neighbor (KNN) with those of the feature selection algorithm into consideration, and proposes a combination strategy of feature selection based on an integrated optimization algorithm and weighted KNN, in order to improve the performance of network intrusion detection. Experimental results show that the weighted KNN can increase the efficiency at the expense of a small amount of the accuracy. Thus, the proposed combination strategy of feature selection based on an integrated optimization algorithm and weighted KNN can then improve both the efficiency and the accuracy of network intrusion detection.

An Improved Moth-Flame Optimization Algorithm for Engineering Problems

In this paper, an improved moth-flame optimization algorithm (IMFO) is presented to solve engineering problems. Two novel effective strategies composed of Lévy flight and dimension-by-dimension evaluation are synchronously introduced into the moth-flame optimization algorithm (MFO) to maintain a great global exploration ability and effective balance between the global and local search. The search strategy of Lévy flight is used as a regulator of the moth-position update mechanism of global search to maintain a good research population diversity and expand the algorithm’s global search capability, and the dimension-by-dimension evaluation mechanism is added, which can effectively improve the quality of the solution and balance the global search and local development capability. To substantiate the efficacy of the enhanced algorithm, the proposed algorithm is then tested on a set of 23 benchmark test functions. It is also used to solve four classical engineering design problems, with great progress. In terms of test functions, the experimental results and analysis show that the proposed method is effective and better than other well-known nature-inspired algorithms in terms of convergence speed and accuracy. Additionally, the results of the solution of the engineering problems demonstrate the merits of this algorithm in solving challenging problems with constrained and unknown search spaces.