Balanced-evolution genetic algorithm for combinatorial optimization problems: the general outline and implementation of balanced-evolution strategy based on linear diversity index

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Abstract

How to rationally inject randomness to control population diversity is still a difficult problem in evolutionary algorithms. We propose balanced-evolution genetic algorithm (BEGA) as a case study of this problem. Similarity guide matrix (SGM) is a two-dimensional matrix to express the population (or subpopulation) distribution in coding space. Different from binary-coding similarity indexes, SGM is able to be suitable for binary-coding and symbol-coding problems, simultaneously. In BEGA, opposite-direction and forward-direction regions are defined by using two SGMs as reference points, respectively. In opposite-direction region, diversity subpopulation always tries to increase Hamming distances between themselves and the current population. In forward-direction region, intensification subpopulation always tries to decrease Hamming distances between themselves and the current elitism population. Thus, diversity subpopulation is more suitable for injecting randomness. Linear diversity index (LDI) measures the individual density around the center-point individual in coding space, which is characterized by itself linearity. According to LDI, we control the search-region ranges of diversity and intensification subpopulations by using negative and positive perturbations, respectively. Thus, the search efforts between exploration and exploitation are balanced. We compared BEGA with CHC, dual-population genetic algorithm, variable dissortative mating genetic algorithm, quantum-inspired evolutionary algorithm, and greedy genetic algorithm for 12 benchmarks. Experimental results were acceptable. In addition, it is worth noting that BEGA is able to directly solve bounded knapsack problem (i.e. symbol-coding problem) as one EA-based solver, and does not transform bounded knapsack problem into an equivalent binary knapsack problem.

Keywords

Population diversity control Feedback control scheme Similarity guide matrix Linear diversity index Symbol-coding problem Bounded knapsack problem 

Notes

Acknowledgements

The authors would like to thank anonymous reviewers for their constructive comments, especially for improving the concepts of similarity guide matrix and linear diversity index. This work was supported by National Natural Science Foundation of China (Grant No. 61272518) and YangFan Innovative and Entrepreneurial Research Team Project of Guangdong Province.

