References:

• Yadav, Anupam.

"AEFA: Artificial electric field algorithm for global optimization." Swarm and Evolutionary Computation 48 (2019): 93-108.

AEO(npop, max_iter, lb, ub, objfun)

Artificial Ecosystem-based Optimization (AEO) algorithm implementation in Julia.

Arguments:

• npop: Number of individuals in the population.
• max_iter: Maximum number of iterations.
• lb: Lower bounds for the search space.
• ub: Upper bounds for the search space.
• objfun: Function to evaluate the fitness of individuals.

Returns:

• AEOResult: A struct containing:
  • BestF: The best fitness value found.
  • BestX: The position corresponding to the best fitness.
  • his_best_fit: A vector of best fitness values at each iteration.

References:

• Zhao, Weiguo, Liying Wang, and Zhenxing Zhang. "Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm." Neural Computing and Applications 32, no. 13 (2020): 9383-9425.

AFT(noThieves, max_iter, lb, ub, objfun)

The Ali Baba and the Forty Thieves (AFT) algorithm is a meta-heuristic optimization algorithm inspired by the story of Ali Baba and the Forty Thieves. It is designed to solve numerical optimization problems by simulating the behavior of thieves searching for treasures.

Arguments:

• noThieves: Number of thieves in the algorithm.
• max_iter: Maximum number of iterations.
• lb: Lower bounds for the search space.
• ub: Upper bounds for the search space.
• objfun: Objective function to evaluate the fitness of solutions.

Returns:

• AFTResult: A struct containing:
  • fitness: The best fitness value found.
  • gbest: The position corresponding to the best fitness.
  • ccurve: A vector of best fitness values at each iteration.

References:

• Braik, Malik, Mohammad Hashem Ryalat, and Hussein Al-Zoubi. "A novel meta-heuristic algorithm for solving numerical optimization problems: Ali Baba and the forty thieves." Neural Computing and Applications 34, no. 1 (2022): 409-455.

AHA(npop, max_iter, lb, ub, objfun)

The Artificial Hummingbird Algorithm (AHA) is a meta-heuristic optimization algorithm inspired by the foraging behavior of hummingbirds. It is designed to solve numerical optimization problems by simulating the way hummingbirds search for food.

Arguments:

• npop: Number of hummingbirds (population size).
• max_iter: Maximum number of iterations.
• lb: Lower bounds for the search space.
• ub: Upper bounds for the search space.
• objfun: Objective function to evaluate the fitness of solutions.

Returns:

• AHAResult: A struct containing:
  • BestF: The best fitness value found.
  • BestX: The position corresponding to the best fitness.
  • HisBestFit: A vector of best fitness values at each iteration.

References:

• Zhao, Weiguo, Liying Wang, and Seyedali Mirjalili. "Artificial hummingbird algorithm: A new bio-inspired optimizer with its engineering applications." Computer Methods in Applied Mechanics and Engineering 388 (2022): 114194.

References:

• Xiao, Y., Cui, H., Khurma, R. A., & Castillo, P. A. (2025). Artificial lemming algorithm: a novel bionic meta-heuristic technique for solving real-world engineering optimization problems. Artificial Intelligence Review, 58(3), 84.

References:

• Mirjalili, Seyedali. "The ant lion optimizer." Advances in engineering software 83 (2015): 80-98.

References:

• Abualigah, Laith, Ali Diabat, Seyedali Mirjalili, Mohamed Abd Elaziz, and Amir H. Gandomi. "The arithmetic optimization algorithm." Computer methods in applied mechanics and engineering 376 (2021): 113609.

References:

• Wang, Xiaopeng, Václav Snášel, Seyedali Mirjalili, Jeng-Shyang Pan, Lingping Kong, and Hisham A. Shehadeh. "Artificial Protozoa Optimizer (APO): A novel bio-inspired metaheuristic algorithm for engineering optimization." Knowledge-Based Systems 295 (2024): 111737.

References:

• Wang, Liying, Qingjiao Cao, Zhenxing Zhang, Seyedali Mirjalili, and Weiguo Zhao. "Artificial rabbits optimization: A new bio-inspired meta-heuristic algorithm for solving engineering optimization problems." Engineering Applications of Artificial Intelligence 114 (2022): 105082.

References:

• Abdollahzadeh, B., Gharehchopogh, F. S., & Mirjalili, S. (2021). African vultures optimization algorithm: A new nature-inspired metaheuristic algorithm for global optimization problems. Computers & Industrial Engineering, 158, 107408.

References:

• Yuan, Chong, Dong Zhao, Ali Asghar Heidari, Lei Liu, Yi Chen, Zongda Wu, and Huiling Chen. "Artemisinin optimization based on malaria therapy: Algorithm and applications to medical image segmentation." Displays 84 (2024): 102740.

References:

• Alsattar, Hassan A., A. A. Zaidan, and B. B. Zaidan.

"Novel meta-heuristic bald eagle search optimisation algorithm." Artificial Intelligence Review 53 (2020): 2237-2264.

