元启发算法

元啟發算法（英文：metaheuristic）, 又稱 萬能啟發式演算法、萬用啟發式演算法。在计算机科学和数学优化中，元启发是一种高级的程序或启发式算法，专门用于搜索、生成或选取一个启发式结果（局部搜索算法），该结果可以为一个最优化问题提供足够好的求解，尤其适用于信息不完备或者计算能力受限时的最优化问题。

元啟發算法(metaheuristic)，meta 代表其比一般啟發式演算法在搜尋能力上更為高階。而 heuristic 則代表其算法能夠在一個合理的計算成本內找到一個接近真實最佳解的解，但啟發式演算法並不能夠保證其解的可行性與最佳性。^[1] 式通常是使用大量的試誤以在龐大的解空間中搜尋最佳解。

元啟發算法皆在全域搜索與區域搜索中取得權衡，若算法著重區域搜索能力則容易落入區域最佳解陷阱，若著重全域搜索則可能無法收斂解。

模擬退火法 (Simulated annealing algorithm, SA)
社會認知算法 (Social cognitive optimization, SCO)
簡化群體演算法 (Simplified swarm optimizatiom, SSO)^[2] ^[3]
調和搜尋演算法 (Harmony search, HS) ^[4]
水循環算法 (Water cycle algorithm, WCA)^[5]
汽車跟蹤最佳化演算法 (Car tracking optimization algorithm)^[6]
細菌覓食法 (bacterial foraging algorithm)^[7]

仿生元啟發式演算法

該類型演算法以生物的習性或群體生物行為作為靈感加以發展成為演算法。

基因演算法 (Genetic algorithm, GA)
細菌覓食法 (bacterial foraging algorithm)^[7]
粒子群演算法 (Particle swarm optimization, PSO)
蟻群演算法 (Ant colony optimization, ACO)
布穀鳥搜索算法 (Cuckoo Search, CS) ^[8]
蝙蝠算法 (Bat algorithm, BA) ^[9]
螢火蟲算法 (Firefly algorithm, FA) ^[10]
猴群演算法 (Monkey algorithm) ^[11]
獅子演算法 (Lion optimization algorithm, LOA)^[12]
人工蜂群演算法 (Artificial bee colony, ABC)^[13]
病毒最佳化演算法 (Virus Optimization Algorithm, VOA)^[14]
飛蛾搜尋演算法 (Moth search algorithm)^[15]
鯊魚氣味演算法 (Shark smell optimization, SSO)^[16]
蚯蚓最佳化演算法 (Earthworm optimization algorithm, EWA)^[17]
帝王企鵝演算法 (Emperor Penguins Colony, EPC)^[18]
抹香鲸算法 (Sperm whale algorithm,SWA)^[19]
人類精神搜索 (Human mental search, HMS)^[20]
海洋掠食者算法 (Marine Predators Algorithm, MPA)^[21]
狩獵搜索 (Hunting search, HuS)^[22]
遷徙鳥類最佳化 (Migrating birds optimization, MBO)^[23]
靴子進階演算法（Boots Advanced Algorithm,BAA)

