Using Adaptive Integration of Variables Algorithm for Analysis and Optimization of 2D Irregular Nesting Problem

  • José Arzola-RuizEmail author
  • Arlys Michel Lastre-Aleaga
  • Alexis Cordovés
  • Umer Asgher
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 953)


In this article a new evolutionary technique using 2D irregular-shaped nesting problem optimization algorithm applied on material cutting processes having processes like cutting of irregular foils pieces and complex geometrical shapes is proposed. This technique is adaptive and improves results of material cutting process and its optimization in comparison to other methods reflected in the earlier literature. A formalization and mathematical modelling are based on CAD/CAPP/CAM/CAP integration methodology for irregular two-dimensional pieces produced as a multilevel optimization with constraints of component part and the bi-level distribution and cutting process on foils. The decision of selection and the final solutions using adaptive algorithm based on dynamical modification of the objectives during the pieces’ distribution and using the population obtained for the elaboration of cutting trajectories of the cutter device. This procedure defines a new approach for the bi-level optimization of geometric iterative increasing polygon pieces’ configurations using the particular case of the Integration of Variables method called Exploration of a Function of Variable Codes algorithm. As final result a new optimal manufacturing integration scheme that include human-machine interaction as a component part is deducted.


Irregular cutting Stock problem Nesting, distribution of irregular parts Adaptive Evolutionary methods Graphic treatment Boundary surfaces 


  1. 1.
    Jie, L., Jialin, H., Yaoguang, H., Guangquan, Z.: Multilevel decision-making: a survey. Inf. Sci. 346, 463–487 (2016)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Lu, J., Shi, C., Zhang, G.: On bi-level multi-follower decision making: general framework and solutions. Inf. Sci. 176, 1607–1627 (2006)CrossRefGoogle Scholar
  3. 3.
    Lu, J., Zhang, G., Montero, J., Garmendia, L.: Multifollower trilevel decision making models and system. IEEE Trans. Ind. Inf. 8, 974–985 (2006)CrossRefGoogle Scholar
  4. 4.
    Kalashnikov, V.V., Dempe, S., Pérez-Valdés, G.A., Kalashnykova, N.I., Camacho-Vallejo, J.F.: Bi-level programming and applications. Math. Prob. Eng. 181, 423, 442 (2015)zbMATHGoogle Scholar
  5. 5.
    Glackin, J., Ecker, J.G., Kupferschmid, M.: Solving bi-level linear programs using multiple objective linear programming. J. Optim. Theory Appl. 140, 197–212 (2009)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Wan, Z., Wang, G., Sun, B.: A hybrid intelligent algorithm by combining particle swarm optimization with chaos searching technique for solving non-linear bi-level programming problems. Swarm Evol. Comput. 8, 26–32 (2013)CrossRefGoogle Scholar
  7. 7.
    Angulo, E., Castillo, E., García-Ródenas, R., Sánchez-Vizcaíno, J.: A continuous bi-level model for the expansion of highway networks. Comput. Oper. Res. 41, 262–276 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Fontaine, P., Minner, S.: Benders decomposition for discrete–continuous linear bi-level problems with application to traffic network design. Transp. Res. Part B: Methodol. 70, 163–172 (2014)CrossRefGoogle Scholar
  9. 9.
    NieP, Y.: Dynamic discrete-time multi-leader–follower games with leaders in turn. Comput. Math Appl. 61, 2039–2043 (2015)MathSciNetGoogle Scholar
  10. 10.
    Nishizaki, I., Sakawa, M.: Computational methods through genetic algorithms for obtaining Stackelberg solutions to two-level integer programming problems. Cybern. Syst. 36, 565–579 (2005)CrossRefGoogle Scholar
  11. 11.
    Bard, J.F.: Practical Bi-level Optimization: Algorithms and Applications. Kluwer Academic Publishers, Dordrecht (1998)CrossRefGoogle Scholar
  12. 12.
    Audet, C., Haddad, J., Savard, G.: Disjunctive cuts for continuous linear bi-level programming. Optim. Lett. 1, 259–267 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Zhang, T., Hu, T., Guo, X., Chen, Z., Zheng, Y.: Solving high dimensional bi-level multi-objective programming problem using a hybrid particle swarm optimization algorithm with crossover operator. Knowl. Based Syst. 53, 13–19 (2013)CrossRefGoogle Scholar
  14. 14.
    Han, J., Lu, J., Hu, Y., Zhang, G.: Tri-level decision-making with multiple followers: model, algorithm and case study. Inf. Sci. 311, 182–204 (2016)CrossRefGoogle Scholar
  15. 15.
    Arzola, R.J., Simeón, R.E., Maceo, A.: El Método de Integración de Variables: una generalización de los Algoritmos Genéticos. In: Proceedings of Intensive Workshop: Optimal Design of Materials and Structures, París (2003)Google Scholar
  16. 16.
    Arzola-Ruiz, J.: Análisis y Síntesis de Sistemas de ingeniería (2009).
  17. 17.
    Arzola-Ruiz, J.: Sistemas de Ingeniería. Editorial Felix Valera, La Habana (2000)Google Scholar
  18. 18.
    Arzola-Ruiz, J.: Selección de Propuestas. Editorial_Científico-Técnica, La Habana (1989)Google Scholar
  19. 19.
    Lastre-Aleaga, A.: Optimización de la distribución y corte de piezas irregulares en chapas. Ph.D. thesis, Holguín (2009)Google Scholar
  20. 20.
    Mitchell, F.H.: CIM Systems. An introduction to Computer Integrated Manufacturing. Prentice Hall, Upper Saddle River (1991)Google Scholar
  21. 21.
    Bennell, J.A., Oliveira, J.F.: The geometry of nesting problems: a tutorial. Eur. J. Oper. Res. 184(2), 397–415 (2008)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Arzola-Ruiz, J.: Sistemas de Ingeniería, 2nd edn. Editorial Félix Valera, La Habana (2012)Google Scholar
  23. 23.
    Lastres–Aleaga, A.M., Arzola-Ruiz, J., Cordovés-García, A.: Optimización de la distribución de piezas irregulares en chapas. Ingeniería Mecánica 13(2), 1–12 (2010)Google Scholar
  24. 24.
    Lastres–Aleaga, A.M. Optimización de la distribución y corte de piezas irregulares en chapas. Tesis en opción al grado científico de Doctor en Ciencias Técnicas, Holguín (2010)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • José Arzola-Ruiz
    • 1
    Email author
  • Arlys Michel Lastre-Aleaga
    • 2
  • Alexis Cordovés
    • 2
  • Umer Asgher
    • 3
  1. 1.Studies Center of Mathematics for Technical Sciences (CEMAT)Technological University of HavanaHabanaCuba
  2. 2.Equinoccial Technological UniversityQuitoEcuador
  3. 3.School of Mechanical and Manufacturing Engineering (SMME)National University of Sciences and Technology (NUST)IslamabadPakistan

Personalised recommendations