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The grasshopper optimization algorithm (GOA) is a meta-heuristic algorithm proposed in 2017 mimics the biological behavior of grasshopper swarms seeking food sources in nature for solving optimization problems. Nonetheless, some shortcomings exist in the origin GOA, and GOA global search ability is more or less insufficient and precision also needs...
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... Two main stages of optimization are exploration and exploitation of the search space; Grasshoppers provide these two stages during food foraging and locating its source through these social interactions. The GOA algorithm is mainly based on three factors, the social interaction: gravity force and wind advection [69][70][71][72]. ...
... The mathematical model used to simulate the grasshopper behaviour swarm can be expressed as follows [69][70][71][72]: ...
... where, r 1 , r 2 and r 3 are random numbers that interval rang [0, 1], they are employed to deliver random behaviours. The social interaction force S i can be determined using the following equation [69][70][71][72]: (26) where, N g the number of grasshoppers in the swarm; d i j represents the distance measured between the grasshopper i-th and grasshopper j-th. The function s defines the strength of two social forces (repulsion and attraction between grasshoppers); it can be estimated by the following formula [69][70][71][72]: ...
In this paper, a quasi-static modelling for assessment and screening of electric field generated by an EHV overhead alternating current (AC) transmission line installed adjacent to a sensitive area is treated, based on an improved computing paradigm that is a hybrid charge simulation method (CSM) and grasshopper optimization algorithm (GOA). The intelligent algorithm is applied to adjust the optimal number and position of simulating changes to improve the accuracy of the electric field calculation method, as well as to determine the geometric coordinates of the passive and active shielding conductors and to evaluate the voltage to be injected in the case of active shielding; to significantly reduce the electric field in the area to be protected. The results showed that when the sag effect is considered, the electric field value at mid-span is higher than in the vicinity of the suspension pylons, the average value can be considered approximately equal to the electric field value, when the sag effect is neglected. The performance of screening effect shows that active shielding is more reliable than passive shielding for electric field attenuation. An undesirable side effect for transmission line energy efficiency arises from the shielding wires which consist of the increase in the maximum gradient of the electric field and the energy losses by Corona phenomena on the surface of the conductors. The methodology adopted performance is in perfect agreement with the results reported in the CIGRE (International Council on Large Electric Systems) standard.
... It evaluates the magnitudes of differences (disregarding their direction) by assigning ranks and computing a statistic based on these ranks. This figure aids in discerning whether distinctions are probably attributable to random variation Table B.5 [91]. ...
... The performance disparity between two classifiers is deemed significant if their respective average ranks exhibit a difference equal to or exceeding the CD (Eq. (48)) [91]. ...
This paper presents a unique hybrid classifier that combines deep neural networks with a type-III fuzzy system for decision-making. The ensemble incorporates ResNet-18, Efficient Capsule neural network, ResNet-50, the Histogram of Oriented Gradients (HOG) for feature extraction, neighborhood component analysis (NCA) for feature selection, and Support Vector Machine (SVM) for classification. The innovative inputs fed into the type-III fuzzy system come from the outputs of the mentioned neural networks. The system’s rule parameters are fine-tuned using the Improved Chaos Game Optimization algorithm (ICGO). The conventional CGO’s simple random mutation is substituted with wavelet mutation to enhance the CGO algorithm while preserving non-parametricity and computational complexity. The ICGO was evaluated using 126 benchmark functions and 5 engineering problems, comparing its performance with well-known algorithms. It achieved the best results across all functions except for 2 benchmark functions. The introduced classifier is applied to seven malware datasets and consistently outperforms notable networks like AlexNet, ResNet-18, GoogleNet, and Efficient Capsule neural network in 35 separate runs, achieving over 96% accuracy. Additionally, the classifier’s performance is tested on the MNIST and Fashion-MNIST in 10 separate runs. The results show that the new classifier excels in accuracy, precision, sensitivity, specificity, and F1-score compared to other recent classifiers. Based on the statistical analysis, it has been concluded that the ICGO and propose method exhibit significant superiority compared to the examined algorithms and methods. The source code for ICGO is available publicly at https://nimakhodadadi.com/algorithms-%2B-codes.
Graphical abstract
... The second group comprises the category of ZP functions illustrated in Table 5, while the third group is formed by CEC 2019 functions illustrated in Table 6. The fourth, fifth, sixth, and seventh groups included CEC 2014 functions in different dimensions, respectively (Table S1-S3) 141 . ...
... The performance disparity between two classifiers is deemed significant if their respective average ranks exhibit a difference equal to or exceeding the CD (Eq. 20) 141 . ...
