BHJO: A Novel Hybrid Metaheuristic Algorithm Combining the Beluga Whale, Honey Badger, and Jellyfish Search Optimizers for Solving Engineering Design Problems

Hybridizing metaheuristic algorithms involves synergistically combining different optimization techniques to effectively address complex and challenging optimization problems.This approach aims to leverage the strengths of multiple algorithms,enhancing solution quality,convergence speed,and robustness,thereby offering a more versatile and efficient means of solving intricate real-world optimization tasks.In this paper,we introduce a hybrid algorithm that amalgamates three distinct metaheuristics:the Beluga Whale Optimization(BWO),the Honey Badger Algorithm(HBA),and the Jellyfish Search(JS)optimizer.The proposed hybrid algorithm will be referred to as BHJO.Through this fusion,the BHJO algorithm aims to leverage the strengths of each optimizer.Before this hybridization,we thoroughly examined the exploration and exploitation capabilities of the BWO,HBA,and JS metaheuristics,as well as their ability to strike a balance between exploration and exploitation.This meticulous analysis allowed us to identify the pros and cons of each algorithm,enabling us to combine them in a novel hybrid approach that capitalizes on their respective strengths for enhanced optimization performance.In addition,the BHJO algorithm incorporates Opposition-Based Learning(OBL)to harness the advantages offered by this technique,leveraging its diverse exploration,accelerated convergence,and improved solution quality to enhance the overall performance and effectiveness of the hybrid algorithm.Moreover,the performance of the BHJO algorithm was evaluated across a range of both unconstrained and constrained optimization problems,providing a comprehensive assessment of its efficacy and applicability in diverse problem domains.Similarly,the BHJO algorithm was subjected to a comparative analysis with several renowned algorithms,where mean and standard deviation values were utilized as evaluation metrics.This rigorous comparison aimed to assess the performance of the BHJOalgorithmabout its counterparts,shedding light on its effectiveness and reliability in solving optimization problems.Finally,the obtained numerical statistics underwent rigorous analysis using the Friedman post hoc Dunn’s test.The resulting numerical values revealed the BHJO algorithm’s competitiveness in tackling intricate optimization problems,affirming its capability to deliver favorable outcomes in challenging scenarios.

A global harmony search algorithm for finding optimal capacitor location and size in distribution networks

Shunt capacitors are broadly applied in distribution systems to scale down power losses, improve voltage profile and boost system capacity. The amount of capacitors added and location of deployment in the system highly determine the advantage of compensation. A novel global harmony search(GHS) algorithm in parallel with the backward/ forward sweep power flow technique and radial harmonic power flow was used to investigate the optimal placement and sizing of capacitors in radial distribution networks for minimizing power loss and total cost by taking account load unbalancing, mutual coupling and harmonics. The optimal capacitor placement outcomes show that the GHS algorithm can reduce total power losses up to 60 k W and leads to more than 18% of cost saving. The results also demonstrate that the GHS algorithm is more effective in minimization of power loss and total costs compared with genetic algorithm(GA), particle swarm optimization(PSO) and harmony search(HS) algorithm. Moreover, the proposed algorithm converges within 800 iterations and is faster in terms of computational time and gives better performance in finding optimal capacitor location and size compared with other optimization techniques.

Optimal Polygonal Approximation of Digital Planar Curves Using Genetic Algorithm and Tabu Search

Three heuristic algorithms for optimal polygonal approximation of digital planar curves is presented. With Genetic Algorithm (GA), improved Genetic Algorithm (IGA) based on Pareto optimal solution and Tabu Search (TS), a near optimal polygonal approximation was obtained. Compared to the famous Teh chin algorithm, our algorithms have obtained the approximated polygons with less number of vertices and less approximation error. Compared to the dynamic programming algorithm, the processing time of our algorithms are much less expensive.

