Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
119 tokens/sec
GPT-4o
56 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
6 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Stochastic Population Update Can Provably Be Helpful in Multi-Objective Evolutionary Algorithms (2306.02611v2)

Published 5 Jun 2023 in cs.NE and cs.AI

Abstract: Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update, a key component in multi-objective EAs (MOEAs), is usually performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the best solutions from the current population and newly-generated solutions (irrespective of the selection criteria used such as Pareto dominance, crowdedness and indicators). In this paper, we question this practice. We analytically present that stochastic population update can be beneficial for the search of MOEAs. Specifically, we prove that the expected running time of two well-established MOEAs, SMS-EMOA and NSGA-II, for solving two bi-objective problems, OneJumpZeroJump and bi-objective RealRoyalRoad, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed population update method. This work is an attempt to challenge a common practice in the design of existing MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (60)
  1. H. E. Aguirre and K. Tanaka. Insights on properties of multiobjective MNK-landscapes. In Proceedings of the 2004 IEEE Congress on Evolutionary Computation (CEC’04), pages 196–203, Portland, OR, 2004.
  2. T. Bäck. Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford, UK, 1996.
  3. SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research, 181:1653–1669, 2007.
  4. C. Bian and C. Qian. Better running time of the non-dominated sorting genetic algorithm II (NSGA-II) by using stochastic tournament selection. In Proceedings of the 17th International Conference on Parallel Problem Solving from Nature (PPSN’22), pages 428–441, Dortmund, Germany, 2022.
  5. A general approach to running time analysis of multi-objective evolutionary algorithms. In Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI’18), pages 1405–1411, Stockholm, Sweden, 2018.
  6. Stochastic population update can provably be helpful in multi-objective evolutionary algorithms. In Proceedings of the 32nd International Joint Conference on Artificial Intelligence (IJCAI’23), pages 5513–5521, Macao, SAR, China, 2023.
  7. Analyzing hypervolume indicator based algorithms. In Proceedings of the 10th International Conference on Parallel Problem Solving from Nature (PPSN’08), pages 651–660, Dortmund, Germany, 2008.
  8. The first proven performance guarantees for the non-dominated sorting genetic algorithm II (NSGA-II) on a combinatorial optimization problem. In Proceedings of the 32nd International Joint Conference on Artificial Intelligence (IJCAI’23), pages 5522–5530, Macao, SAR, China, 2023.
  9. Evolutionary Algorithms for Solving Multi-objective Problems. Springer, New York, NY, 2007.
  10. Design and analysis of diversity-based parent selection schemes for speeding up evolutionary multi-objective optimisation. Theoretical Computer Science, 832:123–142, 2020.
  11. Analysing the robustness of NSGA-II under noise. In Proceedings of the 25th ACM Conference on Genetic and Evolutionary Computation (GECCO’23), pages 642–651, Lisbon, Portugal, 2023.
  12. A proof that using crossover can guarantee exponential speed-ups in evolutionary multi-objective optimisation. In Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI’23), pages 12390–12398, Washington, DC, 2023.
  13. K. Deb. Multi-objective Optimization using Evolutionary Algorithms. Wiley, Chichester, UK, 2001.
  14. K. Deb and H. Jain. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Transactions on Evolutionary Computation, 18(4):577–601, 2014.
  15. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2):182–197, 2002.
  16. Runtime analyses of multi-objective evolutionary algorithms in the presence of noise. In Proceedings of the 32nd International Joint Conference on Artificial Intelligence (IJCAI’23), pages 5549–5557, Macao, SAR, China, 2023.
  17. B. Doerr. Exponential upper bounds for the runtime of randomized search heuristics. Theoretical Computer Science, 851:24–38, 2021.
  18. Runtime analysis of evolutionary diversity maximization for OneMinMax. In Proceedings of the 18th ACM Conference on Genetic and Evolutionary Computation (GECCO’16), pages 557–564, Denver, CO, 2016.
  19. Lower bounds for the runtime of a global multi-objective evolutionary algorithm. In Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC’13), pages 432–439, Cancun, Mexico, 2013.
  20. B. Doerr and F. Neumann, editors. Theory of Evolutionary Computation: Recent Developments in Discrete Optimization. Springer, Cham, Switzerland, 2020.
  21. B. Doerr and Z. Qu. A first runtime analysis of the NSGA-II on a multimodal problem. IEEE Transactions on Evolutionary Computation, 27(5):1288–1297, 2023.
  22. B. Doerr and Z. Qu. From understanding the population dynamics of the NSGA-II to the first proven lower bounds. In Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI’23), pages 12408–12416, Washington, DC, 2023.
  23. B. Doerr and Z. Qu. Runtime analysis for the NSGA-II: Provable speed-ups from crossover. In Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI’23), pages 12399–12407, Washington, DC, 2023.
  24. B. Doerr and W. Zheng. Theoretical analyses of multi-objective evolutionary algorithms on multi-modal objectives. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI’21), pages 12293–12301, Virtual, 2021.
  25. Introduction to Evolutionary Computing. Springer-Verlag, Berlin, Germany, 2015.
  26. Plateaus can be harder in multi-objective optimization. Theoretical Computer Science, 411(6):854–864, 2010.
  27. Illustration of fairness in evolutionary multi-objective optimization. Theoretical Computer Science, 412(17):1546–1556, 2011.
  28. O. Giel. Expected runtimes of a simple multi-objective evolutionary algorithm. In Proceedings of the 2003 IEEE Congress on Evolutionary Computation (CEC’03), pages 1918–1925, Canberra, Australia, 2003.
