Unimodal Functions Research Articles

A multistrategy hybrid adaptive whale optimization algorithm

Abstract To solve the problems of whale optimization algorithm (WOA) with slow convergence speed, low accuracy, and poor global search ability, a multistrategy hybrid adaptive whale optimization algorithm (MHWOA) was proposed. In this algorithm, the logistic–tent hybrid chaos algorithm was used to initialize the population, which could make the population distribution more random and uniform. The opposition-based learning strategy was adopted to expand the population of individuals and complete the population selection. To balance the exploitation phase and exploration phase, a dynamic parameter was constructed based on the sigmoid excitation function, and an active adaptive weight was added to adjust the global and local search, which accelerated the convergence speed also. The perturbation mechanism of the Student T-distribution was introduced with random perturbation to expand the search range and improve the global search ability of the algorithm. In total, 23 benchmark functions were selected to conduct convergence performance and optimization performance experiments of the proposed algorithm. The average value and standard deviation were determined as evaluation indexes. The MHWOA was compared with other improved WOA variants and advanced algorithms. The results showed that the proposed MHWOA had better iterative convergence and optimization performance than different algorithms on the optimization of unimodal functions, multimodal functions, and fixed dimension functions. Meanwhile, the MHWOA was applied to the optimal designs of pressure vessels and springs. The experimental results displayed that the MHWOA obtained better solutions than other meta-heuristic algorithms. This study has practical solid application value, which can be applied to solving various engineering problems.

White-Tailed Eagle Algorithm for Global Optimization and Low-Cost and Low-CO2 Emission Design of Retaining Structures

This study proposes a new metaheuristic optimization algorithm, namely the white-tailed eagle algorithm (WEA), for global optimization and optimum design of retaining structures. Metaheuristic optimization methods are now broadly implemented to address problems in a variety of scientific domains. These algorithms are typically inspired by the natural behavior of an agent, which can be humans, animals, plants, or any physical agent. However, a specific metaheuristic algorithm (MA) may not be able to find the optimal solution for every situation. As a result, researchers will aim to propose and discover new methods in order to identify the best solutions to a variety of problems. The white-tailed eagle algorithm (WEA) is a simple but effective nature-inspired algorithm inspired by the social life and hunting activity of white-tailed eagles. The WEA’s hunting is divided into two phases. In the first phase (exploration), white-tailed eagles seek prey inside the searching region. The eagle goes inside the designated space according to the position of the best eagle to find the optimum hunting position (exploitation). The proposed approach is tested using 13 unimodal and multimodal benchmark test functions, and the results are compared to those obtained by some well-established optimization methods. In addition, the new algorithm automates the optimum design of retaining structures under seismic load, considering two objectives: economic cost and CO2 emissions. The results of the experiments and comparisons reveal that the WEA is a high-performance algorithm that can effectively explore the decision space and outperform almost all comparative algorithms in the majority of the problems.

Downscaling population and urban land use for socio-economic scenarios in the UK

Projecting the distribution of population is critical in supporting analysis of the impacts and risks associated with climate change. In this paper, we apply a computational algorithm parameterised for the UK Shared Socioeconomic Pathway (UK-SSP) narratives to create 1-km gridded urban land use and population projections for the UK to the end of the twenty-first century. Using a unimodal neighbourhood function, we model heterogeneity in urban sprawl patterns. The urban land use maps are used as weights to create downscaled population projections. We undertake a model uncertainty analysis using 500 simulations with varying parameter settings per UK-SSP. Results illustrate how sprawl can emerge from scenario conditions even when population numbers decline, and irrespective of socio-economic wellbeing. To avoid negative environmental externalities associated with uncontrolled sprawl, such as in UK-SSP5 and UK-SSP3, planning policies will be vital. Uncertainties about future population development in the UK are higher in rural areas than in urban areas. This has an effect on the competition for land and influences confidence in projections of broader land system change.