References:

• Wang, Jun, Wen-chuan Wang, Xiao-xue Hu, Lin Qiu, and Hong-fei Zang.

"Black-winged kite algorithm: a nature-inspired meta-heuristic for solving benchmark functions and engineering problems." Artificial Intelligence Review 57, no. 4 (2024): 98.

References:

• Das, Amit Kumar, and Dilip Kumar Pratihar. "Bonobo optimizer (BO): an intelligent heuristic with self-adjusting parameters over continuous spaces and its applications to engineering problems." Applied Intelligence 52, no. 3 (2022): 2942-2974.

References:

• Arora, Sankalap, and Satvir Singh. "Butterfly optimization algorithm: a novel approach for global optimization." Soft computing 23 (2019): 715-734.

References:

• Shehadeh, Hisham A. "Chernobyl disaster optimizer (CDO): A novel meta-heuristic method for global optimization." Neural Computing and Applications 35, no. 15 (2023): 10733-10749.

References:

• Akbari, Mohammad Amin, Mohsen Zare, Rasoul Azizipanah-Abarghooee, Seyedali Mirjalili, and Mohamed Deriche. "The cheetah optimizer: A nature-inspired metaheuristic algorithm for large-scale optimization problems." Scientific reports 12, no. 1 (2022): 10953.

References:

• Naruei, Iraj, and Farshid Keynia. "A new optimization method based on COOT bird natural life model." Expert Systems with Applications 183 (2021): 115352.

References:

• Ghasemi, Mojtaba, Mohammad-Amin Akbari, Changhyun Jun, Sayed M. Bateni, Mohsen Zare, Amir Zahedi, Hao-Ting Pai, Shahab S. Band, Massoud Moslehpour, and Kwok-Wing Chau. "Circulatory System Based Optimization (CSBO): an expert multilevel biologically inspired meta-heuristic algorithm." Engineering Applications of Computational Fluid Mechanics 16, no. 1 (2022): 1483-1525.

References:

• Braik, Malik, Alaa Sheta, and Heba Al-Hiary. "A novel meta-heuristic search algorithm for solving optimization problems: capuchin search algorithm." Neural computing and applications 33, no. 7 (2021): 2515-2547.

References:

• Khishe, Mohammad, and Mohammad Reza Mosavi. "Chimp optimization algorithm." Expert systems with applications 149 (2020): 113338.

References:

• Braik, Malik Shehadeh. "Chameleon Swarm Algorithm: A bio-inspired optimizer for solving engineering design problems." Expert Systems with Applications 174 (2021): 114685.

References:

• Braik, Malik, Alaa Sheta, and Heba Al-Hiary. "A novel meta-heuristic search algorithm for solving optimization problems: capuchin search algorithm." Neural computing and applications 33, no. 7 (2021): 2515-2547.

References:

• Xue J, Shen B. Dung beetle optimizer: A new meta-heuristic algorithm for global optimization. The Journal of Supercomputing. 2023 May;79(7):7305-36.

References:

• Ghafil, H. N., & Jármai, K. (2020). Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications. Applied Soft Computing, 93, 106392.

References:

• Agushaka, Jeffrey O., Absalom E. Ezugwu, and Laith Abualigah. "Dwarf mongoose optimization algorithm." Computer methods in applied mechanics and engineering 391 (2022): 114570.

References:

• Zhao, Shijie, Tianran Zhang, Shilin Ma, and Miao Chen. "Dandelion Optimizer: A nature-inspired metaheuristic algorithm for engineering applications." Engineering Applications of Artificial Intelligence 114 (2022): 105075.

DSO(npop, max_iter, lb, ub, dim, objfun)

The Deep Sleep Optimiser (DSO) is a human-inspired metaheuristic optimization algorithm that mimics the sleep patterns of humans to find optimal solutions in various optimization problems.

Arguments:

• npop: Number of search agents (population size).
• max_iter: Number of iterations (generations).
• lb: Lower bounds of the search space.
• ub: Upper bounds of the search space.
• objfun: Objective function to be minimized.

Returns:

• ::DSOResult: A struct containing:
  • Best_Cost: The best cost found during the optimization.
  • Best_Position: The position corresponding to the best cost.
  • Best_iteration: A vector of best costs at each iteration.

References:

• Oladejo, Sunday O., Stephen O. Ekwe, Lateef A. Akinyemi, and Seyedali A. Mirjalili, The deep sleep optimiser: A human-based metaheuristic approach., IEEE Access (2023).

References:

• Lian, Junbo, Ting Zhu, Ling Ma, Xincan Wu, Ali Asghar Heidari, Yi Chen, Huiling Chen, and Guohua Hui.

"The educational competition optimizer." International Journal of Systems Science 55, no. 15 (2024): 3185-3222.

References:

• Abdel-Basset, Mohamed, Doaa El-Shahat, Mohammed Jameel, and Mohamed Abouhawwash.

"Exponential distribution optimizer (EDO): a novel math-inspired algorithm for global optimization and engineering problems." Artificial Intelligence Review 56, no. 9 (2023): 9329-9400.

