Article

Article title HYBRID BIOINSPIRED ALGORITHM FOR SOLVING SYMBOLIC REGRESSION PROBLEM
Authors B.K. Lebedev, O.B. Lebedev
Section SECTION I. EVOLUTIONARY MODELLING, GENETIC AND BIONIC ALGORITHMS
Month, Year 06, 2015 @en
Index UDC 621.3.049.771.14
DOI
Abstract The problem of symbolic regression is to find mathematical expressions in symbolic form, approximating the relationship between the finite set of values of the independent variables and the corresponding values of the dependent variables. The criterion of quality approach (objective function) is the mean square error: the sum of the squares of the difference between the model and the values of the dependent variable for all values of the independent variable as an argument. Symbolic regression – method of constructing regression models by trying different superpositions of arbitrary functions from a given set. The paper is offered hybrid algorithm for solving symbolic regression. Use the traditional idea of an algebraic formula in the form of syntax tree. Leaf nodes correspond to variables or numeric constants rather than leaf nodes contain the operation that is performed on the child nodes. A distinctive feature of the process tree representation as a linear recording is preclude loss plurality of terminal elements, but the model can be an arbitrary function of the superposition of a set. In the process of synthesis of algebraic formula two problems are solved. The first task is to build a tree structure with anonymous tips. The second task is to specify the values of the tree tops. Leaf nodes are compared with the terminal set, a non-leaf nodes are matched with a functional set. The first problem is solved by ant colony. To solve the second problem is used a genetic algorithm. The rating formula is calculated after solving both problems – the construction of an ant tree unnamed peak and subsequent identification of vertices using ant colony The structure of the graph to find solutions G=(X,U). It is possible to create a solution space in which organized the search process based on the simulation of adaptive behavior of an ant colony. Formulated the necessary conditions under which the built in G route is represented as a legitimate expression D, is a solution of a symbolic regression. Developed heuristic of ant behavior when ant moving in graph to find solutions. For large dimension of time parameters of the algorithm outperformed compared algorithms for the best value of the objective function. Experimental time complexity of the algorithm on a single iteration for fixed values of the control parameters is O(nlgn), where n – the power terminal set.

Download PDF

Keywords Symbolic regression; syntax tree; terminal set; functional set; ant colony; genetic search; hybrid algorithm
References 1. Ian H. Witten, Eibe Frank and Mark A. Hall Data Mining: Practical Machine Learning Tools and Techniques. 3rd Edition. Morgan Kaufmann, 2011.
2. Sammut C., Webb G.I. Symbolic regression, Encyclopedia of Machine Learning. Berlin: Springer, 2010.
3. Barsegyan A.A., Kupriyanov M.S., Stepanenko V.V., Kholod I.I. Metody i modeli analiza dannykh: OLAP i Data Mining [Methods and models of data analysis: OLAP and Data Mining]. St. Peterburg: BKhV-Peterburg, 2004, 336 p.
4. Radchenko S.G. Metodologiya regressionnogo analiza: Monografiya [Methodology regression analysis: Monograph]. K.: Korniychuk, 2011, 376 p.
5. Dreyper N., Smit G. Prikladnoy regressionnyy analiz [Applied regression analysis]. Moscow: Vil'yams, 2007, 912 p.
6. Strizhov V.V., Krymova E.A. Metody vybora regressionnykh modeley [Methods selection of regression models]. Moscow: VTs RAN, 2010, 60 p.
7. Zelinka I., Oplatkova Z., Nolle L. Analytic programming and symbolic regression by means of arbitrary evolutionary algorithms, Int. J. Simulation Syst. Sci. Technol., 2005, Vol. 6, No. 9, pp. 44-56.
8. Lebedev B.K., Lebedev V.B. Evolyutsionnaya protsedura obucheniya pri raspoznavanii obrazov [Evolutionary procedure learning in pattern recognition], Izvestiya TRTU [Izvestiya TSURe], 2004, No. 8 (43), pp. 83-88.
9. Rudoy G.I., Strizhov V.V. Algoritmy induktivnogo porozhdeniya superpozitsiy dlya approksimatsii izmeryaemykh dannykh [Algorithms for inductive generation of superpositions for approximation of the measured data], Informatika i ee primeneniya [Informatics and Applications], 2013, Vol. 7, Issue 1, pp. 44-53.
10. Bukhtoyarov V.V., Semenkin E.S. Razrabotka i issledovanie gibridnogo metoda geneticheskogo programmirovaniya [Research and development of hybrid method of genetic programming], Programmnye produkty i sistemy [Software products and systems], 2010, No. 3, pp. 34-38.
11. Kureichik V.M., Lebedev B.K. and Lebedev V.B. VLSI Floorplanning Based on the Integration of Adaptive Search Models, Journal of Computer and Systems Sciences International, 2013, Vol. 52, No. 1, pp. 80-96. ISSN 1064_2307.
12. Koza, J.R. Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Springer. 2005.
13. Lebedev B.K. and. Lebedev V.B. Synthesis of Mathematical Expressions by Methods of Genetic Search, Proceedings of the International Scientific Conferences “Intelligent Systems (IEEE AIS’06)”and “Intelligent CAD’s (CAD- 2006)”. Scientific publication in 3 vol. Vol. 3. Moscow: Physmathlit, 2006, pp. 29-34.
14. Barmpalexis P.,Kachrimanis K., Tsakonas A., Georgarakis E. Symbolic regression via genetic programming in the optimization of a controlled release pharmaceutical formulation, Chemometrics and Intelligent Laboratory Systems, 2011, Vol. 107, No. 1, pp. 75-82.
15. Colin G. Johnson. Artificial Immune Systems Programming for Symbolic Regression, Genetic Programming: 6th European Conference, 2003, pp. 345-353. ISBN=3-540- 00971-X.
16. Ushakov S.A. Ispol'zovanie raspredelennykh iskusstvennykh immunnykh sistem dlya resheniya zadachi simvol'noy regressii [The use of distributed artificial immune system for solving symbolic regression], Innovatika. Nauchnyy elektronnyy zhurnal [Innovation. Scientific electronic journal], 2014, No. 1. Certificate of registration EL № FS 77-5722.
17. Lebedev O.B. Modeli adaptivnogo povedeniya murav'inoy kolonii v zadachakh proektirovaniya [Models of adaptive behavior, ant colony in the task of designing]. Taganrog: Izd-vo YuFU, 2013, 199 p.
18. Lebedev B.K., Lebedev V.B. Optimizatsiya metodom kristallizatsii rossypi al'ternativ (KRA) [Optimization by the crystallization of alternatives field (CAF) method], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2013, No. 7 (144), pp. 11-17.
19. Lebedev B.K., Lebedev O.B. Modelirovanie adaptivnogo povedeniya murav'inoy kolonii pri poiske resheniy, interpretiruemykh derev'yami [Modelling of an ant colony adaptive behaviour by search of the decisions interpreted by trees], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2012, No. 7 (132), pp. 27-35.
20. Lebedev V.B., Lebedev O.B. Roevoy intellekt na osnove integratsii modeley adaptivnogo povedeniya murav'inoy i pchelinoy koloniy [Swarm intelligence on the basis of the adaptive behaviour models integration of the ant and beer colonies], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2013, No. 7 (144), pp. 41-47.
21. Kureichik V.M., Lebedev B.K., Lebedev O.B. A hybrid partitioning algorithm based on natural mechansms of decision making, Scientific and Technical Information Processing, 2012, No. 39 (6), pp. 317-327.

Comments are closed.