References

  1. Alba E, Dorronsoro B (2005) The exploration/exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Trans Evol Comput 9:126–142.  https://doi.org/10.1109/TEVC.2005.843751 CrossRefGoogle Scholar
  2. Baluja S (1992) A massively distributed parallel genetic algorithm. Tech. Rep. No. CMU-CS- 92-196R. Carnegie Mellon UniversityGoogle Scholar
  3. Burke E, Gustafson S, Kendall G, Krasnogor N (2002) Advanced population diversity measures in genetic programming. In: Proceedings of parallel problem solving from nature. Springer, pp 341–350.  https://doi.org/10.1007/3-540-45712-7_33
  4. Burke E, Gustafson S, Kendall G (2004) Diversity in genetic programming: an analysis of measures and correlation with fitness. IEEE Trans Evol Comput 8:47–62.  https://doi.org/10.1109/TEVC.2003.819263 CrossRefGoogle Scholar
  5. Cao ZJ, Shi YH, Rong XF, Liu BL, Du ZQ, Yang B (2015) Random grouping brain storm optimization algorithm with a new dynamically changing step size. In: Proceedings of the International Conference on Swarm Intelligence, Lecture Notes in Computer Science. Springer, pp 357–364.  https://doi.org/10.1007/978-3-319-20466-6_38
  6. Chen G, Low CP, Yang ZH (2009) Preserving and exploiting genetic diversity in evolutionary programming algorithms. IEEE Trans Evol Comput 13:661–673.  https://doi.org/10.1109/TEVC.2008.2011742 CrossRefGoogle Scholar
  7. Črepinšek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45:1–33.  https://doi.org/10.1145/2480741.2480752 MATHGoogle Scholar
  8. Darwen PJ, Yao X (2001) Why more choices cause less cooperation in iterated prisoner’s dilemma. In: Proceedings of the 2001 Congress on Evolutionary Computation. IEEE, pp 987–994.  https://doi.org/10.1109/cec.2001.934298
  9. De Jong K (1975) An analysis of the behavior of a class of genetic adaptive systems. Dissertation, University of MichiganGoogle Scholar
  10. De Jong K (2007) Parameter setting in EAs: a 30 year perspective. In: Lobo FG, Lima CF, Michalewicz Z (eds) Parameter setting in evolutionary algorithms. Springer, Berlin, pp 1–18Google Scholar
  11. Dekkers A, Aarts E (1991) Global optimization and simulated annealing. Math Program 50:367–393.  https://doi.org/10.1007/BF01594945 MathSciNetCrossRefMATHGoogle Scholar
  12. Eiben AE, Schippers C (1998) On evolutionary exploration and exploitation. Fundam Inform 35:35–50.  https://doi.org/10.3233/FI-1998-35123403 MATHGoogle Scholar
  13. Eiben AE, Smit SK (2011) Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm Evol Comput 1:19–31.  https://doi.org/10.1016/j.swevo.2011.02.001 CrossRefGoogle Scholar
  14. Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3:124–141.  https://doi.org/10.1109/4235.771166 CrossRefGoogle Scholar
  15. Eshelman LJ (1991) The CHC adaptive search algorithm: how to have safe search when engaging in nontraditional genetic recombination. In: Gregory JR (ed) Foundations of genetic algorithms, vol 1. Morgan Kaufmann Publishers Inc, San Francisco, pp 265–283Google Scholar
  16. Fernandes C, Rosa A (2006) Self-regulated population size in evolutionary algorithms. In: Runarsson TP, Beyer HG et al (eds) Parallel problem solving from nature–PPSN IX. Springer, Iceland, pp 920–929CrossRefGoogle Scholar
  17. Fernandes C, Rosa A (2008) Self-adjusting the intensity of assortative mating in genetic algorithms. Soft Comput 12:955–979.  https://doi.org/10.1007/s00500-007-0265-9 CrossRefGoogle Scholar
  18. García-Martínez C, Lozano M (2008) Local search based on genetic algorithms. In: Siarry P, Michalewicz Z (eds) Advances in metaheuristics for hard optimization. Springer, Berlin, pp 199–221CrossRefGoogle Scholar
  19. Glover F (1997) Heuristics for integer programming using surrogate constraints. Decis Sci 8:156–166.  https://doi.org/10.1111/j.1540-5915.1977.tb01074.x CrossRefGoogle Scholar
  20. Han KH, Kim JH (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6:580–593.  https://doi.org/10.1109/TEVC.2002.804320 CrossRefGoogle Scholar
  21. Harik GR, Lobo FG, Goldberg DE (1999) The compact genetic algorithm. IEEE Trans Evol Comput 3:287–297.  https://doi.org/10.1109/4235.797971 CrossRefGoogle Scholar
  22. Holland JH (1975) Adaptation in natural and artificial systems. The MIT Press, Ann ArborGoogle Scholar
  23. Jaccard P (1912) The distribution of the flora in the alpine zone. New Phytol 11:37–50.  https://doi.org/10.1111/j.1469-8137.1912.tb05611.x CrossRefGoogle Scholar
  24. Koumousis VK, Katsaras CP (2006) A saw-tooth genetic algorithm combining the effects of variable population size and reinitialization to enhance performance. IEEE Trans Evol Comput 10:19–28.  https://doi.org/10.1109/TEVC.2005.860765 CrossRefGoogle Scholar
