Evolutionary algorithm

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Short description: Subset of evolutionary computation
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Glossary

In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation,[1] a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). Evolution of the population then takes place after the repeated application of the above operators.

Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolutionary processes and planning models based upon cellular processes. In most real applications of EAs, computational complexity is a prohibiting factor.[2] In fact, this computational complexity is due to fitness function evaluation. Fitness approximation is one of the solutions to overcome this difficulty. However, seemingly simple EA can solve often complex problems;[3][4][5] therefore, there may be no direct link between algorithm complexity and problem complexity.

Evolutionary algorithms can be seen as a kind of Monte-Carlo method.[6]

Implementation

The following is an example of a generic single-objective genetic algorithm.

Step One: Generate the initial population of individuals randomly. (First generation)

Step Two: Repeat the following regenerational steps until termination:

  1. Evaluate the fitness of each individual in the population (time limit, sufficient fitness achieved, etc.)
  2. Select the fittest individuals for reproduction. (Parents)
  3. Breed new individuals through crossover and mutation operations to give birth to offspring.
  4. Replace the least-fit individuals of the population with new individuals.

Types

Similar techniques differ in genetic representation and other implementation details, and the nature of the particular applied problem.

  • Genetic algorithm – This is the most popular type of EA. One seeks the solution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved),[2] by applying operators such as recombination and mutation (sometimes one, sometimes both). This type of EA is often used in optimization problems.
  • Genetic programming – Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem. There are many variants of Genetic Programming, including Cartesian genetic programming, gene expression programming, grammatical evolution, linear genetic programming, multi expression programming etc.
  • Evolutionary programming – Similar to genetic programming, but the structure of the program is fixed and its numerical parameters are allowed to evolve.
  • Evolution strategy – Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates. The method is mainly used for numerical optimization, although there are also variants for combinatorial tasks.[7][8]
  • Differential evolution – Based on vector differences and is therefore primarily suited for numerical optimization problems.
  • Coevolutionary algorithm – Similar to genetic algorithms and evolution strategies, but the created solutions are compared on the basis of their outcomes from interactions with other solutions. Solutions can either compete or cooperate during the search process. Coevolutionary algorithms are often used in scenarios where the fitness landscape is dynamic, complex, or involves competitive interactions.[9][10]
  • Neuroevolution – Similar to genetic programming but the genomes represent artificial neural networks by describing structure and connection weights. The genome encoding can be direct or indirect.
  • Learning classifier system – Here the solution is a set of classifiers (rules or conditions). A Michigan-LCS evolves at the level of individual classifiers whereas a Pittsburgh-LCS uses populations of classifier-sets. Initially, classifiers were only binary, but now include real, neural net, or S-expression types. Fitness is typically determined with either a strength or accuracy based reinforcement learning or supervised learning approach.
  • Quality–Diversity algorithms – QD algorithms simultaneously aim for high-quality and diverse solutions. Unlike traditional optimization algorithms that solely focus on finding the best solution to a problem, QD algorithms explore a wide variety of solutions across a problem space and keep those that are not just high performing, but also diverse and unique.[11][12][13]

Theoretical background

The following theoretical principles apply to all or almost all EAs.

No free lunch theorem

The no free lunch theorem of optimization states that all optimization strategies are equally effective when the set of all optimization problems is considered. Under the same condition, no evolutionary algorithm is fundamentally better than another. This can only be the case if the set of all problems is restricted. This is exactly what is inevitably done in practice. Therefore, to improve an EA, it must exploit problem knowledge in some form (e.g. by choosing a certain mutation strength or a problem-adapted coding). Thus, if two EAs are compared, this constraint is implied. In addition, an EA can use problem specific knowledge by, for example, not randomly generating the entire start population, but creating some individuals through heuristics or other procedures.[14][15] Another possibility to tailor an EA to a given problem domain is to involve suitable heuristics, local search procedures or other problem-related procedures in the process of generating the offspring. This form of extension of an EA is also known as a memetic algorithm. Both extensions play a major role in practical applications, as they can speed up the search process and make it more robust.[14][16]