Multi-strategy modified INFO algorithm: Performance analysis and application to functional electrical stimulation system

A functional electrical stimulation (FES) system holds a significant importance for the paralyzed individuals as it can help them to perform the tasks they are unable to do. It is crucial to develop an efficient control mechanism for the FES system as it acts on the human musculoskeletal system which presents noise and uncertainties. Therefore, this paper proposes a novel control method for efficient operation of the FES system. In this regard, a proportional-integral-derivative controller with filter (PID-F) mechanism is proposed for the first time in literature for efficient operation of the FES system. Besides, a novel multi-strategy based weighted mean of vectors algorithm (m-INFO) is also developed using a modified opposition-based learning and Lévy flight mechanism together with Nelder-Mead simplex search method. Unimodal, multimodal, low-dimensional and CEC2019 benchmark functions are used to demonstrate the excellent performance of the proposed m-INFO algorithm against several other metaheuristic optimizers. The proposed m-INFO algorithm is then used as an efficient tool to design the PID-F controlled FES system. To achieve optimal tuning, a simple yet effective objective function is also proposed. The excellent ability of the developed m-INFO algorithm-based PID-F controller for FES system is demonstrated through comparative statistical, transient response and frequency response analyses using original weighted mean of vectors, marine predators and moth-flame optimization algorithms based PID-F controlled FES systems.

A balanced butterfly optimization algorithm for numerical optimization and feature selection

Butterfly optimization algorithm (BOA) is a relatively novel optimization technique for solving function optimization as well as real-world applications. However, the paramount challenge in BOA is that it is prone to stagnation in local optima. The purpose of this study is to balance the exploration and exploitation abilities of BOA when two new strategies are introduced. The dynamic inertia weight based on Logistic model as the first strategy is introduced to modify the position updating equation. Another strategy is the opposition-based learning. A new variant of BOA called BBOA based on these two strategies is proposed. Ten widely used benchmark test functions and 30 complex benchmarks from CEC 2014 are selected to verify the effectiveness of BBOA. The used benchmark problems are composed of unimodal, multimodal, rotated, shifted, hybrid and composite functions. The experimental results and analysis show that the proposed BBOA has better exploration ability than the conventional BOA when solving different characteristics functions. Finally, BBOA is applied to solve three real-world engineering applications and sixteen feature selection problems. The results demonstrate that BBOA can outperform other competitors in terms of the accuracy of solution on constrained engineering design and feature selection problems.

An adaptive differential evolution algorithm based on belief space and generalized opposition-based learning for resource allocation

Differential evolution (DE) algorithm is prone to premature convergence and local optimization in solving complex optimization problems. In order to solve these problems, the belief space strategy, generalized opposition-based learning strategy and parameter adaptive strategy are introduced into DE to propose an improved adaptive DE algorithm, namely ACDE/F in this paper. In the ACDE/F, the idea of cultural algorithm and different mutation strategies are introduced into belief space to balance the global exploration ability and local optimization ability. A generalized opposition-based learning strategy is designed to improve the convergence speed of local optimization and increase the population diversity. A parameter adaptive adjustment strategy is developed to reasonably adjust the mutation factor and crossover factor to avoid to fall into local optimum. In order to test and verify the optimization performance of the ACDE/F, the unimodal functions and multimodal functions from CEC 2005 and CEC 2017 are selected in here. The experiment results show that the ACDE/F has better optimization performance than the DE with different strategies, WMSDE, DE2/F, GOAL-RNADE and DE/best/1. In addition, the actual gate allocation problem is selected to verify the practical application ability of the ACDE/F. The ACDE/F obtains the maximum allocation rate and average allocation rate of 98% and 96.8%, respectively. Therefore, the experimental results show that the ACDE/F can effectively solve the gate allocation problem and obtain ideal gate allocation results.

Multisensory interactions on auditory and somatosensory information in expert pianists

Fine-tuned sensory functions typically characterize skilled individuals. Although numerous studies demonstrated enhanced unimodal sensory functions at both neural and behavioral levels in skilled individuals, little is known about their multisensory interaction function, especially multisensory integration and selective attention that involve volitional control of information derived from multiple sensory organs. In the current study, expert pianists and musically untrained individuals performed five sets of intensity discrimination tasks at the auditory and somatosensory modalities with different conditions: (1) auditory stimulus, (2) somatosensory stimulus, (3) congruent auditory and somatosensory stimuli (i.e., multisensory integration), (4) auditory and task-irrelevant somatosensory stimuli, and (5) somatosensory and task-irrelevant auditory stimuli. In the fourth and fifth conditions, participants were instructed to ignore a task-irrelevant stimulus and to pay attention to a task-relevant stimulus (i.e., selective attention), respectively. While the discrimination perception was superior in the condition (3) compared to the better one of the individual unimodal conditions only in the pianists, the task-irrelevant somatosensory stimulus worsened the auditory discrimination more in the pianists than the nonmusicians. These findings indicate unique multisensory interactions in expert pianists, which enables pianists to efficiently integrate the auditory and somatosensory information, but exacerbates top-down selective inhibition of somatosensory information during auditory processing.

A Nature-Inspired Metaheuristic Optimization Algorithm Based on Crocodiles Hunting Search (CHS)

The increasing difficulty of actual-world optimization problems has prompted computer researchers to regularly produce additional process improvement techniques. Metaheuristic and evolutionary computing are very popular in nature-inspired optimization methods. This paper introduces the crocodile search algorithm (CHS), which is a revision of a new metaphorical algorithm based on the hunting behavior of crocodile herds. Various adaptive and arbitrary variables are combined within this algorithm to indicate the exploitation and investigation of the exploration area in various discoveries of optimization. The performance of the CHS is measured in different test phases. Initially, a collection of famous experiment events including unimodal, multi-modal, and composite functions are applied to examine exploitation, exploration, local optima avoidance, and convergence of CHS. The CHS algorithm achieves a regular frame for the airfoil with a pretty low drag, which explains that the methods can be efficient while working physical difficulties including restrained plus unknown search.

Improved Particle Swarm Optimization Algorithms for Optimal Designs with Various Decision Criteria

Particle swarm optimization (PSO) is an attractive, easily implemented method which is successfully used across a wide range of applications. In this paper, utilizing the core ideology of genetic algorithm and dynamic parameters, an improved particle swarm optimization algorithm is proposed. Then, based on the improved algorithm, combining the PSO algorithm with decision making, nested PSO algorithms with two useful decision making criteria (optimistic coefficient criterion and minimax regret criterion) are proposed . The improved PSO algorithm is implemented on two unimodal functions and two multimodal functions, and the results are much better than that of the traditional PSO algorithm. The nested algorithms are applied on the Michaelis–Menten model and two parameter logistic regression model as examples. For the Michaelis–Menten model, the particles converge to the best solution after 50 iterations. For the two parameter logistic regression model, the optimality of algorithms are verified by the equivalence theorem. More results for other models applying our algorithms are available upon request.

The Narrow Capture Problem with Partially Absorbing Targets and Stochastic Resetting

We consider a particle undergoing diffusion with stochastic resetting in a bounded domain $\calU\subset \R^d$ for $d=2,3$. The domain is perforated by a set of partially absorbing targets within which the particle may be absorbed at a rate $\kappa$. Each target is assumed to be much smaller than $|\calU|$, which allows us to use asymptotic and Green's function methods to solve the diffusion equation in Laplace space. In particular, we construct an inner solution within the interior and local exterior of each target, and match it with an outer solution in the bulk of $\calU$. This yields an asymptotic expansion of the Laplace transformed flux into each target in powers of $\nu=-1/\ln \epsilon$ ($d=2$) and $\epsilon$ ($d=3$), respectively, where $\epsilon$ is the non-dimensionalized target size. The fluxes determine how the mean first-passage time to absorption depends on the reaction rate $\kappa$ and the resetting rate $r$. For a range of parameter values, the MFPT is a unimodal function of $r$, with a minimum at an optimal resetting rate $r_{\rm opt}$ that depends on $\kappa$ and the target configuration.

Statistical analysis based reactive power optimization using improved differential evolutionary algorithm

AbstractThis study presents a novel improved differential evolutionary (IDE) algorithm for optimizing reactive power management (RPM) problems. The effectiveness of IDE algorithm is tested on different unimodal and multimodal benchmark functions. The objective function of the RPM is considered as the minimization of active power losses. Initially, the power flow analysis approach is employed to detect the optimal position of flexible AC transmission system (FACTS) devices. The proposed method is used to determine the optimal value of control variables such as generator's reactive power generation, transformer tap settings, and reactive power sources. Furthermore, the efficacy of the IDE approach is compared with other promising optimization methods such as variants of differential evolution algorithm, moth flame optimization (MFO), brainstorm‐based optimization algorithm (BSOA), and particle swarm optimization (PSO) on various IEEE standard test bus (i.e., IEEE‐30, ‐57, ‐118, and ‐300) systems with active and reactive loading incorporating FACTS devices. A Static VAR compensator (SVC) for shunt compensation and a thyristor‐controlled series compensator (TCSC) for series compensation were used as FACTS devices. The proposed IDE method significantly reduces the active power loss, that is, 55.65% in IEEE 30, 39.68% in IEEE 57, 16.32% in IEEE 118, and 8.56% in IEEE 300 bus system at nominal loading. Finally, the statistical analysis such as Wilcoxon signed‐rank test (WSRT) and ANOVA test were thoroughly analysed to demonstrate the firmness and accuracy of the proposed technique.

Domain Learning Particle Swarm Optimization With a Hybrid Mutation Strategy

When traditional particle swarm optimization algorithms deal with highly complex, ultra-high-dimensional problems, traditional particle learning strategies can only provide little help. In this paper, a particle swarm optimization algorithm with a hybrid variation domain dimension learning strategy is proposed, which uses the domain dimension average of the current particle dimension to generate guiding particles. At the same time, an improved inertia weight is also used, which effectively avoids the algorithm from easily falling into local optimum. To verify the strong competitiveness of the algorithm, the algorithm is tested on nineteen benchmark functions and compared with several well-known particle swarm algorithms. The experimental results show that the algorithm proposed in this paper has a significant effect on unimodal functions, and has a better effect on multimodal functions. Guided particles, improved inertia weight and mutation strategy can effectively balance local search and global search, and can better converge to the global optimal solution.

Magnetorheological damper parameter identification using a novel metaheuristic algorithm

In this study, a new optimization algorithm is proposed based on swarm intelligence theory. In the algorithm, the movement of each individual toward the best member of the population is not represented as a linear vector; instead, it can change nonlinearly according to the discrete‐time that is represented by the iteration number. By implementing this change, the speed of each member of the population can be controlled, which results in finding a better solution. As there is a dependency on the iteration number, it is named the Iteration Dependent Optimizer (IDO). The performance of the proposed algorithm is evaluated based on unconstrained unimodal and multimodal benchmark functions and constrained engineering optimization problems. Then the algorithm is used to solve a practical problem in civil engineering, in which unknown parameters of the model of a large‐scale magnetorheological (MR) damper, which is commonly used in structural control, are identified. The results of statistical study and direct comparisons demonstrate the advantages and capabilities of the proposed model and indicate that IDO can compete favorably with some other well‐studied algorithms.

Optimal foraging algorithm with direction prediction and Gaussian oscillation for constrained optimization problems

Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G.

An automatic kriging machine learning method to calibrate meta-heuristic algorithms for solving optimization problems

For years, meta-heuristic algorithms have been widely studied and many improved versions have been developed: from the evolution of the swarm topologies of the Particle Swarm Optimization algorithm, to the using of machine learning to Differential Evolutionary algorithms. However, the tuning of the fundamental meta-heuristic parameters has been less studied, but may lead to significant improvements on the convergence accuracy of these algorithms. This paper aims at developing an automated methodology to calibrate the parameters of population-based meta-heuristic algorithms for optimization problems. Based on the kriging estimation of the best combination of parameters, the Automated parameter tuning of Meta-heuristics (AptM) methodology gives the optimal algorithm setup for each considered problem in order to lead to a better convergence accuracy. The proposed AptM methodology is used to tune three different meta-heuristic algorithms, each applied to twelve mathematical unimodal or multimodal objective functions. AptM methodology performance is assessed by comparison of classical setups usually used in the literature. The numerical results show that the AptM methodology allows a significant improvement of the convergence accuracy of meta-heuristics with an average improvement of 62.02%, 69.12% and 64.94% on optimization problems defined in dimensions 10, 30 and 50 respectively. An experimental criterion is defined based on the convergence accuracy of the AptM methodology over the classical setups, assessing the AptM performances. The previous experimental criterion allows to compare the AptM methodology over the base-set. The AptM methodology shows a significant improvement of the algorithms performance on 97.2% of the tested problems.

