Editing Metaheuristic (section)

== Applications ==

Most metaheuristics are search methods and when using them, the evaluation function should be subject to greater demands than a mathematical optimization. Not only does the desired target state have to be formulated, but the evaluation should also reward improvements to a solution on the way to the target in order to support and accelerate the search process. The [[Fitness function|fitness functions]] of evolutionary or memetic algorithms can serve as an example. 

Metaheuristics are used for all types of optimization problems, ranging from [[Continuous optimization|continuous]] through mixed integer problems to [[combinatorial optimization]] or combinations thereof.<ref name=":5" /><ref>{{Cite book |url=https://link.springer.com/book/10.1007/11890584 |title=Hybrid Metaheuristics |date=2006 |publisher=Springer |isbn=978-3-540-46384-9 |editor-last=Almeida |editor-first=Francisco |series=Lecture Notes in Computer Science |volume=4030 |location=Berlin, Heidelberg |doi=10.1007/11890584 |editor-last2=Blesa Aguilera |editor-first2=María J. |editor-last3=Blum |editor-first3=Christian |editor-last4=Moreno Vega |editor-first4=José Marcos |editor-last5=Pérez Pérez |editor-first5=Melquíades |editor-last6=Roli |editor-first6=Andrea |editor-last7=Sampels |editor-first7=Michael}}</ref><ref>{{Cite book |url=http://link.springer.com/10.1007/978-3-642-23247-3 |title=Handbook of Memetic Algorithms |date=2012 |publisher=Springer Berlin Heidelberg |isbn=978-3-642-23246-6 |editor-last=Neri |editor-first=Ferrante |series=Studies in Computational Intelligence |volume=379 |location=Berlin, Heidelberg |language=en |doi=10.1007/978-3-642-23247-3 |editor-last2=Cotta |editor-first2=Carlos |editor-last3=Moscato |editor-first3=Pablo}}</ref> In combinatorial optimization, an optimal solution is sought over a [[discrete mathematics|discrete]] search-space. An example problem is the [[travelling salesman problem]] where the search-space of candidate solutions grows faster than [[exponential growth|exponentially]] as the size of the problem increases, which makes an [[exhaustive search]] for the optimal solution infeasible.<ref>{{Cite journal |last1=Dorigo |first1=M. |last2=Gambardella |first2=L.M. |date=April 1997 |title=Ant colony system: a cooperative learning approach to the traveling salesman problem |url=https://ieeexplore.ieee.org/document/585892 |journal=IEEE Transactions on Evolutionary Computation |volume=1 |issue=1 |pages=53–66 |doi=10.1109/4235.585892}}</ref><ref>{{Cite journal |last1=Merz |first1=Peter |last2=Freisleben |first2=Bernd |date=2002 |title=Memetic Algorithms for the Traveling Salesman Problem |url=https://www.researchgate.net/publication/2928026 |journal=Complex Systems |volume=13 |issue=4}}</ref> Additionally, multidimensional combinatorial problems, including most design problems in [[engineering]]<ref name=":2" /><ref>Tomoiagă B, Chindriş M, Sumper A, Sudria-Andreu A, Villafafila-Robles R. [http://www.mdpi.com/1996-1073/6/3/1439/pdf Pareto Optimal Reconfiguration of Power Distribution Systems Using a Genetic Algorithm Based on NSGA-II. ] Energies. 2013; 6(3):1439–1455.</ref><ref>{{Cite journal|title = Swarm intelligence and gravitational search algorithm for multi-objective optimization of synthesis gas production|journal = Applied Energy|date = 2013-03-01|pages = 368–374|volume = 103|doi= 10.1016/j.apenergy.2012.09.059|first1 = T.|last1 = Ganesan|first2 = I.|last2 = Elamvazuthi|first3 = Ku Zilati|last3 = Ku Shaari|first4 = P.|last4 = Vasant| bibcode=2013ApEn..103..368G }}</ref><ref>{{Cite book|date = 2011-11-01|pages = 86–91|doi = 10.1109/ICCSCE.2011.6190501|first1 = T.|last1 = Ganesan|first2 = I.|last2 = Elamvazuthi|first3 = P.|last3 = Vasant| title=2011 IEEE International Conference on Control System, Computing and Engineering | chapter=Evolutionary normal-boundary intersection (ENBI) method for multi-objective optimization of green sand mould system |isbn = 978-1-4577-1642-3|s2cid = 698459}}</ref> such as form-finding and behavior-finding, suffer from the [[curse of dimensionality]], which also makes them infeasible for exhaustive search or [[Analytical solution|analytical method]]s. 