[1]
Zahra Beheshti; Siti Mariyam Hj. Shamsuddin. A Review of Population-based Meta-Heuristic Algorithm (PDF). Int. J. Advance. Soft Comput. Appl. March,2013, 5 (1): 1–35. 请检查|date=中的日期值 (帮助)
[2]
Yeh, Wei-Chang. A two-stage discrete particle swarm optimization for the problem of multiple multi-level redundancy allocation in series systems. Expert Systems with Applications. 2009-07-01, 36 (5): 9192–9200. ISSN 0957-4174. doi:10.1016/j.eswa.2008.12.024 （英语）.
[3]
Yeh, Wei-Chang. An improved simplified swarm optimization. Knowledge-Based Systems. 2015-07-01, 82: 60–69. ISSN 0950-7051. doi:10.1016/j.knosys.2015.02.022 （英语）.
[4]
Geem, Z. W.; Kim, J. H.; Loganathan, G. V. A new heuristic optimization algorithm: harmony search. simulation. 2001, 76 (2): 60–68 [2021-03-15]. （原始内容存档于2020-10-17）.
[5]
Eskandar, Hadi; Sadollah, Ali; Bahreininejad, Ardeshir; Hamdi, Mohd. Water cycle algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures. 2012-11-01,. 110-111: 151–166. ISSN 0045-7949. doi:10.1016/j.compstruc.2012.07.010 （英语）.
[6]
Chen, Jian; Cai, Hui; Wang, Wei. A new metaheuristic algorithm: car tracking optimization algorithm. Soft Computing. 2018-06-01, 22 (12): 3857–3878. ISSN 1433-7479. doi:10.1007/s00500-017-2845-7 （英语）.
[7]
Pang, Shinsiong; Chen, Mu-Chen. Optimize railway crew scheduling by using modified bacterial foraging algorithm. Computers & Industrial Engineering. 2023-06-01, 180. ISSN 0360-8352. doi:10.1016/j.cie.2023.109218 （英语）.
[8]
Yang, X. S.; Deb, S. Cuckoo search via Lévy flights. IEEE. 2009: 210–214. doi:10.1109/NABIC.2009.5393690.
[9]
Yang, X. S. A New Metaheuristic Bat-Inspired Algorithm. Nature Inspired Cooperative Strategies for Optimization (NICSO 2010). 2010: 65–74 [2021-03-15]. （原始内容存档于2021-03-08）.
[10]
Xin-She Yang. Nature-inspired Metaheuristic Algorithms. Luniver Press. 2010: 5–. ISBN 978-1-905986-28-6.
[11]
Ruiqing Zhao; Wansheng Tang. Monkey algorithm for global numerical optimization. Journal of Uncertain Systems. 2008, 2 (3): 165–176.
[12]
Yazdani, Maziar; Jolai, Fariborz. Lion Optimization Algorithm (LOA): A nature-inspired metaheuristic algorithm. Journal of Computational Design and Engineering. 2016-01-01, 3 (1): 24–36. ISSN 2288-5048. doi:10.1016/j.jcde.2015.06.003.
[13]
D Karaboga. An idea based on honey bee swarm for numerical optimization. Technical report-tr06. 2005, 200: 1–10.
[14]
Liang, Yun-Chia; Josue Rodolfo Cuevas Juarez. A novel metaheuristic for continuous optimization problems: Virus optimization algorithm. Engineering Optimization. 2016, 48 (1): 73–93.
[15]
Wang, Gai-Ge. Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memetic Computing. 2018-06-01, 10 (2): 151–164. ISSN 1865-9292. doi:10.1007/s12293-016-0212-3 （英语）.
[16]
Abedinia, Oveis; Amjady, Nima; Ghasemi, Ali. A new metaheuristic algorithm based on shark smell optimization. Complexity. 2016, 21 (5): 97–116. ISSN 1099-0526. doi:10.1002/cplx.21634 （英语）.
[17]
Wang, Gai-Ge; Deb, Suash; Coelho, Leandro Dos Santos. Earthworm optimisation algorithm: a bio-inspired metaheuristic algorithm for global optimisation problems. International Journal of Bio-Inspired Computation. 2018-01-01, 12 (1): 1–22. ISSN 1758-0366. doi:10.1504/IJBIC.2018.093328.
[18]
Harifi, Sasan; Khalilian, Madjid; Mohammadzadeh, Javad; Ebrahimnejad, Sadoullah. Emperor Penguins Colony: a new metaheuristic algorithm for optimization. Evolutionary Intelligence. 2019-06-01, 12 (2): 211–226. ISSN 1864-5917. doi:10.1007/s12065-019-00212-x （英语）.
[19]
Ebrahimi, A.; Khamehchi, E. Sperm whale algorithm: An effective metaheuristic algorithm for production optimization problems. Journal of Natural Gas Science and Engineering. 2016-02-01, 29: 211–222. ISSN 1875-5100. doi:10.1016/j.jngse.2016.01.001 （英语）.
[20]
Mousavirad, Seyed Jalaleddin; Ebrahimpour-Komleh, Hossein. Human mental search: a new population-based metaheuristic optimization algorithm. Applied Intelligence. 2017-10-01, 47 (3): 850–887. ISSN 1573-7497. doi:10.1007/s10489-017-0903-6 （英语）.
[21]
Faramarzi, Afshin; Heidarinejad, Mohammad; Mirjalili, Seyedali; Gandomi, Amir H. Marine Predators Algorithm: A nature-inspired metaheuristic. Expert Systems with Applications. 2020-08-15, 152: 113377. ISSN 0957-4174. doi:10.1016/j.eswa.2020.113377 （英语）.
[22]
A novel meta-heuristic optimization algorithm inspired by group hunting of animals: Hunting search. Computers & Mathematics with Applications. 2010-10-01, 60 (7): 2087–2098 [2021-03-22]. ISSN 0898-1221. doi:10.1016/j.camwa.2010.07.049. （原始内容存档于2021-04-23）（英语）.
[23]
Duman, Ekrem; Uysal, Mitat; Alkaya, Ali Fuat. Migrating Birds Optimization: A new metaheuristic approach and its performance on quadratic assignment problem. Information Sciences. 2012-12-25, 217: 65–77 [2021-03-22]. ISSN 0020-0255. doi:10.1016/j.ins.2012.06.032. （原始内容存档于2012-12-19）（英语）.