A two-sided model of paid peering

Internet users have suffered collateral damage in tussles over paid peering between large ISPs and large content providers. Paid peering is a relationship where two networks exchange traffic with payment, which provides direct access to each other’s customers without having to pay a third party to carry that traffic for them. The issue will arise again when the United States Federal Communications Commission (FCC) considers a new net neutrality order.We first consider the effect of paid peering on broadband prices. We adopt a two-sided market model in which an ISP maximizes profit by setting broadband prices and a paid peering price. We analytically derive the profit-maximizing prices, and show that they satisfy a generalization of the well-known Lerner rule. Our result shows that paid peering fees reduce the premium plan price, increase the video streaming price and the total price for premium tier customers who subscribe to video streaming services; however, the ISP passes on to its customers only a portion of the revenue from paid peering. ISP profit increases but video streaming profit decreases as an ISP moves from settlement-free peering to paid peering price.We next consider the effect of paid peering on consumer surplus. We find that consumer surplus is a uni-modal function of the paid peering fee. The paid peering fee that maximizes consumer surplus depends on elasticities of demand for broadband and for video streaming. However, consumer surplus is maximized when paid peering fees are significantly lower than those that maximize ISP profit. However, it does not follow that settlement-free peering is always the policy that maximizes consumer surplus. The peering price depends critically on the incremental ISP cost per video streaming subscriber; at different costs, it can be negative, zero, or positive.

Fully Elman Neural Network: A Novel Deep Recurrent Neural Network Optimized by an Improved Harris Hawks Algorithm for Classification of Pulmonary Arterial Wedge Pressure.

Heart failure (HF) is one of the most prevalent life-threatening cardiovascular diseases in which 6.5 million people are suffering in the USA and more than 23 million worldwide. Mechanical circulatory support of HF patients can be achieved by implanting a left ventricular assist device (LVAD) into HF patients as a bridge to transplant, recovery or destination therapy and can be controlled by measurement of normal and abnormal pulmonary arterial wedge pressure (PAWP). While there are no commercial long-term implantable pressure sensors to measure PAWP, real-time non-invasive estimation of abnormal and normal PAWP becomes vital. In this work, first an improved Harris Hawks optimizer algorithm called HHO+ is presented and tested on 24 unimodal and multimodal benchmark functions. Second, a novel fully Elman neural network (FENN) is proposed to improve the classification performance. Finally, four novel 18-layer deep learning methods of convolutional neural networks (CNNs) with multi-layer perceptron (CNN-MLP), CNN with Elman neural networks (CNN-ENN), CNN with fully Elman neural networks (CNN-FENN), and CNN with fully Elman neural networks optimized by HHO+ algorithm (CNN-FENN-HHO+) for classification of abnormal and normal PAWP using estimated HVAD pump flow were developed and compared. The estimated pump flow was derived by a non-invasive method embedded into the commercial HVAD controller. The proposed methods are evaluated on an imbalanced clinical dataset using 5-fold cross-validation. The proposed CNN-FENN-HHO+ method outperforms the proposed CNN-MLP, CNN-ENN and CNN-FENN methods and improved the classification performance metrics across 5-fold cross-validation with an average sensitivity of 79%, accuracy of 78% and specificity of 76%. The proposed methods can reduce the likelihood of hazardous events like pulmonary congestion and ventricular suction for HF patients and notify identified abnormal cases to the hospital, clinician and cardiologist for emergency action, which can diminish the mortality rate of patients with HF.