The novelty of this article lies in introducing a novel stochastic technique named the Hippopotamus Optimization (HO) algorithm. The HO is conceived by drawing inspiration from the inherent behaviors observed in hippopotamuses, showcasing an innovative approach in metaheuristic methodology. The HO is conceptually defined using a trinary-phase model that incorporates their position updating in rivers or ponds, defensive strategies against predators, and evasion methods, which are mathematically formulated. It attained the top rank in 115 out of 161 benchmark functions in finding optimal value, encompassing unimodal and high-dimensional multimodal functions, fixed-dimensional multimodal functions, as well as the CEC 2019 test suite and CEC 2014 test suite dimensions of 10, 30, 50, and 100 and Zigzag Pattern benchmark functions, this suggests that the HO demonstrates a noteworthy proficiency in both exploitation and exploration. Moreover, it effectively balances exploration and exploitation, supporting the search process. In light of the results from addressing four distinct engineering design challenges, the HO has effectively achieved the most efficient resolution while concurrently upholding adherence to the designated constraints. The performance evaluation of the HO algorithm encompasses various aspects, including a comparison with WOA, GWO, SSA, PSO, SCA, FA, GOA, TLBO, MFO, and IWO recognized as the most extensively researched metaheuristics, AOA as recently developed algorithms, and CMA-ES as high-performance optimizers acknowledged for their success in the IEEE CEC competition. According to the statistical post hoc analysis, the HO algorithm is determined to be significantly superior to the investigated algorithms. The source codes of the HO algorithm are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/160088-hippopotamus-optimization-algorithm-ho.
... The problem can be mathematically expressed as follows: are Pmin and Pmax, respectively, while its minimum and maximum heat capacities are Hmin and Hmax. As described in references [40,42], Figure 9 depicts the feasible operating region of a combined cycle cogeneration unit bounded by the boundary curve MNOPQR. The proposed hybrid methods are applied to a single-area cogeneration system [43], which consists of one conventional power unit (unit 1), three co-generation units (unit 2, unit 3 and unit 4) and ...
The Quantum-Based Optimisation Method (QBOM) is a novel optimization approach based on quantum computing concepts. The novel optimization method's durability is studied using its capacity to conjoin with existing optimization techniques. This study uses The QBOM with the Pattern Search (PS) technique to solve engineering optimization problems. The first strategy, Hybrid I, uses QBOM for global search optimization, followed by PS searching in the nearby region for the optimum solution. The second strategy, Hybrid II, uses QBOM as a local search optimization within Pattern Search. In each iteration, QBOM starts searching inside PS for a better solution than the one detected at that stage, which is labelled as PS's new search point. These two hybrid techniques attempt to expand the possibilities of QBOM's local search mechanism while demonstrating its resilience. The hybridised methodologies are used to solve benchmark optimization problems and six real-world engineering optimization problems. The study revealed that the two hybrid techniques worked brilliantly, producing solutions that exceeded previous methods described in the literature for certain benchmark optimization problems. Not only did the hybridised methods produce better results in less computational time, but they also demonstrated that QBOM could be used to improve the search mechanism and accelerate the performance of the evolutionary algorithm in the local search to match its execution in the global search.
... Lévy flight simulates this motion to enhance exploitation (Zhou et al., 2018;Wu et al., 2023). Thus, Eqn (27) is revised to Eqn (28): ...
Real-world optimization problems are ubiquitous across scientific domains, and many engineering challenges can be reimagined as optimization problems with relative ease. Consequently, researchers have focused on developing optimizers to tackle these challenges. The Snake Optimizer (SO) is an effective tool for solving complex optimization problems, drawing inspiration from snake patterns. However, the original SO requires the specification of six specific parameters to operate efficiently. In response to this, enhanced snake optimizers, namely ESO1 and ESO2, were developed in this study. In contrast to the original SO, ESO1 and ESO2 rely on a single set of parameters determined through sensitivity analysis when solving mathematical functions. This streamlined approach simplifies the application of ESOs for users dealing with optimization problems. ESO1 employs a logistic map to initialize populations, while ESO2 further refines ESO1 by integrating a Lévy flight to simulate snake movements during food searches. These enhanced optimizers were compared against the standard SO and 12 other established optimization methods to assess their performance. ESO1 significantly outperforms other algorithms in 15, 16, 13, 15, 21, 16, 24, 16, 19, 18, 13, 15, and 22 out of 24 mathematical functions. Similarly, ESO2 outperforms them in 16, 17, 18, 22, 23, 23, 24, 20, 19, 20, 17, 22, and 23 functions. Moreover, ESO1 and ESO2 were applied to solve complex structural optimization problems, where they outperformed existing methods. Notably, ESO2 generated solutions that were, on average, 1.16%, 0.70%, 2.34%, 3.68%, and 6.71% lighter than those produced by SO, and 0.79%, 0.54%, 1.28%, 1.70%, and 1.60% lighter than those of ESO1 for respective problems. This study pioneers the mathematical evaluation of ESOs and their integration with the finite element method for structural weight design optimization, establishing ESO2 as an effective tool for solving engineering problems.