Convergence

For EAs in which, in addition to the offspring, at least the best individual of the parent generation is used to form the subsequent generation (so-called elitist EAs), there is a general proof of convergence under the condition that an optimum exists. Without loss of generality, a maximum search is assumed for the proof:

From the property of elitist offspring acceptance and the existence of the optimum it follows that per generation [math]\displaystyle{ k }[/math] an improvement of the fitness [math]\displaystyle{ F }[/math] of the respective best individual [math]\displaystyle{ x' }[/math] will occur with a probability [math]\displaystyle{ P \gt 0 }[/math]. Thus:

[math]\displaystyle{ F(x'_1) \leq F(x'_2) \leq F(x'_3) \leq \cdots \leq F(x'_k) \leq \cdots }[/math]

I.e., the fitness values represent a monotonically non-decreasing sequence, which is bounded due to the existence of the optimum. From this follows the convergence of the sequence against the optimum.

Since the proof makes no statement about the speed of convergence, it is of little help in practical applications of EAs. But it does justify the recommendation to use elitist EAs. However, when using the usual panmictic population model, elitist EAs tend to converge prematurely more than non-elitist ones.[17] In a panmictic population model, mate selection (step 2 of the section about implementation) is such that every individual in the entire population is eligible as a mate. In non-panmictic populations, selection is suitably restricted, so that the dispersal speed of better individuals is reduced compared to panmictic ones. Thus, the general risk of premature convergence of elitist EAs can be significantly reduced by suitable population models that restrict mate selection.[18][19]

Virtual alphabets

With the theory of virtual alphabets, David E. Goldberg showed in 1990 that by using a representation with real numbers, an EA that uses classical recombination operators (e.g. uniform or n-point crossover) cannot reach certain areas of the search space, in contrast to a coding with binary numbers.[20] This results in the recommendation for EAs with real representation to use arithmetic operators for recombination (e.g. arithmetic mean or intermediate recombination). With suitable operators, real-valued representations are more effective than binary ones, contrary to earlier opinion.[21][22]

Comparison to biological processes

A possible limitation[according to whom?] of many evolutionary algorithms is their lack of a clear genotype–phenotype distinction. In nature, the fertilized egg cell undergoes a complex process known as embryogenesis to become a mature phenotype. This indirect encoding is believed to make the genetic search more robust (i.e. reduce the probability of fatal mutations), and also may improve the evolvability of the organism.[23][24] Such indirect (also known as generative or developmental) encodings also enable evolution to exploit the regularity in the environment.[25] Recent work in the field of artificial embryogeny, or artificial developmental systems, seeks to address these concerns. And gene expression programming successfully explores a genotype–phenotype system, where the genotype consists of linear multigenic chromosomes of fixed length and the phenotype consists of multiple expression trees or computer programs of different sizes and shapes.[26][improper synthesis?]

Applications

The areas in which evolutionary algorithms are practically used are almost unlimited[5] and range from industry,[27][28] engineering,[2][3][29] complex scheduling,[4][30][31] agriculture,[32] robot movement planning[33] and finance[34][35] to research[36][37] and art. The application of an evolutionary algorithm requires some rethinking from the inexperienced user, as the approach to a task using an EA is different from conventional exact methods and this is usually not part of the curriculum of engineers or other disciplines. For example, the fitness calculation must not only formulate the goal but also support the evolutionary search process towards it, e.g. by rewarding improvements that do not yet lead to a better evaluation of the original quality criteria. For example, if peak utilisation of resources such as personnel deployment or energy consumption is to be avoided in a scheduling task, it is not sufficient to assess the maximum utilisation. Rather, the number and duration of exceedances of a still acceptable level should also be recorded in order to reward reductions below the actual maximum peak value.[38] There are therefore some publications that are aimed at the beginner and want to help avoiding beginner's mistakes as well as leading an application project to success.[38][39][40] This includes clarifying the fundamental question of when an EA should be used to solve a problem and when it is better not to.

