Improved particle swarm optimization based on particles' explorative capability enhancement

Accelerating the convergence speed and avoiding the local optimal solution are two main goals of particle swarm optimization（PSO）. The very basic PSO model and some variants of PSO do not consider the enhancement of the explorative capability of each particle. Thus these methods have a slow convergence speed and may trap into a local optimal solution. To enhance the explorative capability of particles, a scheme called explorative capability enhancement in PSO（ECE-PSO） is proposed by introducing some virtual particles in random directions with random amplitude. The linearly decreasing method related to the maximum iteration and the nonlinearly decreasing method related to the fitness value of the globally best particle are employed to produce virtual particles. The above two methods are thoroughly compared with four representative advanced PSO variants on eight unimodal and multimodal benchmark problems. Experimental results indicate that the convergence speed and solution quality of ECE-PSO outperform the state-of-the-art PSO variants.

MY EXPLORATIVE RESULTS ON SOIL NITROGEN

The efficient application of nitrogen fertilizers in farming and its theoretical basis are of great concern to soil scientists both at home and abroad.Since 1961, my colleagues and I have been involved in the rational application of nitrogen fertilizers in crop production by probing the transformation of nitrogen and its compounds in soils.A total of 96 research papers have been published, two monographs edited and eight prizes received from the State S&T Commission,the CAS and the Government of Jiangsu Province.Our main contributions may be listed as follows:

UNDO, An Aid for Explorative Learning?

New users of an application system, especially computer novices, can become confused and frus- trated after experiencing the first, perhaps not recoverable error situations during the early stages of explora- tion and learning. System facilities, which let users UNDO and REDO executed commands, are suggested to be an aid for active learning and can be used as a method for systematic exploration through recovering from unknown and newly explored (perhaps wrong) system states by cancelling executed commands with UNDO. An explorative learning experiment on a commercial graphics editor with a modified user inter- face revealed reasons, why one-step recall UNDO does not guarantee successful explorative learning of a complex cognitive skill such as graphics editing on computer.

Geological characteristics and exploration breakthroughs of coal rock gas in Carboniferous Benxi Formation,Ordos Basin,NW China

To explore the geological characteristics and exploration potential of the Carboniferous Benxi Formation coal rock gas in the Ordos Basin,this paper presents a systematic research on the coal rock distribution,coal rock reservoirs,coal rock quality,and coal rock gas features,resources and enrichment.Coal rock gas is a high-quality resource distinct from coalbed methane,and it has unique features in terms of burial depth,gas source,reservoir,gas content,and carbon isotopic composition.The Benxi Formation coal rocks cover an area of 16×104km^(2),with thicknesses ranging from 2 m to 25 m,primarily consisting of bright and semi-bright coals with primitive structures and low volatile and ash contents,indicating a good coal quality.The medium-to-high rank coal rocks have the total organic carbon(TOC)content ranging from 33.49%to 86.11%,averaging75.16%.They have a high degree of thermal evolution(Roof 1.2%-2.8%),and a high gas-generating capacity.They also have high stable carbon isotopic values(δ13C1of-37.6‰to-16‰;δ13C2of-21.7‰to-14.3‰).Deep coal rocks develop matrix pores such as gas bubble pores,organic pores,and inorganic mineral pores,which,together with cleats and fractures,form good reservoir spaces.The coal rock reservoirs exhibit the porosity of 0.54%-10.67%(averaging 5.42%)and the permeability of(0.001-14.600)×10^(-3)μm^(2)(averaging 2.32×10^(-3)μm^(2)).Vertically,there are five types of coal rock gas accumulation and dissipation combinations,among which the coal rock-mudstone gas accumulation combination and the coal rock-limestone gas accumulation combination are the most important,with good sealing conditions and high peak values of total hydrocarbon in gas logging.A model of coal rock gas accumulation has been constructed,which includes widespread distribution of medium-to-high rank coal rocks continually generating gas,matrix pores and cleats/fractures in coal rocks acting as large-scale reservoir spaces,tight cap rocks providing sealing,source-reservoir integration,and five types of efficient enrichment patterns(lateral pinchout complex,lenses,low-amplitude structures,nose-like structures,and lithologically self-sealing).According to the geological characteristics of coal rock gas,the Benxi Formation is divided into 8 plays,and the estimated coal rock gas resources with a buried depth of more than 2000 m are more than 12.33×10^(12)m^(3).The above understandings guide the deployment of risk exploration.Two wells drilled accordingly obtained an industrial gas flow,driving the further deployment of exploratory and appraisal wells.Substantial breakthroughs have been achieved,with the possible reserves over a trillion cubic meters and the proved reserves over a hundred billion cubic meters,which is of great significance for the reserves increase and efficient development of natural gas in China.

