Evolving Systems

, Volume 9, Issue 2, pp 157–168 | Cite as

Devolutionary genetic algorithms with application to the minimum labeling Steiner tree problem

  • Nassim DehoucheEmail author
Original Paper


This paper characterizes and discusses devolutionary genetic algorithms and evaluates their performances in solving the minimum labeling Steiner tree (MLST) problem. We define devolutionary algorithms as the process of reaching a feasible solution by devolving a population of super-optimal unfeasible solutions over time. We claim that distinguishing them from the widely used evolutionary algorithms is relevant. The most important distinction lies in the fact that in the former type of processes, the value function decreases over successive generation of solutions, thus providing a natural stopping condition for the computation process. We show how classical evolutionary concepts, such as crossing, mutation and fitness can be adapted to aim at reaching an optimal or close-to-optimal solution among the first generations of feasible solutions. We additionally introduce a novel integer linear programming formulation of the MLST problem and a valid constraint used for speeding up the devolutionary process. Finally, we conduct an experiment comparing the performances of devolutionary algorithms to those of state of the art approaches used for solving randomly generated instances of the MLST problem. Results of this experiment support the use of devolutionary algorithms for the MLST problem and their development for other NP-hard combinatorial optimization problems.


Hybrid Meta-heuristics Integer linear programming Evolutionary computation Minimum labelling Steiner tree problem 


  1. Acampora G, Panigrahi BK (2015) Thematic issue on hybrid nature-inspired algorithms: concepts, analysis and applications. Memet Comput 7(1):1–2CrossRefGoogle Scholar
  2. Alba E, Resende MGC, Urquhart ME, Lim M-H (2012) Thematic issue on memetic algoriths: theory and applications in OR/MS. Memet Comput 4(2):87–88CrossRefGoogle Scholar
  3. Barril Otero FE, Masegosa AD, Terrazas G (2014) Thematic issue on advances in nature inspired cooperative strategies for optimization. Memet Comput 6(3):147–148CrossRefGoogle Scholar
  4. Beasley JE (1989) An SST-based algorithm for the Steiner problem in graphs. Networks 19:1–16MathSciNetCrossRefzbMATHGoogle Scholar
  5. Blum C, Aguilera M, Roli A, Sampels M (2008) Hybrid metaheuristics: an emerging approach to optimization, 1st edn. Springer, BerlinCrossRefzbMATHGoogle Scholar
  6. Cerulli R, Fink A, Gentili M, Voss S (2006) Extensions of the minimum labelling spanning tree problem. J Telecommun Inf Technol 4:39–45Google Scholar
  7. Chang RS, Leu SJ (1997) The minimum labelling spanning tree. Inf Process Lett 63(5):277–282CrossRefzbMATHGoogle Scholar
  8. Chwatal AM, Raidl GR (2011) Solving the minimum label spanning tree problem by mathematical programming techniques. Adv Oper Res 2011:143732. doi: 10.1155/2011/143732 MathSciNetzbMATHGoogle Scholar
  9. Consoli S, Darby-Dowman K, Mladenovic N, Moreno-Perez JA (2009) Variable neighbourhood search for the minimum labelling Steiner tree problem. Ann Oper Res 172(1):71–96MathSciNetCrossRefzbMATHGoogle Scholar
  10. Consoli S, Moreno-Perez JA, Darby-Dowman K, Mladenovic N (2008) Discrete particle swarm optimization for the minimum labelling steiner tree problem. In: Krasnogor N, Nicosia G, Pavone M, Pelta D (eds) Nature inspired cooperative strategies for optimization, vol 129, Studies in computational intelligenceSpringer, New York, pp 313–322Google Scholar
  11. Czyzyk J, Mesnier MP, More JJ (1998) The NEOS server. IEEE Comput Sci Eng 5(3):68–75CrossRefGoogle Scholar
  12. Dougherty MJ (1998) Is the human race evolving or devolving? Sci Am. Accessed 18 Apr 2017
  13. Freire H, Oliveira PM, Solteiro Pires EJ, Bessa M (2015) Many-objective optimization with corner-based search. Memet Comput 7(2):105–118CrossRefGoogle Scholar
  14. Hakimi SL (1971) Steiner’s problem in graphs and its implications. Networks 1:113–133MathSciNetCrossRefzbMATHGoogle Scholar
  15. Hu B, Leitner M, Raidl GR (2008) Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem. J Heuristics 14(5):473–499CrossRefzbMATHGoogle Scholar
  16. Junger M, Thienel S (2001) The ABACUS system for branch-and-cut-and-price algorithms in integer programming and combinatorial optimization. Softw Pract Exp 30:1325–1352CrossRefzbMATHGoogle Scholar
  17. Kapsalis A, Rayward-Smith VJ, Smith GD (1993) Solving the graphical Steiner tree problem using genetic algorithms. J Oper Res Soc 44(4):397–406CrossRefzbMATHGoogle Scholar
  18. Lai X, Zhou Y, He J, Zhang J (2013) Performance analysis of evolutionary algorithms for the minimum label spanning tree problem. IEEE Trans Evolut Comput 18(6):860–872Google Scholar
  19. Mittelmann HD (2007) Recent benchmarks of optimization software. In: 22nd European conference on operational research, EURO XXII Prague, Czech RepublicGoogle Scholar
  20. Nekkaa M, Boughaci D (2015) A memetic algorithm with support vector machine for feature selection and classification. Memet Comput 7(1):59–73CrossRefGoogle Scholar
  21. Polzin T, Daneshmand SV (2001) A comparison of Steiner tree relaxations. Discrete Appl Math 112:241–261MathSciNetCrossRefzbMATHGoogle Scholar
  22. Rocha M, Neves J (1999) Preventing premature convergence to local optima in genetic algorithms via random offspring generation. In: Multiple approaches to intelligent systems, Lecture notes in computer science, vol 1611, pp 127–136Google Scholar
  23. Safe M, Carballido J, Ponzoni I, Brignol N (2004) On stopping criteria for genetic algorithms. In: Advances in artificial intelligence, SBIA 2004, Lecture Notes in Computer Science, vol 3171, pp 405–413Google Scholar
  24. Shapiro J (2001) Genetic algorithms in machine learning. In: Machine learning and its applications, Lecture notes in computer science, vol 2049, pp 146–168Google Scholar
  25. Studniarski M (2010) Stopping criteria for genetic algorithms with application to multiobjective optimization. In: Parallel problem solving from nature, PPSN XI, Lecture notes in computer science, vol 6238, pp 697–706Google Scholar
  26. Tawhid MA, Fouad A (2016) A simplex social spider algorithm for solving integer programming and minimax problems. Memet Comput 8(3):169–188CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Business Administration DivisionMahidol University International CollegeSalayaThailand

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