[1] [1]
Zahra Beheshti; Siti Mariyam Hj. Shamsuddin. A Review of Population-based Meta-Heuristic Algorithm (PDF). Int. J. Advance. Soft Comput. Appl. March,2013, 5 (1): 1–35. 请检查|date=中的日期值 (帮助)

[2] [2]
Yeh, Wei-Chang. A two-stage discrete particle swarm optimization for the problem of multiple multi-level redundancy allocation in series systems. Expert Systems with Applications. 2009-07-01, 36 (5): 9192–9200. ISSN 0957-4174. doi:10.1016/j.eswa.2008.12.024 （英语）.

[3] [3]
Yeh, Wei-Chang. An improved simplified swarm optimization. Knowledge-Based Systems. 2015-07-01, 82: 60–69. ISSN 0950-7051. doi:10.1016/j.knosys.2015.02.022 （英语）.

[4] [4]
Geem, Z. W.; Kim, J. H.; Loganathan, G. V. A new heuristic optimization algorithm: harmony search. simulation. 2001, 76 (2): 60–68 [2021-03-15]. （原始内容存档于2020-10-17）.

[5] [5]
Eskandar, Hadi; Sadollah, Ali; Bahreininejad, Ardeshir; Hamdi, Mohd. Water cycle algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures. 2012-11-01,. 110-111: 151–166. ISSN 0045-7949. doi:10.1016/j.compstruc.2012.07.010 （英语）.

[6] [6]
Chen, Jian; Cai, Hui; Wang, Wei. A new metaheuristic algorithm: car tracking optimization algorithm. Soft Computing. 2018-06-01, 22 (12): 3857–3878. ISSN 1433-7479. doi:10.1007/s00500-017-2845-7 （英语）.

[:0-7] [7]
Pang, Shinsiong; Chen, Mu-Chen. Optimize railway crew scheduling by using modified bacterial foraging algorithm. Computers & Industrial Engineering. 2023-06-01, 180. ISSN 0360-8352. doi:10.1016/j.cie.2023.109218 （英语）.

[8] [8]
Yang, X. S.; Deb, S. Cuckoo search via Lévy flights. IEEE. 2009: 210–214. doi:10.1109/NABIC.2009.5393690.

[9] [9]
Yang, X. S. A New Metaheuristic Bat-Inspired Algorithm. Nature Inspired Cooperative Strategies for Optimization (NICSO 2010). 2010: 65–74 [2021-03-15]. （原始内容存档于2021-03-08）.

[Yang2010-10] [10]
Xin-She Yang. Nature-inspired Metaheuristic Algorithms. Luniver Press. 2010: 5–. ISBN 978-1-905986-28-6.