On the apparent line-of-sight alignment of the peak X-ray intensity of the magnetosheath and the tangent to the magnetopause,as viewed by SMILE-SXI

The Soft X-ray Imager(SXI)on board the Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)spacecraft will be able to view the Earth’s magnetosheath in soft X-rays.Simulated images of the X-ray emission visible from the position of SMILE are created for a range of solar wind densities by using 3 years of the SMILE mission orbit,together with models of the expected X-ray emissivity from the Earth’s magnetosheath.Results from global magnetohydrodynamic simulations and a simple model for exospheric neutral densities are used to compare the locations of the lines of sight along which integrated soft X-ray intensities peak with the lines of sight lying tangent to surfaces(defined here to be the magnetopause)along which local soft X-ray intensities peak or exhibit their strongest gradients,or both,for strongly southward interplanetary magnetic field conditions when no depletion or low-latitude boundary layers are expected.Where,in the parameter space of the various times and seasons,orbital phases,solar wind conditions,and magnetopause models,the alignment of the X-ray emission peak with the magnetopause tangent is good,or is not,is presented.The main results are as follows.The spacecraft needs to be positioned well outside the magnetopause;low-altitude times near perigee are not good.In addition,there are seasonal aspects:dayside-apogee orbits are generally very good because the spacecraft travels out sunward at high altitude,but nightside-apogee orbits,behind the Earth,are bad because the spacecraft only rarely leaves the magnetopause.Dusk-apogee and dawnapogee orbits are intermediate.Dayside-apogee orbits worsen slightly over the first three mission years,whereas nightside-apogee orbits improve slightly.Additionally,many more times of good agreement with the peak-to-tangent hypothesis occur when the solar wind is in a high-density state,as opposed to a low-density state.In a high-density state,the magnetopause is compressed,and the spacecraft is more often a good distance outside the magnetopause.

Using restored two-dimensional X-ray images to reconstruct the three-dimensional magnetopause

Astronomical imaging technologies are basic tools for the exploration of the universe,providing basic data for the research of astronomy and space physics.The Soft X-ray Imager(SXI)carried by the Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)aims to capture two-dimensional(2-D)images of the Earth’s magnetosheath by using soft X-ray imaging.However,the observed 2-D images are affected by many noise factors,destroying the contained information,which is not conducive to the subsequent reconstruction of the three-dimensional(3-D)structure of the magnetopause.The analysis of SXI-simulated observation images shows that such damage cannot be evaluated with traditional restoration models.This makes it difficult to establish the mapping relationship between SXIsimulated observation images and target images by using mathematical models.We propose an image restoration algorithm for SXIsimulated observation images that can recover large-scale structure information on the magnetosphere.The idea is to train a patch estimator by selecting noise–clean patch pairs with the same distribution through the Classification–Expectation Maximization algorithm to achieve the restoration estimation of the SXI-simulated observation image,whose mapping relationship with the target image is established by the patch estimator.The Classification–Expectation Maximization algorithm is used to select multiple patch clusters with the same distribution and then train different patch estimators so as to improve the accuracy of the estimator.Experimental results showed that our image restoration algorithm is superior to other classical image restoration algorithms in the SXI-simulated observation image restoration task,according to the peak signal-to-noise ratio and structural similarity.The restoration results of SXI-simulated observation images are used in the tangent fitting approach and the computed tomography approach toward magnetospheric reconstruction techniques,significantly improving the reconstruction results.Hence,the proposed technology may be feasible for processing SXI-simulated observation images.