Optimal fuzzy PID controller with adjustable factors based on flexible polyhedron search algorithm

A new kind of optimal fuzzy PID controller is proposed, which contains two parts. One is an on line fuzzy inference system, and the other is a conventional PID controller. In the fuzzy inference system, three adjustable factors x p, x i , and x d are introduced. Their functions are to further modify and optimize the result of the fuzzy inference so as to make the controller have the optimal control effect on a given object. The optimal values of these adjustable factors are determined based on the ITAE criterion and the Nelder and Mead′s flexible polyhedron search algorithm. This optimal fuzzy PID controller has been used to control the executive motor of the intelligent artificial leg designed by the authors. The result of computer simulation indicates that this controller is very effective and can be widely used to control different kinds of objects and processes.

Optimal Energy Consumption Optimization in a Smart House by Considering Electric Vehicles and Demand Response via a Hybrid Gravitational Search and Particle Swarm Optimization Algorithm

Buildings are the main energy consumers across the world,especially in urban communities.Building smartization,or the smartification of housing,therefore,is a major step towards energy grid smartization too.By controlling the energy consumption of lighting,heating,and cooling systems,energy consumption can be optimized.All or some part of the energy consumed in future smart buildings must be supplied by renewable energy sources(RES),which mitigates environmental impacts and reduces peak demand for electrical energy.In this paper,a new optimization algorithm is applied to solve the optimal energy consumption problem by considering the electric vehicles and demand response in smart homes.In this way,large power stations that work with fossil fuels will no longer be developed.The current study modeled and evaluated the performance of a smart house in the presence of electric vehicles(EVs)with bidirectional power exchangeability with the power grid,an energy storage system(ESS),and solar panels.Additionally,the solar RES and ESS for predicting solar-generated power prediction uncertainty have been considered in this work.Different case studies,including the sales of electrical energy resulting from PV panels’generated power to the power grid,time-variable loads such as washing machines,and different demand response(DR)strategies based on energy price variations were taken into account to assess the economic and technical effects of EVs,BESS,and solar panels.The proposed model was simulated in MATLAB.A hybrid particle swarm optimization(PSO)and gravitational search(GS)algorithm were utilized for optimization.Scenario generation and reduction were performed via LHS and backward methods,respectively.Obtained results demonstrate that the proposed model minimizes the energy supply cost by considering the stochastic time of use(STOU)loads,EV,ESS,and PV system.Based on the results,the proposed model markedly reduced the electricity costs of the smart house.

Cuckoo search algorithm-based optimal deployment method of heterogeneous multistatic radar for barrier coverage

This paper proposes an optimal deployment method of heterogeneous multistatic radars to construct arc barrier coverage with location restrictions.This method analyzes and proves the properties of different deployment patterns in the optimal deployment sequence.Based on these properties and considering location restrictions,it introduces an optimization model of arc barrier coverage and aims to minimize the total deployment cost of heterogeneous multistatic radars.To overcome the non-convexity of the model and the non-analytical nature of the objective function,an algorithm combining integer line programming and the cuckoo search algorithm(CSA)is proposed.The proposed algorithm can determine the number of receivers and transmitters in each optimal deployment squence to minimize the total placement cost.Simulations are conducted in different conditions to verify the effectiveness of the proposed method.

Implementing an Optimal Energy Management System for a Set of Microgrids Using the Harmony Search Algorithm

A microgrid(MG)refers to a set of loads,generation resources and energy storage systems acting as a controllable load or a generator to supply power and heating to a local area.The MG-generated power management is a central topic for MG design and operation.The existence of dispersed generation(DG)resources has faced MG management with new issues.Depending on the level of exchanges between an MG and the main grid,the MG operation states can be divided into independent or grid-connected ones.Energy management in MGs aims to supply power at the lowest cost for optimal load response.This study examines MG energy management in two operational modes of islanded and grid-connected,and proposes a structure with two control layers(primary and secondary)for energy management.At the principal level of control,the energy management system is determined individually for all MG by taking into consideration the probability constraints and RES uncertainty by the Weibull the probability density function(PDF),generation resources’power as well as the generation surplus and deficit of each MG.Then,the information of the power surplus and deficit of each MG must be sent to the central energy management system.To confirm the proposed structure,a case system with two MGs and a condensive load is simulated by using a multi-time harmony search algorithm.Several scenarios are applied to evaluate the performance of this algorithm.The findings clearly show the effectiveness of the proposed system in the energy management of several MGs,leading to the optimal performance of the resources per MG.Moreover,the proposed control scheme properly controls the MG and grid’s performance in their interactions and offers a high level of robustness,stable behavior under different conditions and high quality of power supply.