Related techniques

Swarm algorithms[clarification needed] include:

  • Ant colony optimization is based on the ideas of ant foraging by pheromone communication to form paths.[41] Primarily suited for combinatorial optimization and graph problems.
  • The runner-root algorithm (RRA) is inspired by the function of runners and roots of plants in nature.[42]
  • Artificial bee colony algorithm is based on the honeybee foraging behaviour. Primarily proposed for numerical optimization and extended to solve combinatorial, constrained and multi-objective optimization problems.
  • Bees algorithm is based on the foraging behaviour of honeybees. It has been applied in many applications such as routing and scheduling.
  • Cuckoo search is inspired by the brooding parasitism of the cuckoo species. It also uses Lévy flights, and thus it suits for global optimization problems.
  • Particle swarm optimization is based on the ideas of animal flocking behaviour.[41] Also primarily suited for numerical optimization problems.

Other population-based metaheuristic methods

  • Hunting search – A method inspired by the group hunting of some animals, such as wolves, that organize their position to surround the prey, each of them relative to the position of the others and especially that of their leader. It is a continuous optimization method[43] adapted as a combinatorial optimization method.[44]
  • Adaptive dimensional search – Unlike nature-inspired metaheuristic techniques, an adaptive dimensional search algorithm does not implement any metaphor as an underlying principle. Rather it uses a simple performance-oriented method, based on the update of the search dimensionality ratio (SDR) parameter at each iteration.[45]
  • Firefly algorithm is inspired by the behavior of fireflies, attracting each other by flashing light. This is especially useful for multimodal optimization.
  • Harmony search – Based on the ideas of musicians' behavior in searching for better harmonies. This algorithm is suitable for combinatorial optimization as well as parameter optimization.
  • Gaussian adaptation – Based on information theory. Used for maximization of manufacturing yield, mean fitness or average information. See for instance Entropy in thermodynamics and information theory.
  • Memetic algorithm – A hybrid method, inspired by Richard Dawkins's notion of a meme, it commonly takes the form of a population-based algorithm coupled with individual learning procedures capable of performing local refinements. Emphasizes the exploitation of problem-specific knowledge and tries to orchestrate local and global search in a synergistic way.

Examples

In 2020, Google stated that their AutoML-Zero can successfully rediscover classic algorithms such as the concept of neural networks.[46]

The computer simulations Tierra and Avida attempt to model macroevolutionary dynamics.

Gallery

[47][48][49]