[11] [11]
Ruiqing Zhao; Wansheng Tang. Monkey algorithm for global numerical optimization. Journal of Uncertain Systems. 2008, 2 (3): 165–176.

[12] [12]
Yazdani, Maziar; Jolai, Fariborz. Lion Optimization Algorithm (LOA): A nature-inspired metaheuristic algorithm. Journal of Computational Design and Engineering. 2016-01-01, 3 (1): 24–36. ISSN 2288-5048. doi:10.1016/j.jcde.2015.06.003.

[13] [13]
D Karaboga. An idea based on honey bee swarm for numerical optimization. Technical report-tr06. 2005, 200: 1–10.

[14] [14]
Liang, Yun-Chia; Josue Rodolfo Cuevas Juarez. A novel metaheuristic for continuous optimization problems: Virus optimization algorithm. Engineering Optimization. 2016, 48 (1): 73–93.

[15] [15]
Wang, Gai-Ge. Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memetic Computing. 2018-06-01, 10 (2): 151–164. ISSN 1865-9292. doi:10.1007/s12293-016-0212-3 （英语）.

[16] [16]
Abedinia, Oveis; Amjady, Nima; Ghasemi, Ali. A new metaheuristic algorithm based on shark smell optimization. Complexity. 2016, 21 (5): 97–116. ISSN 1099-0526. doi:10.1002/cplx.21634 （英语）.

[17] [17]
Wang, Gai-Ge; Deb, Suash; Coelho, Leandro Dos Santos. Earthworm optimisation algorithm: a bio-inspired metaheuristic algorithm for global optimisation problems. International Journal of Bio-Inspired Computation. 2018-01-01, 12 (1): 1–22. ISSN 1758-0366. doi:10.1504/IJBIC.2018.093328.

[18] [18]
Harifi, Sasan; Khalilian, Madjid; Mohammadzadeh, Javad; Ebrahimnejad, Sadoullah. Emperor Penguins Colony: a new metaheuristic algorithm for optimization. Evolutionary Intelligence. 2019-06-01, 12 (2): 211–226. ISSN 1864-5917. doi:10.1007/s12065-019-00212-x （英语）.

[19] [19]
Ebrahimi, A.; Khamehchi, E. Sperm whale algorithm: An effective metaheuristic algorithm for production optimization problems. Journal of Natural Gas Science and Engineering. 2016-02-01, 29: 211–222. ISSN 1875-5100. doi:10.1016/j.jngse.2016.01.001 （英语）.

[20] [20]
Mousavirad, Seyed Jalaleddin; Ebrahimpour-Komleh, Hossein. Human mental search: a new population-based metaheuristic optimization algorithm. Applied Intelligence. 2017-10-01, 47 (3): 850–887. ISSN 1573-7497. doi:10.1007/s10489-017-0903-6 （英语）.

[21] [21]
Faramarzi, Afshin; Heidarinejad, Mohammad; Mirjalili, Seyedali; Gandomi, Amir H. Marine Predators Algorithm: A nature-inspired metaheuristic. Expert Systems with Applications. 2020-08-15, 152: 113377. ISSN 0957-4174. doi:10.1016/j.eswa.2020.113377 （英语）.

[22] [22]
A novel meta-heuristic optimization algorithm inspired by group hunting of animals: Hunting search. Computers & Mathematics with Applications. 2010-10-01, 60 (7): 2087–2098 [2021-03-22]. ISSN 0898-1221. doi:10.1016/j.camwa.2010.07.049. （原始内容存档于2021-04-23）（英语）.

[23] [23]
Duman, Ekrem; Uysal, Mitat; Alkaya, Ali Fuat. Migrating Birds Optimization: A new metaheuristic approach and its performance on quadratic assignment problem. Information Sciences. 2012-12-25, 217: 65–77 [2021-03-22]. ISSN 0020-0255. doi:10.1016/j.ins.2012.06.032. （原始内容存档于2012-12-19）（英语）.

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元启发算法

仿生元啟發式演算法

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元启发算法

仿生元啟發式演算法

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特色

演算法

參考文獻