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.

Seeker optimization algorithm:a novel stochastic search algorithm for global numerical optimization

A novel heuristic search algorithm called seeker op- timization algorithm （SOA） is proposed for the real-parameter optimization. The proposed SOA is based on simulating the act of human searching. In the SOA, search direction is based on empir- ical gradients by evaluating the response to the position changes, while step length is based on uncertainty reasoning by using a simple fuzzy rule. The effectiveness of the SOA is evaluated by using a challenging set of typically complex functions in compari- son to differential evolution （DE） and three modified particle swarm optimization （PSO） algorithms. The simulation results show that the performance of the SOA is superior or comparable to that of the other algorithms.

A Hybrid Multi-Objective Evolutionary Algorithm for Optimal Groundwater Management under Variable Density Conditions

In this paper, a new hybrid multi-objective evolutionary algorithm （MOEA）, the niched Pareto tabu search combined with a genetic algorithm （NPTSGA）, is proposed for the management of groundwater resources under variable density conditions. Relatively few MOEAs can possess global search ability contenting with intensified search in a local area. Moreover, the overall searching ability of tabu search （TS） based MOEAs is very sensitive to the neighborhood step size. The NPTSGA is developed on the thought of integrating the genetic algorithm （GA） with a TS based MOEA, the niched Pareto tabu search （NPTS）, which helps to alleviate both of the above difficulties. Here, the global search ability of the NPTS is improved by the diversification of candidate solutions arising from the evolving genetic algorithm population. Furthermore, the proposed methodology coupled with a density-dependent groundwater flow and solute transport simulator, SEAWAT, is developed and its performance is evaluated through a synthetic seawater intrusion management problem. Optimization results indicate that the NPTSGA offers a tradeoff between the two conflicting objectives. A key conclusion of this study is that the NPTSGA keeps the balance between the intensification of nondomination and the diversification of near Pareto-optimal solutions along the tradeoff curves and is a stable and robust method for implementing the multi-objective design of variable-density groundwater resources.

A hybrid cuckoo search algorithm with feasibility-based rule for constrained structural optimization

Constrained optimization problems are very important as they are encountered in many science and engineering applications.As a novel evolutionary computation technique,cuckoo search(CS) algorithm has attracted much attention and wide applications,owing to its easy implementation and quick convergence.A hybrid cuckoo pattern search algorithm(HCPS) with feasibility-based rule is proposed for solving constrained numerical and engineering design optimization problems.This algorithm can combine the stochastic exploration of the cuckoo search algorithm and the exploitation capability of the pattern search method.Simulation and comparisons based on several well-known benchmark test functions and structural design optimization problems demonstrate the effectiveness,efficiency and robustness of the proposed HCPS algorithm.

Even Search in a Promising Region for Constrained Multi-Objective Optimization

In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.

Wild Gibbon Optimization Algorithm

Complex optimization problems hold broad significance across numerous fields and applications.However,as the dimensionality of such problems increases,issues like the curse of dimensionality and local optima trapping also arise.To address these challenges,this paper proposes a novel Wild Gibbon Optimization Algorithm(WGOA)based on an analysis of wild gibbon population behavior.WGOAcomprises two strategies:community search and community competition.The community search strategy facilitates information exchange between two gibbon families,generating multiple candidate solutions to enhance algorithm diversity.Meanwhile,the community competition strategy reselects leaders for the population after each iteration,thus enhancing algorithm precision.To assess the algorithm’s performance,CEC2017 and CEC2022 are chosen as test functions.In the CEC2017 test suite,WGOA secures first place in 10 functions.In the CEC2022 benchmark functions,WGOA obtained the first rank in 5 functions.The ultimate experimental findings demonstrate that theWildGibbonOptimization Algorithm outperforms others in tested functions.This underscores the strong robustness and stability of the gibbonalgorithm in tackling complex single-objective optimization problems.