References

  1. ↑ Vikhar, P. A. (2016). "Evolutionary algorithms: A critical review and its future prospects". 2016 International Conference on Global Trends in Signal Processing, Information Computing and Communication (ICGTSPICC). Jalgaon. pp. 261–265. doi:10.1109/ICGTSPICC.2016.7955308. ISBN 978-1-5090-0467-6. 
  2. ↑ 2.0 2.1 2.2 Cohoon, J (2002-11-26). Evolutionary algorithms for the physical design of VLSI circuits. Springer, pp. 683-712, 2003. ISBN 978-3-540-43330-9. https://www.ifte.de/mitarbeiter/lienig/cohoon.pdf. 
  3. ↑ 3.0 3.1 Slowik, Adam; Kwasnicka, Halina (2020). "Evolutionary algorithms and their applications to engineering problems" (in en). Neural Computing and Applications 32 (16): 12363–12379. doi:10.1007/s00521-020-04832-8. ISSN 0941-0643. 
  4. ↑ 4.0 4.1 Mika, Marek; Waligóra, Grzegorz; Węglarz, Jan (2011). "Modelling and solving grid resource allocation problem with network resources for workflow applications" (in en). Journal of Scheduling 14 (3): 291–306. doi:10.1007/s10951-009-0158-0. ISSN 1094-6136. http://link.springer.com/10.1007/s10951-009-0158-0. 
  5. ↑ 5.0 5.1 "International Conference on the Applications of Evolutionary Computation". The conference is part of the Evo* series. The conference proceedings are published by Springer. https://www.evostar.org/. 
  6. ↑ Ashlock, D. (2006). Evolutionary Computation for Modeling and Optimization. Deutschland: Springer New York. Page 491, https://books.google.de/books?id=kz0rofjQrwYC&pg=PA491
  7. ↑ Nissen, Volker; Krause, Matthias (1994), "Constrained Combinatorial Optimization with an Evolution Strategy", in Reusch, Bernd (in en), Fuzzy Logik, Informatik aktuell, Berlin, Heidelberg: Springer, pp. 33–40, doi:10.1007/978-3-642-79386-8_5, ISBN 978-3-642-79386-8, https://link.springer.com/chapter/10.1007/978-3-642-79386-8_5 
  8. ↑ Coelho, V. N.; Coelho, I. M.; Souza, M. J. F.; Oliveira, T. A.; Cota, L. P.; Haddad, M. N.; Mladenovic, N.; Silva, R. C. P. et al. (2016). "Hybrid Self-Adaptive Evolution Strategies Guided by Neighborhood Structures for Combinatorial Optimization Problems.". Evol Comput 24 (4): 637–666. doi:10.1162/EVCO_a_00187. PMID 27258842. 
  9. ↑ Ma, Xiaoliang; Li, Xiaodong; Zhang, Qingfu; Tang, Ke; Liang, Zhengping; Xie, Weixin; Zhu, Zexuan (2019), "A Survey on Cooperative Co-Evolutionary Algorithms.", IEEE Transactions on Evolutionary Computation 23 (3): 421–441, doi:10.1109/TEVC.2018.2868770, https://ieeexplore.ieee.org/document/8454482, retrieved 2023-05-22 
  10. ↑ "Coevolutionary Principles" (in en). Handbook of Natural Computing. Berlin, Heidelberg: Springer Berlin Heidelberg. 2012. pp. 987–1033. doi:10.1007/978-3-540-92910-9_31. ISBN 978-3-540-92910-9. https://link.springer.com/referenceworkentry/10.1007/978-3-540-92910-9_31. 
  11. ↑ Pugh, Justin K.; Soros, Lisa B.; Stanley, Kenneth O. (2016-07-12). "Quality Diversity: A New Frontier for Evolutionary Computation". Frontiers in Robotics and AI 3. doi:10.3389/frobt.2016.00040. ISSN 2296-9144. 
  12. ↑ Lehman, Joel; Stanley, Kenneth O. (2011-07-12). "Evolving a diversity of virtual creatures through novelty search and local competition". Proceedings of the 13th annual conference on Genetic and evolutionary computation. New York, NY, USA: ACM. pp. 211–218. doi:10.1145/2001576.2001606. ISBN 9781450305570. http://dx.doi.org/10.1145/2001576.2001606. 
  13. ↑ Cully, Antoine; Clune, Jeff; Tarapore, Danesh; Mouret, Jean-Baptiste (2015-05-27). "Robots that can adapt like animals". Nature 521 (7553): 503–507. doi:10.1038/nature14422. ISSN 0028-0836. PMID 26017452. Bibcode: 2015Natur.521..503C. http://dx.doi.org/10.1038/nature14422. 