References:

• Faramarzi, Afshin, Mohammad Heidarinejad, Brent Stephens, and Seyedali Mirjalili.

"Equilibrium optimizer: A novel optimization algorithm." Knowledge-based systems 191 (2020): 105190.

References:

• Ouyang, K., Fu, S., Chen, Y., Cai, Q., Heidari, A. A., & Chen, H. (2024).

Escape: an optimization method based on crowd evacuation behaviors. Artificial Intelligence Review, 58(1), 19.

References:

• Luan, Tran Minh, Samir Khatir, Minh Thi Tran, Bernard De Baets, and Thanh Cuong-Le.

"Exponential-trigonometric optimization algorithm for solving complicated engineering problems." Computer Methods in Applied Mechanics and Engineering 432 (2024): 117411.

References:

• Al-Betar, M.A., Awadallah, M.A., Braik, M.S. et al.

Elk herd optimizer: a novel nature-inspired metaheuristic algorithm. Artif Intell Rev 57, 48 (2024). https://doi.org/10.1007/s10462-023-10680-4

F1(x::Vector{Float64}) -> Float64

Tension/Compression Spring Design Optimization.

Minimizes the weight of a tension/compression spring subject to constraints on shear stress, surge frequency, minimum deflection, and geometric limits.

Problem Source

A well-known benchmark in constrained engineering design, commonly used in metaheuristic optimization literature.

Variables

• x[1]: Wire diameter (d)
• x[2]: Mean coil diameter (D)
• x[3]: Number of active coils (N)

Constraints

Four nonlinear inequality constraints:

• Shear stress constraint
• Surge frequency constraint
• Minimum deflection constraint
• Geometry-related limits

Returns

• Penalized objective function value (Float64)

F2(x::Vector{Float64}) -> Float64

Pressure Vessel Design Optimization.

Minimizes the total cost of a cylindrical pressure vessel, which includes material, forming, and welding costs, subject to constraints on thickness, volume, and stress.

Problem Source

A classical benchmark problem in constrained engineering design, widely used in metaheuristic algorithm evaluations.

Variables

• x[1]: Thickness of the shell (Ts)
• x[2]: Thickness of the head (Th)
• x[3]: Inner radius (R)
• x[4]: Length of the cylindrical section without head (L)

Constraints

Four nonlinear inequality constraints:

• Stress constraints on thickness
• Volume constraint
• Geometrical bounds

Returns

• Penalized objective function value (Float64)

Engineering_F3(x::Vector{Float64}) -> Float64

Welded Beam Design Optimization Problem.

Minimizes the cost of a welded beam subject to constraints on shear stress, normal stress, deflection, and geometric properties.

Objective

\[\vec{z} = [z_1, z_2, z_3, z_4] = [h, l, t, b] \\ min_{\vec{z}} f(\vec{z}) = 1.10471 z_1^2 z_2 + 0.04811 z_3 z_4 (14 + z_2)\]

Constraints

\[\begin{aligned} g_1(\vec{z}) &= \tau(z) - \tau_{\max} \leq 0 \\ g_2(\vec{z}) &= \sigma(z) - \sigma_{\max} \leq 0 \\ g_3(\vec{z}) &= z_1 - z_4 \leq 0 \\ g_4(\vec{z}) &= 0.10471 z_1^2 + 0.04811 z_3 z_4 (14 + z_2) - 5 \leq 0 \\ g_5(\vec{z}) &= 0.125 - z_1 \leq 0 \\ g_6(\vec{z}) &= \delta(z) - \delta_{\max} \leq 0 \\ g_7(\vec{z}) &= P - P_c(z) \leq 0 \end{aligned}\]

Definitions

\[\tau(z) = \sqrt{(\tau')^2 + 2\tau'\tau''\frac{z_2}{2R} + (\tau'')^2},\quad \tau' = \frac{P}{\sqrt{2} z_1 z_2},\quad \tau'' = \frac{MR}{J}\]

\[M = P \left( L + \frac{z_2}{2} \right),\quad R = \sqrt{ \frac{z_2^2}{4} + \left( \frac{z_1 + z_3}{2} \right)^2 }\]

\[J = 2 \sqrt{2} z_1 z_2 \left[ \frac{z_2^2}{12} + \left( \frac{z_1 + z_3}{2} \right)^2 \right]\]

\[\sigma(z) = \frac{6PL}{z_4 z_3^2},\quad \delta(z) = \frac{4PL^3}{E z_3^3 z_4}\]

\[P_c(z) = \frac{4.013 E \sqrt{z_3^2 z_4^5 / 36}}{L^2} \left( 1 - \frac{z_3}{2L} \sqrt{\frac{E}{4G}} \right)\]

Constants

• P = 6000 lb
• L = 14 in
• E = 30×10⁶ psi
• G = 12×10⁶ psi
• τₘₐₓ = 13600 psi
• σₘₐₓ = 30000 psi
• δₘₐₓ = 0.25 in

Decision Variables

• x[1] = z₁: Thickness of weld (h)
• x[2] = z₂: Length of weld (l)
• x[3] = z₃: Height of beam (t)
• x[4] = z₄: Width of beam (b)

Returns

• Penalized objective function value (Float64)

F4(x::Vector{Float64}) -> Float64

Speed Reducer Design Optimization.