Metaheuristics are also frequently applied to scheduling problems. A typical representative of this combinatorial task class is job shop scheduling, which involves assigning the work steps of jobs to processing stations in such a way that all jobs are completed on time and altogether in the shortest possible time.<ref name=":1">{{Cite book |url=https://www.wiley.com/en-dk/Metaheuristics+for+Production+Scheduling-p-9781848214972 |title=Metaheuristics for production scheduling |date=2013 |publisher=ISTE |isbn=978-1-84821-497-2 |editor-last=Jarboui |editor-first=Bassem |series=Automation - control and industrial engineering series |location=London |editor-last2=Siarry |editor-first2=Patrick |editor-last3=Teghem |editor-first3=Jacques}}</ref><ref>{{Cite book |url=http://link.springer.com/10.1007/978-3-540-78985-7 |title=Metaheuristics for Scheduling in Industrial and Manufacturing Applications |date=2008 |publisher=Springer Berlin Heidelberg |isbn=978-3-540-78984-0 |editor-last=Xhafa |editor-first=Fatos |series=Studies in Computational Intelligence |volume=128 |location=Berlin, Heidelberg |language=en |doi=10.1007/978-3-540-78985-7 |s2cid=42238720 |editor-last2=Abraham |editor-first2=Ajith}}</ref> In practice, restrictions often have to be observed, e.g. by limiting the permissible sequence of work steps of a job through predefined workflows<ref>{{Cite journal |last1=Jakob |first1=Wilfried |last2=Strack |first2=Sylvia |last3=Quinte |first3=Alexander |last4=Bengel |first4=Günther |last5=Stucky |first5=Karl-Uwe |last6=Süß |first6=Wolfgang |date=2013-04-22 |title=Fast Rescheduling of Multiple Workflows to Constrained Heterogeneous Resources Using Multi-Criteria Memetic Computing |journal=Algorithms |language=en |volume=6 |issue=2 |pages=245–277 |doi=10.3390/a6020245 |issn=1999-4893 |doi-access=free }}</ref> and/or with regard to resource utilisation, e.g. in the form of smoothing the energy demand.<ref>{{Cite journal |last1=Kizilay |first1=Damla |last2=Tasgetiren |first2=M. Fatih |last3=Pan |first3=Quan-Ke |last4=Süer |first4=Gürsel |date=2019 |title=An Ensemble of Meta-Heuristics for the Energy-Efficient Blocking Flowshop Scheduling Problem |journal=Procedia Manufacturing |language=en |volume=39 |pages=1177–1184 |doi=10.1016/j.promfg.2020.01.352|s2cid=213710393 |doi-access=free }}</ref><ref>{{Cite journal |last1=Grosch |first1=Benedikt |last2=Weitzel |first2=Timm |last3=Panten |first3=Niklas |last4=Abele |first4=Eberhard |date=2019 |title=A metaheuristic for energy adaptive production scheduling with multiple energy carriers and its implementation in a real production system |journal=Procedia CIRP |language=en |volume=80 |pages=203–208 |doi=10.1016/j.procir.2019.01.043|s2cid=164850023 |doi-access=free }}</ref> Popular metaheuristics for combinatorial problems include [[genetic algorithms]] by Holland et al.,<ref name="holland75adaptation" /> scatter search<ref name="glover77scattersearch" /> and [[tabu search]]<ref name="glover86future" /> by Glover. 