  14. ↑ 14.0 14.1 Davis, Lawrence (1991). Handbook of genetic algorithms. New York: Van Nostrand Reinhold. ISBN 0-442-00173-8. OCLC 23081440. https://www.worldcat.org/oclc/23081440. 
  15. ↑ Lienig, Jens; Brandt, Holger (1994), Davidor, Yuval; Schwefel, Hans-Paul; Männer, Reinhard, eds., "An evolutionary algorithm for the routing of multi-chip modules", Parallel Problem Solving from Nature — PPSN III (Berlin, Heidelberg: Springer) 866: pp. 588–597, doi:10.1007/3-540-58484-6_301, ISBN 978-3-540-58484-1, http://link.springer.com/10.1007/3-540-58484-6_301, retrieved 2022-10-18 
  16. ↑ Neri, Ferrante, ed (2012) (in en). Handbook of Memetic Algorithms. Studies in Computational Intelligence. 379. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-23247-3. ISBN 978-3-642-23246-6. http://link.springer.com/10.1007/978-3-642-23247-3. 
  17. ↑ Leung, Yee; Gao, Yong; Xu, Zong-Ben (1997). "Degree of population diversity - a perspective on premature convergence in genetic algorithms and its Markov chain analysis". IEEE Transactions on Neural Networks 8 (5): 1165–1176. doi:10.1109/72.623217. ISSN 1045-9227. PMID 18255718. https://ieeexplore.ieee.org/document/623217. 
  18. ↑ Gorges-Schleuter, Martina (1998), Eiben, Agoston E.; Bäck, Thomas; Schoenauer, Marc et al., eds., "A comparative study of global and local selection in evolution strategies", Parallel Problem Solving from Nature — PPSN V, Lecture Notes in Computer Science (Berlin, Heidelberg: Springer Berlin Heidelberg) 1498: pp. 367–377, doi:10.1007/bfb0056879, ISBN 978-3-540-65078-2, http://link.springer.com/10.1007/BFb0056879, retrieved 2022-10-21 
  19. ↑ Dorronsoro, Bernabe; Alba, Enrique (2008). Cellular Genetic Algorithms. Operations Research/Computer Science Interfaces Series. 42. Boston, MA: Springer US. doi:10.1007/978-0-387-77610-1. ISBN 978-0-387-77609-5. http://link.springer.com/10.1007/978-0-387-77610-1. 
  20. ↑ Goldberg, David E. (1990), Schwefel, Hans-Paul; Männer, Reinhard, eds., "The theory of virtual alphabets" (in en), Parallel Problem Solving from Nature, Lecture Notes in Computer Science (Berlin/Heidelberg: Springer-Verlag) 496: pp. 13–22, 1991, doi:10.1007/bfb0029726, ISBN 978-3-540-54148-6, http://link.springer.com/10.1007/BFb0029726, retrieved 2022-10-22 
  21. ↑ Stender, J.; Hillebrand, E.; Kingdon, J. (1994). Genetic algorithms in optimisation, simulation, and modelling. Amsterdam: IOS Press. ISBN 90-5199-180-0. OCLC 47216370. https://www.worldcat.org/oclc/47216370. 
  22. ↑ Michalewicz, Zbigniew (1996). Genetic Algorithms + Data Structures = Evolution Programs (3rd ed.). Berlin Heidelberg: Springer. ISBN 978-3-662-03315-9. OCLC 851375253. https://www.worldcat.org/oclc/851375253. 
  23. ↑ G.S. Hornby and J.B. Pollack. "Creating high-level components with a generative representation for body-brain evolution". Artificial Life, 8(3):223–246, 2002.
  24. ↑ Jeff Clune, Benjamin Beckmann, Charles Ofria, and Robert Pennock. "Evolving Coordinated Quadruped Gaits with the HyperNEAT Generative Encoding" . Proceedings of the IEEE Congress on Evolutionary Computing Special Section on Evolutionary Robotics, 2009. Trondheim, Norway.
  25. ↑ J. Clune, C. Ofria, and R. T. Pennock, "How a generative encoding fares as problem-regularity decreases", in PPSN (G. Rudolph, T. Jansen, S. M. Lucas, C. Poloni, and N. Beume, eds.), vol. 5199 of Lecture Notes in Computer Science, pp. 358–367, Springer, 2008.
  26. ↑ Ferreira, C., 2001. "Gene Expression Programming: A New Adaptive Algorithm for Solving Problems". Complex Systems, Vol. 13, issue 2: 87–129.