Frilled Lizard Optimization: A Novel Bio-Inspired Optimizer for Solving Engineering Applications

This research presents a novel nature-inspired metaheuristic algorithm called Frilled Lizard Optimization(FLO),which emulates the unique hunting behavior of frilled lizards in their natural habitat.FLO draws its inspiration from the sit-and-wait hunting strategy of these lizards.The algorithm’s core principles are meticulously detailed and mathematically structured into two distinct phases:(i)an exploration phase,which mimics the lizard’s sudden attack on its prey,and(ii)an exploitation phase,which simulates the lizard’s retreat to the treetops after feeding.To assess FLO’s efficacy in addressing optimization problems,its performance is rigorously tested on fifty-two standard benchmark functions.These functions include unimodal,high-dimensional multimodal,and fixed-dimensional multimodal functions,as well as the challenging CEC 2017 test suite.FLO’s performance is benchmarked against twelve established metaheuristic algorithms,providing a comprehensive comparative analysis.The simulation results demonstrate that FLO excels in both exploration and exploitation,effectively balancing these two critical aspects throughout the search process.This balanced approach enables FLO to outperform several competing algorithms in numerous test cases.Additionally,FLO is applied to twenty-two constrained optimization problems from the CEC 2011 test suite and four complex engineering design problems,further validating its robustness and versatility in solving real-world optimization challenges.Overall,the study highlights FLO’s superior performance and its potential as a powerful tool for tackling a wide range of optimization problems.

Micromechanical testing and property upscaling of planetary rocks:A critical review

Knowledge of the mechanical behavior of planetary rocks is indispensable for space explorations.The scarcity of pristine samples and the irregular shapes of planetary meteorites make it difficult to obtain representative samples for conventional macroscale rock mechanics experiments(macro-RMEs).This critical review discusses recent advances in microscale RMEs(micro-RMEs)techniques and the upscaling methods for extracting mechanical parameters.Methods of mineralogical and microstructural analyses,along with non-destructive mechanical techniques,have provided new opportunities for studying planetary rocks with unprecedented precision and capabilities.First,we summarize several mainstream methods for obtaining the mineralogy and microstructure of planetary rocks.Then,nondestructive micromechanical testing methods,nanoindentation and atomic force microscopy(AFM),are detailed reviewed,illustrating the principles,advantages,influencing factors,and available testing results from literature.Subsequently,several feasible upscaling methods that bridge the micro-measurements of meteorite pieces to the strength of the intact body are introduced.Finally,the potential applications of planetary rock mechanics research to guiding the design and execution of space missions are environed,ranging from sample return missions and planetary defense to extraterrestrial construction.These discussions are expected to broaden the understanding of the microscale mechanical properties of planetary rocks and their significant role in deep space exploration.

Development and characterization of the PolyU-1 lunar regolith simulant based on Chang’e-5 returned samples

Leading national space exploration agencies and private enterprises are actively engaged in lunar exploration initiatives to accomplish manned lunar landings and establish permanent lunar bases in the forthcoming years.With limited access to lunar surface materials on Earth,lunar regolith simulants are crucial for lunar exploration research.The Chang’e-5(CE-5)samples have been characterized by state-of-the-art laboratory equipment,providing a unique opportunity to develop a high-quality lunar regolith simulant.We have prepared a high-fidelity PolyU-1 simulant by pulverizing,desiccating,sieving,and blending natural mineral materials on Earth based on key physical,mineral,and chemical characteristics of CE-5 samples.The results showed that the simulant has a high degree of consistency with the CE-5 samples in terms of the particle morphology,mineral and chemical composition.Direct shear tests were conducted on the simulant,and the measured internal friction angle and cohesion values can serve as references for determining the mechanical properties of CE-5 lunar regolith.The PolyU-1 simulant can contribute to experimental studies involving lunar regolith,including the assessment of interaction between rovers and lunar regolith,as well as the development of in-situ resource utilization(ISRU)technologies.

A comprehensive review of lunar lava tube base construction and field research on a potential Earth test site

The Moon,as the closest celestial body to the Earth,plays a pivotal role in the progression of deep space exploration,and the establishment of research outposts on its surface represents a crucial step in this mission.Lunar lava tubes are special underground caves formed by volcanic eruptions and are considered as ideal natural shelters and scientific laboratories for lunar base construction.This paper begins with an in-depth overview of the geological origins,exploration history,and distribution locations of lunar lava tubes.Subsequently,it delves into the presentation of four distinctive advantages and typical concepts for constructing bases within lava tubes,summarizing the ground-based attempts made thus far in lunar lava tube base construction.Field studies conducted on a lava tube in Hainan revealed rock compositions similar to those found during the Apollo missions and clear lava tube structures,making it a promising analog site.Lastly,the challenges and opportunities encountered in the field of geotechnical engineering regarding the establishment of lunar lava tube bases are discussed,encompassing cave exploration technologies,in-situ testing methods,geomechanical properties under lunar extreme environments,base design and structural stability assessment,excavation and reinforcement techniques,and simulated Earth-based lava tube base.