Another large field of application are optimization tasks in continuous or mixed-integer search spaces. This includes, e.g., design optimization<ref name=":2">{{Cite journal |last1=Gupta |first1=Shubham |last2=Abderazek |first2=Hammoudi |last3=Yıldız |first3=Betül Sultan |last4=Yildiz |first4=Ali Riza |last5=Mirjalili |first5=Seyedali |last6=Sait |first6=Sadiq M. |date=2021 |title=Comparison of metaheuristic optimization algorithms for solving constrained mechanical design optimization problems |url=https://linkinghub.elsevier.com/retrieve/pii/S095741742100779X |journal=Expert Systems with Applications |language=en |volume=183 |pages=115351 |doi=10.1016/j.eswa.2021.115351}}</ref><ref>{{Citation |last1=Quinte |first1=Alexander |title=Optimization of a Micro Actuator Plate Using Evolutionary Algorithms and Simulation Based on Discrete Element Methods |date=2002 |work=International Conference on Modeling and Simulation of Microsystems: MSM 2002 |pages=192–197 |editor-last=Laudon |editor-first=Matthew |location=Cambridge, Mass |publisher=Computational Publications |isbn=978-0-9708275-7-9 |last2=Jakob |first2=Wilfried |last3=Scherer |first3=Klaus-Peter |last4=Eggert |first4=Horst |url=https://www.researchgate.net/publication/228790476}}</ref><ref>{{Citation |last=Parmee |first=I. C. |title=Strategies for the Integration of Evolutionary/Adaptive Search with the Engineering Design Process |date=1997 |url=http://link.springer.com/10.1007/978-3-662-03423-1_25 |work=Evolutionary Algorithms in Engineering Applications |pages=453–477 |editor-last=Dasgupta |editor-first=Dipankar |access-date=2023-07-17 |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/978-3-662-03423-1_25 |isbn=978-3-642-08282-5 |editor2-last=Michalewicz |editor2-first=Zbigniew}}</ref> or various engineering tasks.<ref>{{Cite book |url=https://link.springer.com/10.1007/978-3-319-06508-3 |title=Applications of Metaheuristics in Process Engineering |date=2014 |publisher=Springer International Publishing |isbn=978-3-319-06507-6 |editor-last=Valadi |editor-first=Jayaraman |location=Cham |language=en |doi=10.1007/978-3-319-06508-3 |s2cid=40197553 |editor-last2=Siarry |editor-first2=Patrick}}</ref><ref>{{Cite book |last1=Sanchez |first1=Ernesto |url=http://link.springer.com/10.1007/978-3-642-27467-1 |title=Industrial Applications of Evolutionary Algorithms |last2=Squillero |first2=Giovanni |last3=Tonda |first3=Alberto |date=2012 |publisher=Springer |isbn=978-3-642-27466-4 |series=Intelligent Systems Reference Library |volume=34 |location=Berlin, Heidelberg |language=en |doi=10.1007/978-3-642-27467-1}}</ref><ref>{{Cite book |url=https://link.springer.com/10.1007/978-3-031-16832-1 |title=Engineering Applications of Modern Metaheuristics |date=2023 |publisher=Springer International Publishing |isbn=978-3-031-16831-4 |editor-last=Akan |editor-first=Taymaz |series=Studies in Computational Intelligence |volume=1069 |location=Cham |language=en |doi=10.1007/978-3-031-16832-1 |s2cid=254222401 |editor-last2=Anter |editor-first2=Ahmed M. |editor-last3=Etaner-Uyar |editor-first3=A. Şima |editor-last4=Oliva |editor-first4=Diego}}</ref> An example of the mixture of combinatorial and continuous optimization is the planning of favourable motion paths for industrial robots.<ref>{{Citation |last=Blume |first=Christian |title=Optimized Collision Free Robot Move Statement Generation by the Evolutionary Software GLEAM |date=2000 |url=http://link.springer.com/10.1007/3-540-45561-2_32 |work=Real-World Applications of Evolutionary Computing |series=Lecture Notes in Computer Science |volume=1803 |pages=330–341 |editor-last=Cagnoni |editor-first=Stefano |access-date=2023-07-17 |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/3-540-45561-2_32 |isbn=978-3-540-67353-8}}</ref><ref>{{Citation |last1=Pholdee |first1=Nantiwat |title=Multiobjective Trajectory Planning of a 6D Robot based on Multiobjective Meta Heuristic Search |date=2018-12-14 |url=https://dl.acm.org/doi/10.1145/3301326.3301356 |work=International Conference on Network, Communication and Computing (ICNCC 2018) |pages=352–356 |publisher=ACM |language=en |doi=10.1145/3301326.3301356 |isbn=978-1-4503-6553-6 |last2=Bureerat |first2=Sujin|s2cid=77394395 }}</ref>