Minimizes the weight of a speed reducer subject to constraints on bending stress, surface stress, transverse deflections, and geometry.

Problem Source

A standard benchmark problem in engineering design, commonly used to test constrained optimization algorithms.

Variables

• x[1]: Face width (in)
• x[2]: Module of teeth (in)
• x[3]: Number of teeth
• x[4]: Length of the first shaft between bearings (in)
• x[5]: Length of the second shaft between bearings (in)
• x[6]: Diameter of the first shaft (in)
• x[7]: Diameter of the second shaft (in)

Constraints

• Bending stress
• Surface stress
• Deflection of shafts
• Geometric and design constraints
• Seven nonlinear inequality constraints in total

Returns

• Penalized objective function value (Float64)

F5(x::Vector{Float64}) -> Float64

Gear Train Design Optimization.

Minimizes the error between an actual and a desired gear ratio in a simple four-gear train. All variables must be integers.

Problem Source

A discrete constrained engineering design problem widely used to evaluate optimization algorithms that handle integer variables.

Variables

• x[1]: Number of teeth on gear 1 (integer)
• x[2]: Number of teeth on gear 2 (integer)
• x[3]: Number of teeth on gear 3 (integer)
• x[4]: Number of teeth on gear 4 (integer)

Constraints

• Each variable must be an integer in the range [12, 60]
• The gear ratio error must be minimized

Returns

• Squared error between actual and desired gear ratio (Float64)

F6(x::Vector{Float64}) -> Float64

Three-Bar Truss Design Optimization.

Minimizes the weight of a three-bar truss structure subject to stress and displacement constraints.

Problem Source

A classical structural optimization benchmark problem used in metaheuristic algorithm research.

Variables

• x[1]: Cross-sectional area of the first bar (continuous)
• x[2]: Cross-sectional area of the second bar (continuous)

Constraints

• Stress in each member must not exceed allowable limits
• Displacement constraints on the structure
• Variable bounds typically in the range [0.1, 10]

Returns

• Penalized objective function value (Float64) representing the weight of the truss

F7(x::Vector{Float64}) -> Float64

Rolling Element Bearing Design Optimization.

Minimizes the bearing’s weight subject to constraints on stress, deflection, and geometry.

Problem Source

A standard constrained engineering design problem often used to benchmark metaheuristic algorithms.

Variables

• x[1]: Bearing inner radius
• x[2]: Bearing outer radius
• x[3]: Width of the bearing
• x[4]: Shaft diameter
• x[5]: Number of rolling elements

Constraints

• Stress limits on the bearing components
• Deflection limits
• Geometric and manufacturing constraints

Returns

• Penalized objective function value (Float64) reflecting the bearing weight or cost

F8(x::Vector{Float64}) -> Float64

Cantilever Beam Design Optimization.

Minimizes the weight of a cantilever beam subject to constraints on bending stress, deflection, and geometric dimensions.

Problem Source

A classical constrained engineering design problem used in metaheuristic algorithm research.

Variables

• x[1]: Width of the beam cross-section
• x[2]: Height of the beam cross-section
• x[3]: Length of the beam segment 1
• x[4]: Length of the beam segment 2
• x[5]: Length of the beam segment 3
• x[6]: Length of the beam segment 4

Constraints

• Maximum bending stress constraints
• Deflection limits at the beam’s free end
• Geometric bounds on variables

Returns

• Penalized objective function value (Float64), representing the beam weight

F9(x::Vector{Float64}) -> Float64

I-Beam Deflection Optimization.

Minimizes the weight of an I-beam subject to constraints on bending stress, shear stress, and deflection under load.

Problem Source

A classical engineering design benchmark widely used in metaheuristic algorithm literature.

Variables

• x[1]: Web height
• x[2]: Flange width
• x[3]: Web thickness
• x[4]: Flange thickness

Constraints

• Bending stress limits
• Shear stress limits
• Maximum deflection allowed
• Geometric constraints

Returns

• Penalized objective function value (Float64), representing the beam weight

F1()

F10()

F11()

F12()

F13()

F14()

F15()

F16()

F17()

F18()

F19()

F2()

F20()

F21()

F22()

F23()

F3()

F4()

F5()

F6()

F7()

F8()

F9()

References:

• Qi, Ailiang, Dong Zhao, Ali Asghar Heidari, Lei Liu, Yi Chen, and Huiling Chen.

"FATA: an efficient optimization method based on geophysics." Neurocomputing 607 (2024): 128289.

References:

• Hashim, Fatma A., Reham R. Mostafa, Abdelazim G. Hussien, Seyedali Mirjalili, and Karam M. Sallam.

