Universal Approach to Solution of Optimization Problems by Symbolic Regression
Source abstract
Abstract
Optimization problems and their solution by symbolic regression methods are considered. The search is performed on non-Euclidean space. In such spaces it is impossible to determine a distance between two potential solutions and, therefore, algorithms using arithmetic operations of multiplication and addition are not used there. The search of optimal solution is performed on the space of codes. It is proposed that the principle of small variations of basic solution be applied as a universal approach to create search algorithms. Small variations cause a neighborhood of a potential solution, and the solution is searched for within this neighborhood. The concept of inheritance property is introduced. It is shown that for non-Euclidean search space, the application of evolution and small variations of possible solutions is effective. Examples of using the principle of small variation of basic solution for different symbolic regression methods are presented.
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Research context
OpenAlex topics: Evolutionary Algorithms and Applications · Model Reduction and Neural Networks · Metaheuristic Optimization Algorithms Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, 119333 Moscow, Russia
Funding
Ministry of Science and Higher Education of the Russian Federation
References (29)
Show source-provided references
1. Koza, J.R. (1992). Genetic Programming, MIT Press.
2. Grammatical Evolution
3. Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., and Fogarty, T.C. (2000). Cartesian Genetic Programming. Genetic Programming. EuroGP, Springer.10.1007/b75085 ↗
4. Analytic Programming—Symbolic Regression by Means of Arbitrary Evolutionary Algorithms
5. Diveev, A.I., and Sofronova, E.A. (2009, January 9–11). Numerical method of network operator for multiobjective synthesis of optimal control system. Proceedings of the Seventh International Conference on Control and Automation (ICCA’09), Christchurch, New Zealand.10.1109/ICCA.2009.5410619 ↗
6. Parse-matrix evolution for Symbolic Regression10.1016/j.engappai.2012.05.015 ↗
7. Automation of Synthesized Optimal Control Problem Solution for Mobile Robot by Genetic Programming
8. Arnaldo, I., O’Reilly, U.-M., and Veeramachaneni, K. (2015, January 11–15). Building predictive models via feature synthesis. Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, Madrid, Spain.10.1145/2739480.2754693 ↗
9. Discovering govering equations from data by sparse identification of nonlinear dynamical systems10.1073/pnas.1517384113 ↗
10. Sparse identification of nonlinear dynamics for rapid model recovery10.1063/1.5027470 ↗
11. McRee, R.K. (2010, January 7–11). Symbolic regression using nearest neighbor indexing. Proceedings of the 12th Annual Conference Companion on Genetic and Evolutionary Comutation, GECCO’10, Portland, OR, USA.10.1145/1830761.1830841 ↗
12. Kong, W., Liaw, C., Mehta, A., and Sivakumar, D. (2019, January 6–9). A new dog learns old tricks: RL finds classic optimization algorithms. Proceedings of the International Conference on Learning Representations, New Orleans, LA, USA.
13. Yao, X. (2000). Inductive Genetic Programming of Polynomial Learning Networks. 2000 IEEE Symposium on Combinations of Evolutionary Computation and Neural Networks, Proceedings of the First IEEE Symposium of Combinations of Evolutionary Computation and Neural Networks, ECNN-2000, San Antonio, TX, USA, 11–13 May 2000, IEEE Press.
14. Distilling free-form natural laws from experimental data10.1126/science.1165893 ↗
15. Diveev, A., Kazaryan, D., and Sofronova, E. (2014, January 16–19). Symbolic regression methods for control system synthesis. Proceedings of the 22nd Mediterranean Conference on Control and Automation, Palermo, Italy.10.1109/MED.2014.6961436 ↗
16. Grand challenges for evolutionary robotics
17. Smetka, T., Homoliak, I., and Hanacek, P. (2016, January 24–27). On the Application of Symbolic Regression and Genetic Programming for Cryptanalysis of Symmetric Encryption Algorithm. Proceedings of the International Carnahan Conference on Security Technology (ICCST 2016), Orlando, FL, USA.10.1109/CCST.2016.7815720 ↗
18. Linden, D.S. (2002, January 15–18). Optimizing signal strength in-situ using an evolvable antenna system. Proceedings of the 2002 NASA/DoD Conference on Evolvable Hardware, Alexandria, VA, USA.
19. McAleer, S., Agostinelli, F., Shmakov, A., and Baldi, P. (2019, January 6–9). Solving the Rubik’s Cube with Approximate Policy Iteration. Proceedings of the International Conference on Learning Representations, New Orleans, LA, USA.
20. Kim, S., Lu, P., Mukherjee, S., Gilbert, M., Jing, L., Ceperic, V., and Soljacic, M. (2019). Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery. arXiv.
21. Application of network operator method for synthesis of optimal structure and parameters of automatic control system10.3182/20080706-5-KR-1001.01031 ↗
22. Cranmer, M., Sanchez-Gonzalez, A., Battaglia, P., Xu, R., Cranmer, K., Spergel, D., and Ho, S. (2006). Discovering Symbolic Models from Deep Learning with Inductive Biases. arXiv.
23. Al Feynman: A physics-inspired method for symbolic regression10.1126/sciadv.aay2631 ↗
24. Small Variations of Basic Solution Method for Non-numerical Optimization10.1016/j.ifacol.2015.11.054 ↗
25. Binary codes capable of correcting deletions, insertions, and reversals
26. Holland, J.H. (1992). Adaptation in Natural and Artificial Systems, MIT Press. [2nd ed.].10.7551/mitpress/1090.001.0001 ↗
27. A Numerical Method for Network Operator for Synthesis of a Control System with Uncertain Initial Values10.1134/S1064230712010066 ↗
28. Cartesian Genetic Programming for Synthesis of Optimal Control System
29. Tracking Trajectory of the Mobile Robot Khepera II Using Approaches of Artificial Intelligence