  29. O. Giel and P. K. Lehre. On the effect of populations in evolutionary multi-objective optimisation. Evolutionary Computation, 18(3):335–356, 2010.
  30. D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Boston, MA, 1989.
  31. J. He and X. Yao. Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence, 127(1):57–85, 2001.
  32. C. Horoba. Analysis of a simple evolutionary algorithm for the multiobjective shortest path problem. In Proceedings of the 10th International Workshop on Foundations of Genetic Algorithms (FOGA’09), pages 113–120, Orlando, FL, 2009.
  33. A runtime analysis of typical decomposition approaches in MOEA/D framework for many-objective optimization problems. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI’21), pages 1682–1688, Virtual, 2021.
  34. Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem. Natural Computing, 3:37–51, 2004.
  35. Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions. IEEE Transactions on Evolutionary Computation, 8(2):170–182, 2004.
  36. A multi-objective genetic algorithm for robust flight scheduling using simulation. European Journal of Operational Research, 177(3):1948–1968, 2007.
  37. MOEAs are stuck in a different area at a time. In Proceedings of the 25th ACM Conference on Genetic and Evolutionary Computation (GECCO’23), pages 303–311, Lisbon, Portugal, 2023.
  38. Non-elitist evolutionary multi-objective optimisation: Proof-of-principle results. In Proceedings of the 25th ACM Conference on Genetic and Evolutionary Computation Companion (GECCO’23 Companion), pages 383–386, Lisbon, Portugal, 2023.
  39. Towards running time analysis of interactive multi-objective evolutionary algorithms. In Proceedings of the 38th AAAI Conference on Artificial Intelligence (AAAI’24), page in press, Vancouver, Canada, 2024.
  40. NSGA-Net: neural architecture search using multi-objective genetic algorithm. In Proceedings of the 21th ACM Conference on Genetic and Evolutionary Computation (GECCO’19), pages 419–427, Prague, Czech Republic, 2019.
  41. H. Markowitz. Portfolio selection. The Journal of Finance, 7(1):77–91, 1952.
  42. F. Neumann. Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem. European Journal of Operational Research, 181(3):1620–1629, 2007.
  43. F. Neumann and M. Theile. How crossover speeds up evolutionary algorithms for the multi-criteria all-pairs-shortest-path problem. In Proceedings of the 11th International Conference on Parallel Problem Solving from Nature (PPSN’10), pages 667–676, Krakow, Poland, 2010.
  44. Population size matters: Rigorous runtime results for maximizing the hypervolume indicator. Theoretical Computer Science, 561:24–36, 2015.
  45. Transonic wing design by inverse optimization using MOGA. In Proceedings of the 6th Annual Conference of the Computational Fluid Dynamics Society of Canada (CFD’98), Quebec, Canada, 1998.
  46. G. Pahl and W. Beitz. Engineering Design: A Systematic Approach. Springer-Verlag, London, UK, 1996.
  47. Selection hyper-heuristics can provably be helpful in evolutionary multi-objective optimization. In Proceedings of the 14th International Conference on Parallel Problem Solving from Nature (PPSN’16), pages 835–846, Edinburgh, Scotland, 2016.
  48. An analysis on recombination in multi-objective evolutionary optimization. Artificial Intelligence, 204:99–119, 2013.
  49. Multiobjective evolutionary optimization of DNA sequences for reliable DNA computing. IEEE Transactions on Evolutionary Computation, 9(2):143–158, 2005.
  50. S. Wietheger and B. Doerr. A mathematical runtime analysis of the non-dominated sorting genetic algorithm III (NSGA-III). In Proceedings of the 32nd International Joint Conference on Artificial Intelligence (IJCAI’23), pages 5657–5665, Macao, SAR, China, 2023.
  51. Q. Zhang and H. Li. MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6):712–731, 2007.
  52. W. Zheng and B. Doerr. Runtime analysis for the NSGA-II: Proving, quantifying, and explaining the inefficiency for many objectives. IEEE Transactions on Evolutionary Computation, in press.
  53. W. Zheng and B. Doerr. Better approximation guarantees for the NSGA-II by using the current crowding distance. In Proceedings of the 24th ACM Conference on Genetic and Evolutionary Computation (GECCO’22), pages 611–619, Boston, MA, 2022.
  54. W. Zheng and B. Doerr. Mathematical runtime analysis for the non-dominated sorting genetic algorithm II (NSGA-II). Artificial Intelligence, 325:104016, 2023.
  55. W. Zheng and B. Doerr. Runtime analysis of the SMS-EMOA for many-objective optimization. In Proceedings of the 38th AAAI Conference on Artificial Intelligence (AAAI’24), page in press, Vancouver, Canada, 2024.
  56. Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation, 1(1):32–49, 2011.
  57. Evolutionary Learning: Advances in Theories and Algorithms. Springer, Singapore, 2019.
  58. E. Zitzler and S. Künzli. Indicator-based selection in multiobjective search. In Proceedings of the 8th International Conference on Parallel Problem Solving from Nature (PPSN’04), pages 832–842, Birmingham, UK, 2004.
  59. SPEA2: Improving the strength Pareto evolutionary algorithm. TIK-Report, 103, 2001.
  60. E. Zitzler and L. Thiele. Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 3(4):257–271, 1999.
User Edit Pencil Streamline Icon: https://streamlinehq.com
Authors (4)
  1. Chao Bian (21 papers)
  2. Yawen Zhou (3 papers)
  3. Miqing Li (24 papers)
  4. Chao Qian (90 papers)
Citations (25)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets