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Deep memetic models for combinatorial optimization problems: application to the tool switching problem

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Abstract

Memetic algorithms are techniques that orchestrate the interplay between population-based and trajectory-based algorithmic components. In particular, some memetic models can be regarded under this broad interpretation as a group of autonomous basic optimization algorithms that interact among them in a cooperative way in order to deal with a specific optimization problem, aiming to obtain better results than the algorithms that constitute it separately. Going one step beyond this traditional view of cooperative optimization algorithms, this work tackles deep meta-cooperation, namely the use of cooperative optimization algorithms in which some components can in turn be cooperative methods themselves, thus exhibiting a deep algorithmic architecture. The objective of this paper is to demonstrate that such models can be considered as an efficient alternative to other traditional forms of cooperative algorithms. To validate this claim, different structural parameters, such as the communication topology between the agents, or the parameter that influences the depth of the cooperative effort (the depth of meta-cooperation), have been analyzed. To do this, a comparison with the state-of-the-art cooperative methods to solve a specific combinatorial problem, the Tool Switching Problem, has been performed. Results show that deep models are effective to solve this problem, outperforming metaheuristics proposed in the literature.

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Notes

  1. We assume that \(C<m\), otherwise the problem is trivial.

  2. For example, if the agent is loaded with a local search method then only one solution will be generated and kept so that \(\#S_{i}=1\), but if the agent is loaded with a population-based method—for example, a classical memetic or genetic algorithm—then a pool of candidate solutions will be generated so that \(\#S_{i}\geqslant 1\), where \(\#S_{i}\) indicates the cardinality of \(S_{i}\).

  3. That is, if \((i,j)\in \varLambda \) then \(a_{i}\) will send information to the agent \(a_{j}\) in each cycle of synchronization inside the execution of the cooperative algorithm as described later in this paper.

  4. For simplicity we have omitted the parameter \(cycles_{max}\); this will be done in the following when necessary to improve the legibility.

  5. All the datasets are available at http://www.unet.edu.ve/~jedgar/ToSP/ToSP.htm.

  6. Hu, Ca and Ox are 1, 2 and 3 in Mayan language, respectively.

  7. It must be noted that Holm test would in this case be equivalent to the test performed in the previous section since the top-ten algorithms are exactly the same ones.

References

  1. Al-Fawzan MA, Al-Sultan KS (2003) A tabu search based algorithm for minimizing the number of tool switches on a flexible machine. Comput Ind Eng 44(1):35–47

    Article  Google Scholar 

  2. Aldous D, Vazirani UV (1994) “Go with the winners” algorithms. In: 35th annual symposium on foundations of computer science, Santa Fe, New Mexico, USA, IEEE Computer Society, pp 492–501, , 20–22 Nov 1994

  3. Amaya JE, Cotta C, Fernández AJ (2008) A memetic algorithm for the tool switching problem. In: Blesa MJ, Blum C, Cotta C, Fernández AJ, Gallardo JE, Roli A, Sampels M (eds) Hybrid metaheuristics, 5th international workshop, HM 2008, Málaga, Proceedings, Lecture Notes in Computer Science, vol 5296, pp 190–202, Springer, Spain, 8–9 Oct 2008

  4. Amaya JE, Cotta C, Fernández Leiva AJ (2010) Hybrid cooperation models for the tool switching problem. In: González JR, Pelta DA, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization, NICSO 2010, Studies in Computational Intelligence, vol 284, pp 39–52, , Granada, Spain, Springer, 12–14 May 2010

    Chapter  Google Scholar 

  5. Amaya JE, Cotta C, Fernández Leiva AJ (2011) Memetic cooperative models for the tool switching problem. Memet Comput 3(3):199–216

    Article  Google Scholar 

  6. Amaya JE, Cotta C, Fernández Leiva AJ (2012) Solving the tool switching problem with memetic algorithms. AI EDAM 26(2):221–235

    Google Scholar 

  7. Amaya JE, Cotta C, Fernández Leiva AJ (2013) Cross entropy-based memetic algorithms: an application study over the tool switching problem. Int J Comput Intell Syst 6(3):559–584

    Article  Google Scholar 

  8. Anandalingam G, Friesz TL (1992) Hierarchical optimization: an introduction. Ann OR 34:1–11

    Article  MathSciNet  MATH  Google Scholar 

  9. Babaoglu O, Jelasity M, Montresor A, Fetzer C, Leonardi S, van Moorsel A, van Steen M (eds) (2005) Self-star properties in complex information systems, lecture notes in computer science, vol 3460. Springer, Berlin

    Google Scholar 

  10. Bard JF (1988) A heuristic for minimizing the number of tool switches on a flexible machine. IIE Trans 20(4):382–391

    Article  Google Scholar 

  11. Berns A, Ghosh S (2009) Dissecting self-\(\star \) properties. In: 3rd IEEE international conference on self-adaptive and self-organizing systems—SASO 2009. IEEE Press, San Francisco, CA, pp 10–19

  12. Byrski A, Schaefer R, Smolka M, Cotta C (2013) Asymptotic guarantee of success for multi-agent memetic systems. Bull Pol Acad Sci Tech Sci 61(1):257–278

    Google Scholar 

  13. Camacho D, Lara-Cabrera R, Merelo Guervós JJ, Castillo PA, Cotta C, Fernández Leiva AJ, Fernández de Vega F, Chávez de la OF (2018) From ephemeral computing to deep bioinspired algorithms: new trends and applications. Future Gener Comput Syst 88:735–746

    Article  Google Scholar 

  14. Corona CC, Pelta DA (2009) Soft computing and cooperative strategies for optimization. Appl Soft Comput 9(1):30–38

    Article  Google Scholar 

  15. Crainic TG, Toulouse M (2007) Explicit and emergent cooperation schemes for search algorithms. In: Maniezzo V, Battiti R, Watson J (eds) Learning and Intelligent Optimization 2007, Lecture Notes in Computer Science, Springer, vol 5313, pp 95–109

  16. Crainic TG, Gendreau M, Hansen P, Mladenovic N (2004) Cooperative parallel variable neighborhood search for the p-median. J Heuristics 10(3):293–314

    Article  Google Scholar 

  17. Cui Z, Xue F, Cai X, Cao Y, Wang G, Chen J (2018) Detection of malicious code variants based on deep learning. IEEE Trans Ind Inform 14(7):3187–3196

    Article  Google Scholar 

  18. Cui Z, Du L, Wang P, Cai X, Zhang W (2019) Malicious code detection based on cnns and multi-objective algorithm. J Parallel Distrib Comput 129:50–58

    Article  Google Scholar 

  19. El-Abd M, Kamel M (2005) A taxonomy of cooperative search algorithms. In: Blesa MJ, Blum C, Roli A, Sampels M (eds) Hybrid metaheuristics, 2nd international workshop, HM 2005, proceedings, lecture notes in computer science, vol 3636, pp 32–41, Barcelona, Spain, Springer, 29–30 Aug 2005

  20. Fernández-Leiva AJ, Gutiérrez-Fuentes Á (2019) On distributed user-centric memetic algorithms. Soft Comput 23(12):4019–4039

    Article  Google Scholar 

  21. Gallardo JE, Cotta C, Fernández AJ (2007) On the hybridization of memetic algorithms with branch-and-bound techniques. IEEE Trans Syst Man Cybern Part B 37(1):77–83

    Article  Google Scholar 

  22. García del Amo IJ, Pelta DA, Masegosa AD, Verdegay JL (2010) A software modeling approach for the design and analysis of cooperative optimization systems. Softw Pract Exp 40(9):811–823

    Google Scholar 

  23. Hertz A, Laporte G, Mittaz M, Stecke K (1998) Heuristics for minimizing tool switches when scheduling part types on a flexible machine. IIE Trans 30:689–694

    Google Scholar 

  24. Jourdan L, Basseur M, Talbi E (2009) Hybridizing exact methods and metaheuristics: a taxonomy. Eur J Oper Res 199(3):620–629

    Article  MathSciNet  MATH  Google Scholar 

  25. Krasnogor N, Smith J (2001) Emergence of profitable search strategies based on a simple inheritance mechanism. In: Spector L et al (eds) Genetic and evolutionary computation conference 2001. Morgan Kaufmann, San Francisco CA, pp 432–439

  26. Laporte G, Salazar-González JJ, Semet F (2004) Exact algorithms for the job sequencing and tool switching problem. IIE Trans 36(1):37–45

    Article  Google Scholar 

  27. LeCun Y, Bengio Y, Hinton GE (2015) Deep learning. Nature 521(7553):436–444

    Article  Google Scholar 

  28. Lim TY (2014) Structured population genetic algorithms: a literature survey. Artif Intell Rev 41(3):385–399

    Article  Google Scholar 

  29. Malek R (2009) Collaboration of metaheuristic algorithms through a multi-agent system. In: Marík V, Strasser TI, Zoitl A (eds) Holonic and multi-agent systems for manufacturing, Proceedings of 4th international conference on industrial applications of holonic and multi-agent systems, HoloMAS 2009, Lecture Notes in Computer Science, Linz, Austria, vol 5696, pp 72–81, Springer, August 31–September 2 2009

  30. Neri F, Cotta C (2012) Memetic algorithms and memetic computing optimization: a literature review. Swarm Evol Comput 2:1–14

    Article  Google Scholar 

  31. Nogueras R, Cotta C (2014) An analysis of migration strategies in island-based multimemetic algorithms. In: Bartz-Beielstein T et al (eds) Parallel Problem Solving from Nature—PPSN XIII, lecture notes in computer science, vol 8672. Springer, Berlin, pp 731–740

    Chapter  Google Scholar 

  32. Schaefer R, Kołodziej J (2002) Genetic search reinforced by the population hierarchy. In: Poli R, Rowe JE, Jong KAD (eds) Foundations of genetic algorithms VII. Morgan Kaufmann, Burlington, pp 383–400

    Google Scholar 

  33. Schaefer R, Byrski A, Kolodziej J, Smolka M (2012) An agent-based model of hierarchic genetic search. Comput Math Appl 64(12):3763–3776

    Article  MathSciNet  MATH  Google Scholar 

  34. Talbi E, Bachelet V (2006) COSEARCH: a parallel cooperative metaheuristic. J Math Model Algorithms 5(1):5–22

    Article  MathSciNet  MATH  Google Scholar 

  35. Tang CS, Denardo EV (1988) Models arising from a flexible manufacturing machine, part I: minimization of the number of tool switches. Oper Res 36(5):767–777

    Article  MATH  Google Scholar 

  36. Vasile M, Ricciardi LA (2017) Multi agent collaborative search. In: Schütze O, Trujillo L, Legrand P, Maldonado Y (eds) NEO 2015—results of the numerical and evolutionary optimization workshop NEO 2015 held at 23-25 Sept 2015 in Tijuana, Mexico, Springer, studies in computational intelligence, vol 663, pp 223–252

  37. Wang G, Cai X, Cui Z, Min G, Chen J (2019) High performance computing for cyber physical social systems by using evolutionary multi-objective optimization algorithm. IEEE Trans Emerg Top Comput. https://doi.org/10.1109/TETC.2017.2703784

  38. Zhou BH, Xi LF, Cao YS (2005) A beam-search-based algorithm for the tool switching problem on a flexible machine. Int J Adv Manuf Technol 25(9):876–882

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to thank the anonymous reviewers for their helpful comments. The first author thanks to the Decanato de Investigación of UNET the partial support of the present research. Second and third author were partially supported by Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech, and also by research projects Ephemech (https://ephemech.wordpress.com/) (TIN2014-56494-C4-1-P), and DeepBio (https://deepbio.wordpress.com) (TIN2017-85727-C4-01-P), funded by Ministerio Español de Economía y Competitividad. Fourth author was also partially supported by “Ayuda del Programa de Fomento e Impulso de la Actividad Investigadora de la Universidad de Cádiz”.

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Authors and Affiliations

  1. Universidad Nacional Experimental del Táchira (UNET), Laboratorio de Computación de Alto Rendimiento (LCAR), San Cristóbal, Venezuela

    Jhon Edgar Amaya

  2. Dept. Lenguajes y Ciencias de la Computación, ETSI Informática, University of Malaga, Campus de Teatinos, 29071, Malaga, Spain

    Carlos Cotta & Antonio J. Fernández-Leiva

  3. Dept. de Ingeniería Informática, ESI, University of Cádiz, Campus de Puerto Real, 11519, Cádiz, Spain

    Pablo García-Sánchez

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  1. Jhon Edgar Amaya
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  2. Carlos Cotta
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  4. Pablo García-Sánchez
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Correspondence to Pablo García-Sánchez.

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Appendices

Tables of computational results

This appendix section shows the computational results for each level in Tables 4, 5, and 6 respectively.

Table 4 Computational results with meta-cooperative models 5\(\varLambda \)(Hu, ..., ...) where Hu=5Ri(MAHC, MATS, MAHC). \(\bar{x}\) = mean number of tool switches. \(\sigma \) = mean standard deviation. Recall we are using the notation \(C\zeta _{m}^{n}\), where C is the magazine capacity, m is the total number of tools and n is the number of jobs
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Table 5 Computational results with meta-cooperative models 5\(\varLambda \)(Ca,\(\star \), \(\star \)) where Ca=Br(Hu, MAHC, CEM). \(\bar{x}\) = mean number of tool switches. \(\sigma \) = mean standard deviation. Recall we are using the notation \(C\zeta _{m}^{n}\), where C is the magazine capacity, m is the total number of tools and n is the number of jobs
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Table 6 Computational results with meta-cooperative models 5\(\varLambda \)(Ox,\(\star \), \(\star \)) where Ox=5Br(Ca, MAHC, CEM). \(\bar{x}\) = mean number of tool switches. \(\sigma \) = mean standard deviation. Recall we are using the notation \(C\zeta _{m}^{n}\), where C is the magazine capacity, m is the total number of tools and n is the number of jobs
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Tests

This appendix shows the results of Holm test for each level in Tables 7 and 8 (Table for level 3 is equivalent to the table for level 2, as they share the best ten algorithms in the comparison). Holm test for the topology in each of the three scenarios and globally are also shown in Tables 9, 10, 11, 12.

Table 7 Results of Holm test (\(\alpha =0.05\)) using 5Br(Hu, MAHC, CEM) as control algorithm
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Table 8 Results of Holms test (\(\alpha =0.05\)) using 5Br(Ca,MAHC,CEM) as control algorithm
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Table 9 Results of Holm test (\(\alpha =0.05\)) using broadcast as control algorithm on the 1-level scenario.
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Table 10 Results of Holm test (\(\alpha =0.05\)) using broadcast as control algorithm on the 2-level scenario
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Table 11 Results of Holm test (\(\alpha =0.05\)) using Broadcast as control algorithm on the 3-level scenario
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Table 12 Results of Holm Test (\(\alpha =0.05\)) using Broadcast as control algorithm across all three scenarios
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Amaya, J.E., Cotta, C., Fernández-Leiva, A.J. et al. Deep memetic models for combinatorial optimization problems: application to the tool switching problem. Memetic Comp. 12, 3–22 (2020). https://doi.org/10.1007/s12293-019-00294-1

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