  27. ↑ Sanchez, Ernesto; Squillero, Giovanni; Tonda, Alberto (2012). Industrial Applications of Evolutionary Algorithms. Intelligent Systems Reference Library. 34. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-27467-1. ISBN 978-3-642-27466-4. http://link.springer.com/10.1007/978-3-642-27467-1. 
  28. ↑ Miettinen, Kaisa (1999) (in en). Evolutionary algorithms in engineering and computer science : recent advances in genetic algorithms, evolution strategies, evolutionary programming, genetic programming, and industrial applications. Chichester: Wiley and Sons. ISBN 0-585-29445-3. OCLC 45728460. https://www.wiley.com/en-us/Evolutionary+Algorithms+in+Engineering+and+Computer+Science%3A+Recent+Advances+in+Genetic+Algorithms%2C+Evolution+Strategies%2C+Evolutionary+Programming%2C+Genetic+Programming+and+Industrial+Applications-p-9780471999027. 
  29. ↑ Gen, Mitsuo; Cheng, Runwei (1999-12-17) (in en). Genetic Algorithms and Engineering Optimization. Wiley Series in Engineering Design and Automation. Hoboken, NJ, USA: John Wiley & Sons, Inc.. doi:10.1002/9780470172261. ISBN 978-0-470-17226-1. http://doi.wiley.com/10.1002/9780470172261. 
  30. ↑ Dahal, Keshav P.; Tan, Kay Chen; Cowling, Peter I. (2007) (in en). Evolutionary scheduling. Berlin: Springer. doi:10.1007/978-3-540-48584-1. ISBN 978-3-540-48584-1. OCLC 184984689. https://www.worldcat.org/oclc/184984689. 
  31. ↑ Jakob, Wilfried; Strack, Sylvia; Quinte, Alexander; Bengel, Günther; Stucky, Karl-Uwe; Süß, Wolfgang (2013-04-22). "Fast Rescheduling of Multiple Workflows to Constrained Heterogeneous Resources Using Multi-Criteria Memetic Computing" (in en). Algorithms 6 (2): 245–277. doi:10.3390/a6020245. ISSN 1999-4893. 
  32. ↑ Mayer, David G. (2002). Evolutionary Algorithms and Agricultural Systems. Boston, MA: Springer US. doi:10.1007/978-1-4615-1717-7. ISBN 978-1-4613-5693-6. http://link.springer.com/10.1007/978-1-4615-1717-7. 
  33. ↑ Blume, Christian (2000), Cagnoni, Stefano, ed., "Optimized Collision Free Robot Move Statement Generation by the Evolutionary Software GLEAM" (in en), Real-World Applications of Evolutionary Computing, LNCS 1803 (Berlin, Heidelberg: Springer) 1803: pp. 330–341, doi:10.1007/3-540-45561-2_32, ISBN 978-3-540-67353-8, http://link.springer.com/10.1007/3-540-45561-2_32, retrieved 2022-12-28 
  34. ↑ Aranha, Claus; Iba, Hitoshi (2008), Wobcke, Wayne; Zhang, Mengjie, eds., "Application of a Memetic Algorithm to the Portfolio Optimization Problem", AI 2008: Advances in Artificial Intelligence, Lecture Notes in Computer Science (Berlin, Heidelberg: Springer Berlin Heidelberg) 5360: pp. 512–521, doi:10.1007/978-3-540-89378-3_52, ISBN 978-3-540-89377-6, http://link.springer.com/10.1007/978-3-540-89378-3_52, retrieved 2022-12-23 
  35. ↑ Chen, Shu-Heng, ed (2002). Evolutionary Computation in Economics and Finance. Studies in Fuzziness and Soft Computing. 100. Heidelberg: Physica-Verlag HD. doi:10.1007/978-3-7908-1784-3. ISBN 978-3-7908-2512-1. http://link.springer.com/10.1007/978-3-7908-1784-3. 
  36. ↑ Lohn, J.D.; Linden, D.S.; Hornby, G.S.; Kraus, W.F. (June 2004). "Evolutionary design of an X-band antenna for NASA's Space Technology 5 mission". IEEE Antennas and Propagation Society Symposium, 2004. 3. pp. 2313–2316 Vol.3. doi:10.1109/APS.2004.1331834. ISBN 0-7803-8302-8. https://ieeexplore.ieee.org/document/1331834. 
  37. ↑ Fogel, Gary; Corne, David (2003) (in en). Evolutionary Computation in Bioinformatics. Elsevier. doi:10.1016/b978-1-55860-797-2.x5000-8. ISBN 978-1-55860-797-2. https://linkinghub.elsevier.com/retrieve/pii/B9781558607972X50008. 