"Fick's Law Algorithm: A physical law-based algorithm for numerical optimization." Knowledge-Based Systems 260 (2023): 110146.

References:

• Ghasemi, M., Golalipour, K., Zare, M., Mirjalili, S., Trojovský, P., Abualigah, L. and Hemmati, R., 2024.

Flood algorithm (FLA): an efficient inspired meta-heuristic for engineering optimization. The Journal of Supercomputing, 80(15), pp.22913-23017.

References:

• Mohammed, Hardi, and Tarik Rashid.

"FOX: a FOX-inspired optimization algorithm." Applied Intelligence 53, no. 1 (2023): 1030-1050.

References:

• Ahmadianfar, Iman, Omid Bozorg-Haddad, and Xuefeng Chu.

"Gradient-based optimizer: A new metaheuristic optimization algorithm." Information Sciences 540 (2020): 131-159.

References:

• Ghasemi, Mojtaba, Mohsen Zare, Amir Zahedi, Mohammad-Amin Akbari, Seyedali Mirjalili, and Laith Abualigah.

"Geyser inspired algorithm: a new geological-inspired meta-heuristic for real-parameter and constrained engineering optimization." Journal of Bionic Engineering 21, no. 1 (2024): 374-408.

References:

• El-Kenawy, El-Sayed M., Nima Khodadadi, Seyedali Mirjalili, Abdelaziz A. Abdelhamid, Marwa M. Eid, and Abdelhameed Ibrahim.

"Greylag goose optimization: nature-inspired optimization algorithm." Expert Systems with Applications 238 (2024): 122147.

References:

• Chopra, Nitish, and Muhammad Mohsin Ansari.

"Golden jackal optimization: A novel nature-inspired optimizer for engineering applications." Expert Systems with Applications 198 (2022): 116924.

References:

• Hu, Gang, Yuxuan Guo, Guo Wei, and Laith Abualigah.

"Genghis Khan shark optimizer: a novel nature-inspired algorithm for engineering optimization." Advanced Engineering Informatics 58 (2023): 102210.

References:

• Zhang, Yiying, Zhigang Jin, and Seyedali Mirjalili.

"Generalized normal distribution optimization and its applications in parameter extraction of photovoltaic models." Energy Conversion and Management 224 (2020): 113301.

References:

• Zhang, Qingke, Hao Gao, Zhi-Hui Zhan, Junqing Li, and Huaxiang Zhang.

"Growth Optimizer: A powerful metaheuristic algorithm for solving continuous and discrete global optimization problems." Knowledge-Based Systems 261 (2023): 110206.

References:

• Saremi, Shahrzad, Seyedali Mirjalili, and Andrew Lewis.

"Grasshopper optimisation algorithm: theory and application." Advances in engineering software 105 (2017): 30-47.

References:

• Abdollahzadeh, Benyamin, Farhad Soleimanian Gharehchopogh, and Seyedali Mirjalili.

"Artificial gorilla troops optimizer: a new nature‐inspired metaheuristic algorithm for global optimization problems." International Journal of Intelligent Systems 36, no. 10 (2021): 5887-5958.

References:

• Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Andrew Lewis.

"Grey wolf optimizer." Advances in engineering software 69 (2014): 46-61.

References:

• Agushaka, Jeffrey O., Absalom E. Ezugwu, and Laith Abualigah.

"Gazelle optimization algorithm: a novel nature-inspired metaheuristic optimizer." Neural Computing and Applications 35, no. 5 (2023): 4099-4131.

References:

• Hashim, Fatma A., Essam H. Houssein, Kashif Hussain, Mai S. Mabrouk, and Walid Al-Atabany.

"Honey Badger Algorithm: New metaheuristic algorithm for solving optimization problems." Mathematics and Computers in Simulation 192 (2022): 84-110.

References:

• Askari, Qamar, Mehreen Saeed, and Irfan Younas.

"Heap-based optimizer inspired by corporate rank hierarchy for global optimization." Expert Systems with Applications 161 (2020): 113702.

References:

• Lian, Junbo, and Guohua Hui.

"Human evolutionary optimization algorithm." Expert Systems with Applications 241 (2024): 122638.

References:

• Yang, Yutao, Huiling Chen, Ali Asghar Heidari, and Amir H. Gandomi.

"Hunger games search: Visions, conception, implementation, deep analysis, perspectives, and towards performance shifts." Expert Systems with Applications 177 (2021): 114864.

References:

• Hashim, F.A., Houssein, E.H., Mabrouk, M.S., Al-Atabany, W. and Mirjalili, S., 2019.

Henry gas solubility optimization: A novel physics-based algorithm. Future Generation Computer Systems, 101, pp.646-667.

References:

• Heidari, Ali Asghar, Seyedali Mirjalili, Hossam Faris, Ibrahim Aljarah, Majdi Mafarja, and Huiling Chen.

"Harris hawks optimization: Algorithm and applications." Future generation computer systems 97 (2019): 849-872.