Natural gas exploration potential and favorable targets of Permian Fengcheng Formation in the western Central Depression of Junggar Basin,NW China

Based on the organic geochemical data and the molecular and stable carbon isotopic compositions of natural gas of the Lower Permian Fengcheng Formation in the western Central Depression of Junggar Basin,combined with sedimentary environment analysis and hydrocarbon-generating simulation,the gas-generating potential of the Fengcheng source rock is evaluated,the distribution of large-scale effective source kitchen is described,the genetic types of natural gas are clarified,and four types of favorable exploration targets are selected.The results show that:(1)The Fengcheng Formation is a set of oil-prone source rocks,and the retained liquid hydrocarbon is conducive to late cracking into gas,with characteristics of high gas-generating potential and late accumulation;(2)The maximum thickness of Fengcheng source rock reaches 900 m.The source rock has entered the main gas-generating stage in Penyijingxi and Shawan sags,and the area with gas-generating intensity greater than 20×10^(8) m^(3)/km^(2) is approximately 6500 km^(2).(3)Around the western Central Depression,highly mature oil-type gas with light carbon isotope composition was identified to be derived from the Fengcheng source rocks mainly,while the rest was coal-derived gas from the Carboniferous source rock;(4)Four types of favorable exploration targets with exploration potential were developed in the western Central Depression which are structural traps neighboring to the source,stratigraphic traps neighboring to the source,shale-gas type within the source,and structural traps within the source.Great attention should be paid to these targets.

Hydrocarbon accumulation and orderly distribution of whole petroleum system in marine carbonate rocks of Sichuan Basin,SW China

Based on the situation and progress of marine oil/gas exploration in the Sichuan Basin,SW China,the whole petroleum system is divided for marine carbonate rocks of the basin according to the combinations of hydrocarbon accumulation elements,especially the source rock.The hydrocarbon accumulation characteristics of each whole petroleum system are analyzed,the patterns of integrated conventional and unconventional hydrocarbon accumulation are summarized,and the favorable exploration targets are proposed.Under the control of multiple extensional-convergent tectonic cycles,the marine carbonate rocks of the Sichuan Basin contain three sets of regional source rocks and three sets of regional cap rocks,and can be divided into the Cambrian,Silurian and Permian whole petroleum systems.These whole petroleum systems present mainly independent hydrocarbon accumulation,containing natural gas of affinity individually.Locally,large fault zones run through multiple whole petroleum systems,forming a fault-controlled complex whole petroleum system.The hydrocarbon accumulation sequence of continental shelf facies shale gas accumulation,marginal platform facies-controlled gas reservoirs,and intra-platform fault-and facies-controlled gas reservoirs is common in the whole petroleum system,with a stereoscopic accumulation and orderly distribution pattern.High-quality source rock is fundamental to the formation of large gas fields,and natural gas in a whole petroleum system is generally enriched near and within the source rocks.The development and maintenance of large-scale reservoirs are essential for natural gas enrichment,multiple sources,oil and gas transformation,and dynamic adjustment are the characteristics of marine petroleum accumulation,and good preservation conditions are critical to natural gas accumulation.Large-scale marginal-platform reef-bank facies zones,deep shale gas,and large-scale lithological complexes related to source-connected faults are future marine hydrocarbon exploration targets in the Sichuan Basin.

Analysis of the joint detection capability of the SMILE satellite and EISCAT-3D radar

The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)satellite is a small magnetosphere–ionosphere link explorer developed cooperatively between China and Europe.It pioneers the use of X-ray imaging technology to perform large-scale imaging of the Earth’s magnetosheath and polar cusp regions.It uses a high-precision ultraviolet imager to image the overall configuration of the aurora and monitor changes in the source of solar wind in real time,using in situ detection instruments to improve human understanding of the relationship between solar activity and changes in the Earth’s magnetic field.The SMILE satellite is scheduled to launch in 2025.The European Incoherent Scatter Sciences Association(EISCAT)-3D radar is a new generation of European incoherent scatter radar constructed by EISCAT and is the most advanced ground-based ionospheric experimental device in the high-latitude polar region.It has multibeam and multidirectional quasi-real-time three-dimensional(3D)imaging capabilities,continuous monitoring and operation capabilities,and multiple-baseline interferometry capabilities.Joint detection by the SMILE satellite and the EISCAT-3D radar is of great significance for revealing the coupling process of the solar wind–magnetosphere–ionosphere.Therefore,we performed an analysis of the joint detection capability of the SMILE satellite and EISCAT-3D,analyzed the period during which the two can perform joint detection,and defined the key scientific problems that can be solved by joint detection.In addition,we developed Web-based software to search for and visualize the joint detection period of the SMILE satellite and EISCAT-3D radar,which lays the foundation for subsequent joint detection experiments and scientific research.

Two stages power generation test of the hot dry rock exploration and production demonstration project in the Gonghe Basin,northeastern Qinghai-Tibet plateau,China

The Hot Dry Rock(HDR)is considered as a clean and renewable energy,poised to significantly contribute to the global energy decarbonization agenda.Many HDR projects worldwide have accumulated valuable experience in efficient drilling and completion,reservoir construction,and fracture simulation.In 2019,China Geological Survey(CGS)initiated a demonstration project of HDR exploration and production in the Gonghe Basin,aiming to overcome the setbacks faced by HDR projects.Over the ensuing four years,the Gonghe HDR project achieved the first power generation in 2021,followed by the second power generation test in 2022.After establishing the primary well group in the initial phase,two directional wells and one branch well were drilled.Noteworthy progress was made in successfully constructing the targeted reservoir,realizing inter-well connectivity,power generation and grid connection,implementing of the real-time micro-seismic monitoring.A closed-loop technical validation of the HDR exploration and production was completed.However,many technical challenges remain in the process of HDR industrialization,such as reservoir fracture network characterization,efficient drilling and completion,multiple fracturing treatment,continuous injection and production,as well as mitigation of induced seismicity and numerical simulation technology.

Simulation of the SMILE Soft X-ray Imager response to a southward interplanetary magnetic field turning

The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)Soft X-ray Imager(SXI)will shine a spotlight on magnetopause dynamics during magnetic reconnection.We simulate an event with a southward interplanetary magnetic field turning and produce SXI count maps with a 5-minute integration time.By making assumptions about the magnetopause shape,we find the magnetopause standoff distance from the count maps and compare it with the one obtained directly from the magnetohydrodynamic(MHD)simulation.The root mean square deviations between the reconstructed and MHD standoff distances do not exceed 0.2 RE(Earth radius)and the maximal difference equals 0.24 RE during the 25-minute interval around the southward turning.

Hem-o-lok clip migration to duodenal bulb post-cholecystectomy:A case report

BACKGROUND Hem-o-lok clips are typically used to control the cystic duct and vessels during laparoscopic cholecystectomy(LC)and common bile duct exploration for stones in the bile duct and gallbladder.Here,we report a unique example of Hem-o-lok clip movement towards the duodenal bulb after LC,appearing as a submucosal tumor(SMT).Additionally,we provide initial evidence of gradual and evolving endoscopic manifestations of Hem-o-lok clip migration to the duodenal bulb wall and review the available literature.CASE SUMMARY A 72-year-old man underwent LC for gallstones,and Hem-o-lok clips were used to ligate both the cystic duct and cystic artery.Esophagogastroduodenoscopy(EGD)2 years later revealed an SMT-like lesion in the duodenal bulb.Due to the symptomatology,the clinical examination did not reveal any major abnormalities,and the patient was followed up as an outpatient.A repeat EGD performed 5 months later revealed an SMT-like lesion in the duodenal bulb with raised edges and a central depression.A third EGD was conducted,during which a Hem-o-lok clip was discovered connected to the front side of the duodenum.The clip was extracted easily using biopsy forceps,and no complications occurred.Two months after the fourth EGD,the scar was surrounded by normal mucosa.CONCLUSION Clinicians should be aware of potential post-LC complications.Hem-o-lok clips should be removed if symptomatic.

Using the Novel Wolverine Optimization Algorithm for Solving Engineering Applications

This paper introduces the Wolverine Optimization Algorithm(WoOA),a biomimetic method inspired by the foraging behaviors of wolverines in their natural habitats.WoOA innovatively integrates two primary strategies:scavenging and hunting,mirroring the wolverine’s adeptness in locating carrion and pursuing live prey.The algorithm’s uniqueness lies in its faithful simulation of these dual strategies,which are mathematically structured to optimize various types of problems effectively.The effectiveness of WoOA is rigorously evaluated using the Congress on Evolutionary Computation(CEC)2017 test suite across dimensions of 10,30,50,and 100.The results showcase WoOA’s robust performance in exploration,exploitation,and maintaining a balance between these phases throughout the search process.Compared to twelve established metaheuristic algorithms,WoOA consistently demonstrates a superior performance across diverse benchmark functions.Statistical analyses,including paired t-tests,Friedman test,and Wilcoxon rank-sum tests,validate WoOA’s significant competitive edge over its counterparts.Additionally,WoOA’s practical applicability is illustrated through its successful resolution of twenty-two constrained scenarios from the CEC 2011 suite and four complex engineering design challenges.These applications underscore WoOA’s efficacy in tackling real-world optimization challenges,further highlighting its potential for widespread adoption in engineering and scientific domains.