Adaptive backtracking search optimization algorithm with pattern search for numerical optimization

The backtracking search optimization algorithm（BSA） is one of the most recently proposed population-based evolutionary algorithms for global optimization. Due to its memory ability and simple structure, BSA has powerful capability to find global optimal solutions. However, the algorithm is still insufficient in balancing the exploration and the exploitation. Therefore, an improved adaptive backtracking search optimization algorithm combined with modified Hooke-Jeeves pattern search is proposed for numerical global optimization. It has two main parts： the BSA is used for the exploration phase and the modified pattern search method completes the exploitation phase. In particular, a simple but effective strategy of adapting one of BSA＇s important control parameters is introduced. The proposed algorithm is compared with standard BSA, three state-of-the-art evolutionary algorithms and three superior algorithms in IEEE Congress on Evolutionary Computation 2014（IEEE CEC2014） over six widely-used benchmarks and 22 real-parameter single objective numerical optimization benchmarks in IEEE CEC2014. The results of experiment and statistical analysis demonstrate the effectiveness and efficiency of the proposed algorithm.

Research on Evacuation Path Planning Based on Improved Sparrow Search Algorithm

Reducing casualties and property losses through effective evacuation route planning has been a key focus for researchers in recent years.As part of this effort,an enhanced sparrow search algorithm(MSSA)was proposed.Firstly,the Golden Sine algorithm and a nonlinear weight factor optimization strategy were added in the discoverer position update stage of the SSA algorithm.Secondly,the Cauchy-Gaussian perturbation was applied to the optimal position of the SSA algorithm to improve its ability to jump out of local optima.Finally,the local search mechanism based on the mountain climbing method was incorporated into the local search stage of the SSA algorithm,improving its local search ability.To evaluate the effectiveness of the proposed algorithm,the Whale Algorithm,Gray Wolf Algorithm,Improved Gray Wolf Algorithm,Sparrow Search Algorithm,and MSSA Algorithm were employed to solve various test functions.The accuracy and convergence speed of each algorithm were then compared and analyzed.The results indicate that the MSSA algorithm has superior solving ability and stability compared to other algorithms.To further validate the enhanced algorithm’s capabilities for path planning,evacuation experiments were conducted using different maps featuring various obstacle types.Additionally,a multi-exit evacuation scenario was constructed according to the actual building environment of a teaching building.Both the sparrow search algorithm and MSSA algorithm were employed in the simulation experiment for multiexit evacuation path planning.The findings demonstrate that the MSSA algorithm outperforms the comparison algorithm,showcasing its greater advantages and higher application potential.

Enhanced Hybrid Equilibrium Strategy in Fog-Cloud Computing Networks with Optimal Task Scheduling

More devices in the Intelligent Internet of Things(AIoT)result in an increased number of tasks that require low latency and real-time responsiveness,leading to an increased demand for computational resources.Cloud computing’s low-latency performance issues in AIoT scenarios have led researchers to explore fog computing as a complementary extension.However,the effective allocation of resources for task execution within fog environments,characterized by limitations and heterogeneity in computational resources,remains a formidable challenge.To tackle this challenge,in this study,we integrate fog computing and cloud computing.We begin by establishing a fog-cloud environment framework,followed by the formulation of a mathematical model for task scheduling.Lastly,we introduce an enhanced hybrid Equilibrium Optimizer(EHEO)tailored for AIoT task scheduling.The overarching objective is to decrease both the makespan and energy consumption of the fog-cloud system while accounting for task deadlines.The proposed EHEO method undergoes a thorough evaluation against multiple benchmark algorithms,encompassing metrics likemakespan,total energy consumption,success rate,and average waiting time.Comprehensive experimental results unequivocally demonstrate the superior performance of EHEO across all assessed metrics.Notably,in the most favorable conditions,EHEO significantly diminishes both the makespan and energy consumption by approximately 50%and 35.5%,respectively,compared to the secondbest performing approach,which affirms its efficacy in advancing the efficiency of AIoT task scheduling within fog-cloud networks.