  25. Lacevic B, Amaldi E (2010) On population diversity measures in euclidean space. In: Proceedings of the 2010 Congress on Evolutionary Computation. IEEE, pp 1–8.  https://doi.org/10.1109/cec.2010.5586498
  26. Lacevic B, Konjicija S, Avdagic Z (2007) Population diversity measure based on singular values of the distance matrix. In: Proceedings of the 2007 Congress on Evolutionary Computation. IEEE, pp 1863–1869.  https://doi.org/10.1109/cec.2007.4424700
  27. Lee CY, Yao X (2004) Evolutionary programming using mutations based on the levy probability distribution. IEEE Trans Evol Comput 8:1–13.  https://doi.org/10.1109/TEVC.2003.816583 CrossRefGoogle Scholar
  28. Lozano M, Herrera F, Cano JR (2008) Replacement strategies to preserve useful diversity in steady-state genetic algorithms. Inf Sci 178:4421–4433.  https://doi.org/10.1016/j.ins.2008.07.031 CrossRefGoogle Scholar
  29. Martello S, Toth P (1990) Knapsack problems: algorithms and computer implementations. Wiley, HobokenMATHGoogle Scholar
  30. Martello S, Pisinger D, Toth P (1999) Dynamic programming and strong bounds for the 0–1 knapsack problem. Manag Sci 45:414–424.  https://doi.org/10.1287/mnsc.45.3.414 CrossRefMATHGoogle Scholar
  31. Mattiussi C, Waibel M, Floreano D (2004) Measures of diversity for populations and distances between individuals with highly reorganizable genomes. Evol Comput 12:495–515.  https://doi.org/10.1162/1063656043138923 CrossRefGoogle Scholar
  32. McGinley B, Maher J, O’Riordan C, Morgan F (2011) Maintaining healthy population diversity using adaptive crossover, mutation, and selection. IEEE Trans Evol Comput 15:692–714.  https://doi.org/10.1109/TEVC.2010.2046173 CrossRefGoogle Scholar
  33. Morrison RW, De Jong K (2002) Measurement of population diversity. In: Collet P, Fonlupt C, Hao J, Lutton E, Schoenauer M (eds) Artificial evolution. Springer, France, pp 31–41CrossRefGoogle Scholar
  34. Park T, Ryu KR (2010) A dual-population genetic algorithm for adaptive diversity control. IEEE Trans Evol Comput 14:865–884.  https://doi.org/10.1109/TEVC.2010.2043362 CrossRefGoogle Scholar
  35. Pelikan M, Goldberg DE, Cantú-paz EE (2000) Linkage problem, distribution estimation, and bayesian networks. Evol Comput 8:311–340.  https://doi.org/10.1162/106365600750078808 CrossRefGoogle Scholar
  36. Pisinger D (1999) Core problems in knapsack algorithms. Oper Res 47:570–575.  https://doi.org/10.1287/opre.47.4.570 MathSciNetCrossRefMATHGoogle Scholar
  37. Platel MD, Platel MD, Schliebs S, Schliebs S, Kasabov N, Kasabov N (2009) Quantum-inspired evolutionary algorithm: a multimodel EDA. IEEE Trans Evol Comput 13:1218–1232.  https://doi.org/10.1109/TEVC.2008.2003010 CrossRefGoogle Scholar
  38. Resende MGC, Ribeiro CC, Glover F, Martí R (2010) Scatter search and path-relinking: fundamentals, advances, and applications. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. Springer, Berlin, pp 87–107CrossRefGoogle Scholar
  39. Shi YH (2015) Brain storm optimization algorithm in objective space. In: IEEE Congress on Evolutionary Computation. IEEE, pp 1227–1234.  https://doi.org/10.1109/cec.2015.7257029
  40. Smit SK, Eiben AE (2009) Comparing parameter tuning methods for evolutionary algorithms. In: Proceedings of the 2009 Congress on Evolutionary Computation. IEEE, pp 399–406.  https://doi.org/10.1109/cec.2009.4982974
  41. Spears WM (2000) Evolutionary algorithms: the role of mutation and recombination. Springer, BerlinCrossRefMATHGoogle Scholar
  42. Truong TK, Li KL, Xu YM (2013) Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem. Appl Soft Comput 13:1774–1780.  https://doi.org/10.1016/j.asoc.2012.11.048 CrossRefGoogle Scholar
  43. Ursem RK (2002) Diversity-guided evolutionary algorithms. In: Guervós JJM, Adamidis P et al (eds) Parallel problem solving from nature—PPSN VII. Springer, Espana, pp 462–471CrossRefGoogle Scholar
  44. Zhan ZH, Zhang J, Shi YH, Liu HL (2012) A modified brain storm optimization. In: IEEE Congress on Evolutionary Computation. IEEE, pp 1–8.  https://doi.org/10.1109/cec.2012.6256594
  45. Zhang J, Chung HSH, Lo W (2007) Clustering-based adaptive crossover and mutation probabilities for genetic algorithms. IEEE Trans Evol Comput 11:326–335.  https://doi.org/10.1109/TEVC.2006.880727 CrossRefGoogle Scholar
  46. Zhu HY, Shi YH (2015) Brain storm optimization algorithms with K-medians clustering algorithms. In: International Conference on Advanced Computation Intelligence. IEEE, pp 107–110.  https://doi.org/10.1109/icaci.2015.7184758
  47. Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Dissertation, Swiss Federal Institute of Technology ZurichGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic EngineeringBeijing University of Posts and TelecommunicationsBeijingChina

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