Far and Near Optimization:A New Simple and Effective Metaphor-LessOptimization Algorithm for Solving Engineering Applications

In this article,a novel metaheuristic technique named Far and Near Optimization(FNO)is introduced,offeringversatile applications across various scientific domains for optimization tasks.The core concept behind FNO lies inintegrating global and local search methodologies to update the algorithm population within the problem-solvingspace based on moving each member to the farthest and nearest member to itself.The paper delineates the theoryof FNO,presenting a mathematical model in two phases:(i)exploration based on the simulation of the movementof a population member towards the farthest member from itself and(ii)exploitation based on simulating themovement of a population member towards the nearest member from itself.FNO’s efficacy in tackling optimizationchallenges is assessed through its handling of the CEC 2017 test suite across problem dimensions of 10,30,50,and 100,as well as to address CEC 2020.The optimization results underscore FNO’s adeptness in exploration,exploitation,and maintaining a balance between them throughout the search process to yield viable solutions.Comparative analysis against twelve established metaheuristic algorithms reveals FNO’s superior performance.Simulation findings indicate FNO’s outperformance of competitor algorithms,securing the top rank as the mosteffective optimizer across a majority of benchmark functions.Moreover,the outcomes derived by employing FNOon twenty-two constrained optimization challenges from the CEC 2011 test suite,alongside four engineering designdilemmas,showcase the effectiveness of the suggested method in tackling real-world scenarios.

Imaging the Architecture of Mineral Systems and the Pathways of Ore-forming Fluids across Mongolia with Magnetotellurics

In the framework of a mineral system approach,a combination of components is required to develop a mineral system.This includes the whole-lithosphere architecture,which controls the transport of ore-forming fluids,and favorable tectonic and geodynamic processes,occurring at various spatial and temporal scales,that influence the genesis and evolution of ore-forming fluids(Huston et al.,2016;Groves et al.,2018;Davies et al.,2020).Knowledge of the deep structural framework can advance the understanding of the development of a mineral system and the emplacement of mineral deposits.Deep geophysical exploration carried out with this aim is increasingly important for targeting new ore deposits in unexplored and underexplored regions(Dentith et al.,2018;Dentith,2019).

Magnificent Frigatebird Optimization: A New Bio-Inspired Metaheuristic Approach for Solving Optimization Problems

This paper introduces a groundbreaking metaheuristic algorithm named Magnificent Frigatebird Optimization(MFO),inspired by the unique behaviors observed in magnificent frigatebirds in their natural habitats.The foundation of MFO is based on the kleptoparasitic behavior of these birds,where they steal prey from other seabirds.In this process,a magnificent frigatebird targets a food-carrying seabird,aggressively pecking at it until the seabird drops its prey.The frigatebird then swiftly dives to capture the abandoned prey before it falls into the water.The theoretical framework of MFO is thoroughly detailed and mathematically represented,mimicking the frigatebird’s kleptoparasitic behavior in two distinct phases:exploration and exploitation.During the exploration phase,the algorithm searches for new potential solutions across a broad area,akin to the frigatebird scouting for vulnerable seabirds.In the exploitation phase,the algorithm fine-tunes the solutions,similar to the frigatebird focusing on a single target to secure its meal.To evaluate MFO’s performance,the algorithm is tested on twenty-three standard benchmark functions,including unimodal,high-dimensional multimodal,and fixed-dimensional multimodal types.The results from these evaluations highlight MFO’s proficiency in balancing exploration and exploitation throughout the optimization process.Comparative studies with twelve well-known metaheuristic algo-rithms demonstrate that MFO consistently achieves superior optimization results,outperforming its competitors across various metrics.In addition,the implementation of MFO on four engineering design problems shows the effectiveness of the proposed approach in handling real-world applications,thereby validating its practical utility and robustness.