  38. ↑ 38.0 38.1 Jakob, Wilfried (2021), Applying Evolutionary Algorithms Successfully - A Guide Gained from Realworld Applications, KIT Scientific Working Papers, 170, Karlsruhe, FRG: KIT Scientific Publishing, doi:10.5445/IR/1000135763, https://publikationen.bibliothek.kit.edu/1000135763/121278298, retrieved 2022-12-23 
  39. ↑ Whitley, Darrell (2001). "An overview of evolutionary algorithms: practical issues and common pitfalls" (in en). Information and Software Technology 43 (14): 817–831. doi:10.1016/S0950-5849(01)00188-4. https://linkinghub.elsevier.com/retrieve/pii/S0950584901001884. 
  40. ↑ Eiben, A.E.; Smith, J.E. (2015). "Working with Evolutionary Algorithms" (in en). Introduction to Evolutionary Computing. Natural Computing Series (2nd ed.). Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 147–163. doi:10.1007/978-3-662-44874-8. ISBN 978-3-662-44873-1. http://link.springer.com/10.1007/978-3-662-44874-8. 
  41. ↑ 41.0 41.1 Slowik, Adam; Kwasnicka, Halina (2018). "Nature Inspired Methods and Their Industry Applications—Swarm Intelligence Algorithms". IEEE Transactions on Industrial Informatics (Institute of Electrical and Electronics Engineers (IEEE)) 14 (3): 1004–1015. doi:10.1109/tii.2017.2786782. ISSN 1551-3203. 
  42. ↑ F. Merrikh-Bayat, "The runner-root algorithm: A metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature", Applied Soft Computing, Vol. 33, pp. 292–303, 2015
  43. ↑ Oftadeh, R.; Mahjoob, M.J.; Shariatpanahi, M. (October 2010). "A novel meta-heuristic optimization algorithm inspired by group hunting of animals: Hunting search". Computers & Mathematics with Applications 60 (7): 2087–2098. doi:10.1016/j.camwa.2010.07.049. 
  44. ↑ Amine Agharghor; Mohammed Essaid Riffi (2017). "First Adaptation of Hunting Search Algorithm for the Quadratic Assignment Problem". Europe and MENA Cooperation Advances in Information and Communication Technologies. Advances in Intelligent Systems and Computing. 520. pp. 263–267. doi:10.1007/978-3-319-46568-5_27. ISBN 978-3-319-46567-8. 
  45. ↑ Hasançebi, O., Kazemzadeh Azad, S. (2015), "Adaptive Dimensional Search: A New Metaheuristic Algorithm for Discrete Truss Sizing Optimization", Computers and Structures, 154, 1–16.
  46. ↑ Gent, Edd (13 April 2020). "Artificial intelligence is evolving all by itself" (in en). Science | AAAS. https://www.science.org/content/article/artificial-intelligence-evolving-all-itself. 
  47. ↑ Simionescu, P.A.; Dozier, G.V.; Wainwright, R.L. (2006). "A Two-Population Evolutionary Algorithm for Constrained Optimization Problems". 2006 IEEE International Conference on Evolutionary Computation. Vancouver, BC, Canada: IEEE. pp. 1647–1653. doi:10.1109/CEC.2006.1688506. ISBN 978-0-7803-9487-2. https://ieeexplore.ieee.org/document/1688506. 
  48. ↑ Simionescu, P.A.; Dozier, G.V.; Wainwright, R.L. (2006). "A Two-Population Evolutionary Algorithm for Constrained Optimization Problems". 2006 IEEE International Conference on Evolutionary Computation. Proc 2006 IEEE International Conference on Evolutionary Computation. Vancouver, Canada. pp. 1647–1653. doi:10.1109/CEC.2006.1688506. ISBN 0-7803-9487-9. http://faculty.tamucc.edu/psimionescu/PDFs/WCCI2006-Paper7204(1).pdf. Retrieved 7 January 2017. 
  49. ↑ Simionescu, P.A. (2014). Computer Aided Graphing and Simulation Tools for AutoCAD Users (1st ed.). Boca Raton, FL: CRC Press. ISBN 978-1-4822-5290-3. 

External links

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