A ranking-system-based switching particle swarm optimizer with dynamic learning strategies

In this paper, a novel ranking-system-based switching particle swarm optimizer (RSPSO) is proposed. In particular, according to a ranking system, the swarm is divided into elite and normal group, then each particle has been assigned a fitness-based (for normal group member) or a distance-based neighborhood (for elite group member). It is remarkable that neighborhood of a particle is time-varying so that communication among swarm during whole searching process is greatly enhanced. In addition, searching process is divided into four stages by the switching framework, where learning strategies and parameter settings are changed in an adaptive way. Moreover, a newly proposed dimensional learning strategy has been hybridized in RSPSO so as to preserve useful information in the swarm and differential evolution algorithm is employed for a further exploration and also diversifying the swarm. Proposed RSPSO is comprehensively evaluated on series of benchmarks including uni-modal, multi-modal and rotated multi-modal functions. Furthermore, ablation study and sensitivity analysis are performed, where influences of the ranking system, time-varying neighborhood as well as other key parameters have been discussed in detail. Experimental results demonstrate the superiority of proposed algorithm which outperforms other five PSO variants on several indicators regarding to both solution accuracy and convergence performance on most benchmarks in a statistic sense.

Research on improved sparrow algorithm based on random walk

The optimization problem is a hot issue in today’s science and engineering research. The sparrow algorithm has the advantages of simple structure, few control parameters and high solution accuracy, and has been widely used in the research of optimization problems. Purposing at the problem that the sparrow search algorithm (SSA) can’t take into account the global and local optimization, an improved sparrow algorithm based on random walk strategy is proposed. After the sparrow search, the random walk is used to perturb the optimal sparrow to demonstrate its search-ability. At the original of the iteration, the random walk boundary is large, which is favourable to demonstrate the whole search-ability. After several iterations, the walk boundary becomes smaller, which improves the local search-ability of the best location of the algorithm. Taking the convergence speed, algorithm stability and convergence precision as evaluation indicators, the improved Sparrow Algorithm (RWSSA) is verified by 4 unimodal functions and 5 multimodal classical test functions, and compared with the traditional Sparrow algorithm. The experimental results show that the capacity of the improved sparrow algorithm based on random walk is significantly improved. At the same time, RWSSA is put into practice the power prediction problem, which checkouts the feasibility of RWSSA in actual engineering problems.

Swarmed Grey Wolf Optimizer

Background: The Particle Swarm Optimization (PSO) algorithm is amongst the utmost favourable optimization algorithms often employed in hybrid procedures by the researchers considering simplicity, smaller count of parameters involved, convergence speed and capability of searching global optima. The PSO algorithm acquires memory and the collaborative swarm interactions enhances the search procedure. The high exploitation ability of PSO which intends to locate the best solution within a limited region of the search domain gives PSO an edge over other optimization algorithms. Whereas, low exploration ability results in lack of assurance of proper sampling of the search domain and thus enhances the chances of rejecting a domain containing high quality solutions. A perfect harmony between exploration and exploitation abilities in the course of selection of best solution is needed. High exploitation capacity makes PSO get trapped in local minima when its initial location is far off from the global minima. OBJECTIVES: The intent of this study is to reform this drawback of PSO of getting trapped in local minima. With an objective to upgrade the potential of Particle Swarm Optimization (PSO) to exploit along with preventing PSO of getting trapped in local minima, we require an algorithm with a positive acceptable exploration capacity. METHODS: We utilized, the recently developed metaheuristic Grey Wolf Optimizer (GWO) emulating the seeking and hunting techniques of Grey wolves for this purpose. In our way, the GWO has been utilized to assist PSO in a manner to unite their strengths and lessen their weaknesses. The proposed hybrid has two driving parameters to adjust and assign the preference to PSO or GWO. RESULTS: To test the act of the proposed hybrid it has been examined in comparison with the PSO and GWO methods. For this, eleven benchmark functions involving different unimodal and multimodal functions have been taken. The PSO, GWO and SGWO pseudo codes were coded in visual basic. In all the functions parameters of PSO and GWO were chosen as: w = 0.7, c1 = c2 = 2, population size = 30, number of iterations = 30. Experiments were redone 25 times for each of the method and for each benchmark function. The methods were compared with regard to their best and worst values besides their average values and standard deviations. The obtained results revealed that in terms of average values and standard deviations our hybrid SGWO outperformed both PSO and GWO notably. CONCLUSION: The outcomes of the experiments reveals that the proposed hybrid is better in comparison to both PSO and GWO in the search ability. Though the SGWO algorithm refines result quality, the computational complexity also gets elevated. Thus, lowering the computational complexity would be another issue of future work. Moreover, we will apply the proposed hybrid in the field of water quality estimation and prediction.