A Discrete Multi-Objective Squirrel Search Algorithm for Energy-Efficient Distributed Heterogeneous Permutation Flowshop with Variable Processing Speed

In the manufacturing industry,reasonable scheduling can greatly improve production efficiency,while excessive resource consumption highlights the growing significance of energy conservation in production.This paper studies the problem of energy-efficient distributed heterogeneous permutation flowshop problem with variable processing speed(DHPFSP-VPS),considering both the minimum makespan and total energy consumption(TEC)as objectives.A discrete multi-objective squirrel search algorithm(DMSSA)is proposed to solve the DHPFSPVPS.DMSSA makes four improvements based on the squirrel search algorithm.Firstly,in terms of the population initialization strategy,four hybrid initialization methods targeting different objectives are proposed to enhance the quality of initial solutions.Secondly,enhancements are made to the population hierarchy system and position updating methods of the squirrel search algorithm,making it more suitable for discrete scheduling problems.Additionally,regarding the search strategy,six local searches are designed based on problem characteristics to enhance search capability.Moreover,a dynamic predator strategy based on Q-learning is devised to effectively balance DMSSA’s capability for global exploration and local exploitation.Finally,two speed control energy-efficient strategies are designed to reduce TEC.Extensive comparative experiments are conducted in this paper to validate the effectiveness of the proposed strategies.The results of comparing DMSSA with other algorithms demonstrate its superior performance and its potential for efficient solving of the DHPFSP-VPS problem.

Parameter Optimization of Tuned Mass Damper Inerter via Adaptive Harmony Search

Dynamic impacts such as wind and earthquakes cause loss of life and economic damage.To ensure safety against these effects,various measures have been taken from past to present and solutions have been developed using different technologies.Tall buildings are more susceptible to vibrations such as wind and earthquakes.Therefore,vibration control has become an important issue in civil engineering.This study optimizes tuned mass damper inerter(TMDI)using far-fault ground motion records.This study derives the optimum parameters of TMDI using the Adaptive Harmony Search algorithm.Structure displacement and total acceleration against earthquake load are analyzed to assess the performance of the TMDI system.The effect of the inerter when connected to different floors is observed,and the results are compared to the conventional tuned mass damper(TMD).It is indicated that the case of connecting the inerter force to the 5th floor gives better results.As a result,TMD and TMDI systems reduce the displacement by 21.87%and 25.45%,respectively,and the total acceleration by 25.45%and 19.59%,respectively.These percentage reductions indicated that the structure resilience against dynamic loads can be increased using control systems.

Well production optimization using streamline features-based objective function and Bayesian adaptive direct search algorithm

Well production optimization is a complex and time-consuming task in the oilfield development.The combination of reservoir numerical simulator with optimization algorithms is usually used to optimize well production.This method spends most of computing time in objective function evaluation by reservoir numerical simulator which limits its optimization efficiency.To improve optimization efficiency,a well production optimization method using streamline features-based objective function and Bayesian adaptive direct search optimization(BADS)algorithm is established.This new objective function,which represents the water flooding potential,is extracted from streamline features.It only needs to call the streamline simulator to run one time step,instead of calling the simulator to calculate the target value at the end of development,which greatly reduces the running time of the simulator.Then the well production optimization model is established and solved by the BADS algorithm.The feasibility of the new objective function and the efficiency of this optimization method are verified by three examples.Results demonstrate that the new objective function is positively correlated with the cumulative oil production.And the BADS algorithm is superior to other common algorithms in convergence speed,solution stability and optimization accuracy.Besides,this method can significantly accelerate the speed of well production optimization process compared with the objective function calculated by other conventional methods.It can provide a more effective basis for determining the optimal well production for actual oilfield development.

Optimizing combination of aircraft maintenance tasks by adaptive genetic algorithm based on cluster search

It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optimal combination under various constraints not only involves numerical calculations but also is an NP-hard combinatorial problem.To solve the problem,an adaptive genetic algorithm based on cluster search,which is divided into two phases,is put forward.In the first phase,according to the density,all individuals can be homogeneously scattered over the whole solution space through crossover and mutation and better individuals are collected as candidate cluster centres.In the second phase,the search is confined to the neighbourhood of some selected possible solutions to accurately solve with cluster radius decreasing slowly,meanwhile all clusters continuously move to better regions until all the peaks in the question space is searched.This algorithm can efficiently solve the combination problem.Taking the optimization on decision-making of aircraft maintenance by the algorithm for an example,maintenance which combines multiple parts or tasks can significantly enhance economic benefit when the halt cost is rather high.