... The average ranks of both Average and Std. about pairwise algorithms on 23 test functions listed in Table 7 and intuitively visualized in Fig. 4. There is no significant difference (ambiguous) between the pairwise algorithms when the different values of Friedman average rank between the pairwise algorithms are less than the CD [23]. From Fig. 4 and Table 7, we can clearly see only CMRWGOA versus AHA have similar performance in terms of the average rank of Mean. ...
An improved grasshopper optimization algorithm (GOA) is proposed in this paper, termed CMRWGOA, which combines both Random Weight (shorted RWGOA) and Cauchy mutation (termed CMGOA) mechanism into the GOA. The GOA received inspiration from the foraging and swarming habits of grasshoppers. The performance of the CMRWGOA was validated by 23 benchmark functions in comparison with four well-known meta-heuristic algorithms (AHA, DA, GOA, and MVO), CMGOA, RWGOA, and the GOA. The non-parametric Wilcoxon, Friedman, and Nemenyi statistical tests are conducted on the CMRWGOA. Furthermore, the CMRWGOA has been evaluated in three real-life challenging optimization problems as a complementary study. Various strictly extensive experimental results reveal that the CMRWGOA exhibit better performance.
The Grasshopper Optimization Algorithm (GOA) is a relatively recent population-based stochastic search algorithm extensively used for solving various nonlinear global optimization problems arising in science and engineering. Like other evolutionary algorithms, this algorithm also has some limitations like poor balance between exploration and exploitation, requires large population size, and premature convergence. To address these limitations and to improve the efficiency of GOA, two hybridized variants of GOA have been proposed in this paper. In these variants, GOA is combined with the feature of another population-based algorithm which is the Self-Organizing Migrating Algorithm (SOMA). First GOA is combined with the exploitation feature of SOMA and a hybrid variant of SOMGOA is proposed. Later to balance exploitation, SOMGOA is merged with tournament selection to maintain the good quality solution of previous and current generations and SOMGOA-t is presented. The effectiveness of both the variants is analysed based on results and comparative analysis is made against the results of GOA and SOMA. A total of twenty-one standard benchmark functions with different intrinsic difficulties and four unconstrained optimization problems (gear train design, frequency modulation sound parameter identification problem, Gas transmission compressor design problem, and Optimal capacity of gas production facility) have been used for testing. The analysis of experimental results involved two statistical tests: the Wilcoxon rank-sum test and the Friedman statistical test. Furthermore, the statistical findings consistently affirm the superiority of the SOMGOA-t when compared to the alternative algorithms (GOA and SOMA). However, the present study is limited to solving unconstrained nonlinear optimization problems.
Since Grey Wolf Optimizer (GWO) first introduction, it continues to be used extensively today, owing to its simplicity, easy handling, and applicability to a wide range of problems. Although there are many different GWO variants in the literature, the problem that the GWO produces early convergence and inefficient results have still continued to emerge in their variants. In order to overcome the drawbacks of theGWO, theGWO integrated together with Levy Flight (LFGWO) is proposed. In order to demonstrate the overall performance of the LFGWO, experiments are conducted using the 23 standard benchmark functions and 10 composition functions of CEC 2019 compared with the other eight state-of-art algorithms. The 28 out of 33 average and 27 out of 33 standard deviation values obtained by LFGWO are all less than those obtained by the other eight optimization algorithms, which verified and demonstrated the performance, stability, and robustness of the LFGWO. The extensibility test with different scales of dimensions 50, 100, 300, and 500, is undertaken by comparing LFGWO with GWO and IGWO to assess the dimensional influence on problem consistency and optimization quality. Moreover, the performance of the LFGWO has also been tested on five real-world problems and infinite impulse response (IIR) challenging model identification, experimental results and statistical tests demonstrate that the performance of LFGWO is significantly better than the other compared algorithms, and the LFGWO is capable of solving real-world problems.