References:

• Amiri, M.H., Mehrabi Hashjin, N., Montazeri, M., Mirjalili, S. and Khodadadi, N., 2024.

Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm. Scientific Reports, 14(1), p.5032.

References:

• Oladejo, Sunday O., Stephen O. Ekwe, and Seyedali Mirjalili.

"The Hiking Optimization Algorithm: A novel human-based metaheuristic approach." Knowledge-Based Systems 296 (2024): 111880.

References:

• MiarNaeimi, Farid, Gholamreza Azizyan, and Mohsen Rashki.

"Horse herd optimization algorithm: A nature-inspired algorithm for high-dimensional optimization problems." Knowledge-Based Systems 213 (2021): 106711.

References:

• Ahmadianfar, Iman, Ali Asghar Heidari, Saeed Noshadian, Huiling Chen, and Amir H. Gandomi.

"INFO: An efficient optimization algorithm based on weighted mean of vectors." Expert Systems with Applications 195 (2022): 116516.

References:

• Ghasemi, Mojtaba, Mohsen Zare, Pavel Trojovský, Ravipudi Venkata Rao, Eva Trojovská, and Venkatachalam Kandasamy.

"Optimization based on the smart behavior of plants with its engineering applications: Ivy algorithm." Knowledge-Based Systems 295 (2024): 111850.

References:

• Chou, Jui-Sheng, and Dinh-Nhat Truong.

"A novel metaheuristic optimizer inspired by behavior of jellyfish in ocean." Applied Mathematics and Computation 389 (2021): 125535.

References:

• Rao, R.

"Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems." International Journal of Industrial Engineering Computations 7, no. 1 (2016): 19-34.

References:

• Houssein, Essam H., Diego Oliva, Nagwan Abdel Samee, Noha F. Mahmoud, and Marwa M. Emam.

"Liver Cancer Algorithm: A novel bio-inspired optimizer." Computers in Biology and Medicine 165 (2023): 107389.

References:

• Houssein, Essam H., Mohammed R. Saad, Fatma A. Hashim, Hassan Shaban, and M. Hassaballah.

"Lévy flight distribution: A new metaheuristic algorithm for solving engineering optimization problems." Engineering Applications of Artificial Intelligence 94 (2020): 103731.

References:

• Ghasemi, Mojtaba, Mohsen Zare, Amir Zahedi, Pavel Trojovský, Laith Abualigah, and Eva Trojovská.

"Optimization based on performance of lungs in body: Lungs performance-based optimization (LPO)." Computer Methods in Applied Mechanics and Engineering 419 (2024): 116582.

References:

• Faramarzi, Afshin, Mohammad Heidarinejad, Seyedali Mirjalili, and Amir H. Gandomi.

"Marine Predators Algorithm: A nature-inspired metaheuristic." Expert systems with applications 152 (2020): 113377.

References:

• Zhao, Weiguo, Zhenxing Zhang, and Liying Wang.

"Manta ray foraging optimization: An effective bio-inspired optimizer for engineering applications." Engineering Applications of Artificial Intelligence 87 (2020): 103300.

References:

• Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Abdolreza Hatamlou.

"Multi-verse optimizer: a nature-inspired algorithm for global optimization." Neural Computing and Applications 27 (2016): 495-513.

References:

• Zheng, Boli, Yi Chen, Chaofan Wang, Ali Asghar Heidari, Lei Liu, and Huiling Chen.

"The moss growth optimization (MGO): concepts and performance." Journal of Computational Design and Engineering 11, no. 5 (2024): 184-221.

References:

• Abdollahzadeh, Benyamin, Farhad Soleimanian Gharehchopogh, Nima Khodadadi, and Seyedali Mirjalili.

"Mountain gazelle optimizer: a new nature-inspired metaheuristic algorithm for global optimization problems." Advances in Engineering Software 174 (2022): 103282.

References:

• Dehghani, Mohammad, and Pavel Trojovský.

"Osprey optimization algorithm: A new bio-inspired metaheuristic algorithm for solving engineering optimization problems." Frontiers in Mechanical Engineering 8 (2023): 1126450.

References:

• Ezugwu, Absalom E., Jeffrey O. Agushaka, Laith Abualigah, Seyedali Mirjalili, and Amir H. Gandomi.

"Prairie dog optimization algorithm." Neural Computing and Applications 34, no. 22 (2022): 20017-20065.

References:

• Bouaouda, Anas, Fatma A. Hashim, Yassine Sayouti, and Abdelazim G. Hussien.

"Pied kingfisher optimizer: a new bio-inspired algorithm for solving numerical optimization and industrial engineering problems." Neural Computing and Applications (2024): 1-59.

References:

• Yuan, Chong, Dong Zhao, Ali Asghar Heidari, Lei Liu, Yi Chen, and Huiling Chen.

"Polar lights optimizer: Algorithm and applications in image segmentation and feature selection." Neurocomputing 607 (2024): 128427.

References:

• Trojovský, Pavel, and Mohammad Dehghani.

"Pelican optimization algorithm: A novel nature-inspired algorithm for engineering applications." Sensors 22, no. 3 (2022): 855.

References:

• Moosavi, Seyyed Hamid Samareh, and Vahid Khatibi Bardsiri.

"Poor and rich optimization algorithm: A new human-based and multi populations algorithm." Engineering applications of artificial intelligence 86 (2019): 165-181.

References:

• Lian, Junbo, Guohua Hui, Ling Ma, Ting Zhu, Xincan Wu, Ali Asghar Heidari, Yi Chen, and Huiling Chen.

"Parrot optimizer: Algorithm and applications to medical problems." Computers in Biology and Medicine 172 (2024): 108064.

References:

• Askari, Qamar, Irfan Younas, and Mehreen Saeed.

"Political Optimizer: A novel socio-inspired meta-heuristic for global optimization." Knowledge-based systems 195 (2020): 105709.

References:

• Abdollahzadeh, Benyamin, Nima Khodadadi, Saeid Barshandeh, Pavel Trojovský, Farhad Soleimanian Gharehchopogh, El-Sayed M. El-kenawy, Laith Abualigah, and Seyedali Mirjalili.

"Puma optimizer (PO): A novel metaheuristic optimization algorithm and its application in machine learning." Cluster Computing (2024): 1-49.

References:

• Zhao, Weiguo, Liying Wang, Zhenxing Zhang, Seyedali Mirjalili, Nima Khodadadi, and Qiang Ge.

"Quadratic Interpolation Optimization (QIO): A new optimization algorithm based on generalized quadratic interpolation and its applications to real-world engineering problems." Computer Methods in Applied Mechanics and Engineering 417 (2023): 116446.

References:

• Fu, Shengwei, et al.

"Red-billed blue magpie optimizer: a novel metaheuristic algorithm for 2D/3D UAV path planning and engineering design problems." Artificial Intelligence Review 57.6 (2024): 134.

References:

• Braik, M., & Al-Hiary, H. (2025).

Rüppell’s fox optimizer: A novel meta-heuristic approach for solving global optimization problems. Cluster Computing, 28(5), 1-77.

References:

• Su, Hang, Dong Zhao, Ali Asghar Heidari, Lei Liu, Xiaoqin Zhang, Majdi Mafarja, and Huiling Chen.

"RIME: A physics-based optimization." Neurocomputing 532 (2023): 183-214.

References:

• Jia, Heming, Xiaoxu Peng, and Chunbo Lang.

"Remora optimization algorithm." Expert Systems with Applications 185 (2021): 115665.

References:

• Abualigah, Laith, Mohamed Abd Elaziz, Putra Sumari, Zong Woo Geem, and Amir H. Gandomi.

"Reptile Search Algorithm (RSA): A nature-inspired meta-heuristic optimizer." Expert Systems with Applications 191 (2022): 116158.

References:

• Dhiman, Gaurav, Meenakshi Garg, Atulya Nagar, Vijay Kumar, and Mohammad Dehghani.

"A novel algorithm for global optimization: rat swarm optimizer." Journal of Ambient Intelligence and Humanized Computing 12 (2021): 8457-8482.

References:

• Ahmadianfar, Iman, Ali Asghar Heidari, Amir H. Gandomi, Xuefeng Chu, and Huiling Chen.

"RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method." Expert Systems with Applications 181 (2021): 115079.

References:

• Moosavi, Seyyed Hamid Samareh, and Vahid Khatibi Bardsiri.

"Satin bowerbird optimizer: A new optimization algorithm to optimize ANFIS for software development effort estimation." Engineering Applications of Artificial Intelligence 60 (2017): 1-15.

References:

• Fu, Youfa, Dan Liu, Jiadui Chen, and Ling He.

"Secretary bird optimization algorithm: a new metaheuristic for solving global optimization problems." Artificial Intelligence Review 57, no. 5 (2024): 1-102.

References:

• Mirjalili, Seyedali.

"SCA: a sine cosine algorithm for solving optimization problems." Knowledge-based systems 96 (2016): 120-133.

References:

• Bai, Jianfu, Yifei Li, Mingpo Zheng, Samir Khatir, Brahim Benaissa, Laith Abualigah, and Magd Abdel Wahab.

"A sinh cosh optimizer." Knowledge-Based Systems 282 (2023): 111081.

References:

• Zhong, C., Li, G., Meng, Z., Li, H., Yildiz, A. R., & Mirjalili, S. (2025).

Starfish optimization algorithm (SFOA): a bio-inspired metaheuristic algorithm for global optimization compared with 100 optimizers. Neural Computing and Applications, 37(5), 3641-3683.

References:

• Dhiman, Gaurav, and Vijay Kumar.

"Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications." Advances in Engineering Software 114 (2017): 48-70.

References:

• Li, Shimin, Huiling Chen, Mingjing Wang, Ali Asghar Heidari, and Seyedali Mirjalili.

"Slime mould algorithm: A new method for stochastic optimization." Future generation computer systems 111 (2020): 300-323.

References:

• Hashim, Fatma A., and Abdelazim G. Hussien.

"Snake Optimizer: A novel meta-heuristic optimization algorithm." Knowledge-Based Systems 242 (2022): 108320.

References:

• Dhiman, Gaurav, and Vijay Kumar.

"Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems." Knowledge-based systems 165 (2019): 169-196.

References:

• Mirjalili, Seyedali, Amir H. Gandomi, Seyedeh Zahra Mirjalili, Shahrzad Saremi, Hossam Faris, and Seyed Mohammad Mirjalili.

"Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems." Advances in engineering software 114 (2017): 163-191.

References:

• Dhiman, Gaurav, and Amandeep Kaur.

"STOA: a bio-inspired based optimization algorithm for industrial engineering problems." Engineering Applications of Artificial Intelligence 82 (2019): 148-174.

References:

• Özbay, Feyza Altunbey.

"A modified seahorse optimization algorithm based on chaotic maps for solving global optimization and engineering problems." Engineering Science and Technology, an International Journal 41 (2023): 101408.

References:

• Deng, Lingyun, and Sanyang Liu.

"Snow ablation optimizer: A novel metaheuristic technique for numerical optimization and engineering design." Expert Systems with Applications 225 (2023): 120069.

References:

• Jiankai Xue & Bo Shen

A novel swarm intelligence optimization approach: sparrow search algorithm Systems Science & Control Engineering, 8:1 (2020), 22-34. DOI: 10.1080/21642583.2019.1708830

References:

• Jia, Heming, et al.

"Superb Fairy-wren Optimization Algorithm: a novel metaheuristic algorithm for solving feature selection problems." Cluster Computing 28.4 (2025): 246.

References:

• Zhao, Weiguo, Liying Wang, and Zhenxing Zhang.

"Supply-demand-based optimization: A novel economics-inspired algorithm for global optimization." Ieee Access 7 (2019): 73182-73206.

References:

• Rao, R. Venkata, Vimal J. Savsani, and Dipakkumar P. Vakharia.

"Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems." Computer-aided design 43, no. 3 (2011): 303-315.

References:

• Minh, Hoang-Le, Thanh Sang-To, Guy Theraulaz, Magd Abdel Wahab, and Thanh Cuong-Le.

"Termite life cycle optimizer." Expert Systems with Applications 213 (2023): 119211.

References:

• Braik, M., Al-Hiary, H., Alzoubi, H., Hammouri, A., Azmi Al-Betar, M., & Awadallah, M. A. (2025).

Tornado optimizer with Coriolis force: a novel bio-inspired meta-heuristic algorithm for solving engineering problems. Artificial Intelligence Review, 58(4), 1-99.

References:

• Kaur, Satnam, Lalit K. Awasthi, Amrit Lal Sangal, and Gaurav Dhiman.

"Tunicate Swarm Algorithm: A new bio-inspired based metaheuristic paradigm for global optimization." Engineering Applications of Artificial Intelligence 90 (2020): 103541.

References:

• Zhao, Shijie, Tianran Zhang, Liang Cai, and Ronghua Yang.

"Triangulation topology aggregation optimizer: A novel mathematics-based meta-heuristic algorithm for continuous optimization and engineering applications." Expert Systems with Applications 238 (2024): 121744.

References:

• Naruei, Iraj, and Farshid Keynia.

"Wild horse optimizer: A new meta-heuristic algorithm for solving engineering optimization problems." Engineering with computers 38, no. Suppl 4 (2022): 3025-3056.

References:

• Han, Muxuan, Zunfeng Du, Kum Fai Yuen, Haitao Zhu, Yancang Li, and Qiuyu Yuan.

"Wave optimization algorithm: A new metaheuristic algorithm for solving optimization problems." Knowledge-Based Systems 236 (2022): 107760.

References:

• Mirjalili, Seyedali, and Andrew Lewis.

"The whale optimization algorithm." Advances in engineering software 95 (2016): 51-67.

References:

• Braik, Malik, Abdelaziz Hammouri, Jaffar Atwan, Mohammed Azmi Al-Betar, and Mohammed A. Awadallah.

"White Shark Optimizer: A novel bio-inspired meta-heuristic algorithm for global optimization problems." Knowledge-Based Systems 243 (2022): 108457.

References:

• Braik, M., & Al-Hiary, H. (2025).

A novel meta-heuristic optimization algorithm inspired by water uptake and transport in plants. Neural Computing and Applications, 1-82.

References:

• Abdel-Basset, Mohamed, Doaa El-Shahat, Mohammed Jameel, and Mohamed Abouhawwash.

"Young's double-slit experiment optimizer: A novel metaheuristic optimization algorithm for global and constraint optimization problems." Computer Methods in Applied Mechanics and Engineering 403 (2023): 115652.

References:

• Trojovská, Eva, Mohammad Dehghani, and Pavel Trojovský.

"Zebra optimization algorithm: A new bio-inspired optimization algorithm for solving optimization algorithm." Ieee Access 10 (2022): 49445-49473.