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Enhanced Optimization with Composite Objectives and Novelty Pulsation

Part of the Genetic and Evolutionary Computation book series (GEVO)

Abstract

An important benefit of multi-objective search is that it maintains a diverse population of candidates, which helps in deceptive problems in particular. Not all diversity is useful, however: candidates that optimize only one objective while ignoring others are rarely helpful. A recent solution is to replace the original objectives by their linear combinations, thus focusing the search on the most useful tradeoffs between objectives. To compensate for the loss of diversity, this transformation is accompanied by a selection mechanism that favors novelty. This paper improves this approach further by introducing novelty pulsation, i.e. a systematic method to alternate between novelty selection and local optimization. In the highly deceptive problem of discovering minimal sorting networks, it finds state-of-the-art solutions significantly faster than before. In fact, our method so far has established a new world record for the 20-line sorting network with 91 comparators. In the real-world problem of stock trading, it discovers solutions that generalize significantly better on unseen data. Composite Novelty Pulsation is therefore a promising approach to solving deceptive real-world problems through multi-objective optimization.

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References

  1. F. Allen, R. Karjalainen. 1999. Using genetic algorithms to find technical trading rules. Journal of Financial Economics 51, 245–271.

    CrossRef  Google Scholar 

  2. S. W. A. Baddar. 2009. Finding Better Sorting Networks. PhD thesis, Kent State University.

    Google Scholar 

  3. J. A. Bowren, J. K. Pugh, and K. O. Stanley. 2016. Fully Autonomous Real-Time Autoencoder Augmented Hebbian Learning through the Collection of Novel Experiences. In Proceedings of ALIFE. 382–389.

    Google Scholar 

  4. A. Brabazon, M. O’Neill. 2006. Biologically Inspired Algorithms for Financial Modelling. Springer.

    Google Scholar 

  5. R. Bradley, A. Brabazon, M. O’Neill. 2010. Objective function design in a grammatical evolutionary trading system. In: 2010 IEEE World Congress on Computational Intelligence, pp. 3487–3494. IEEE Press.

    Google Scholar 

  6. M. Črepinšek, S. Liu, M. Mernik. 2013. Exploration and Exploitation in Evolutionary Algorithms: A Survey. ACM Computing Surveys 45, Article 35.

    Google Scholar 

  7. M. Codish, L. Cruz-Filipe, and P. Schneider-Kamp. 2014. The quest for optimal sorting-networks: Efficient generation of two-layer prefixes. In Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on (pp. 359–366). IEEE.

    Google Scholar 

  8. M. Codish, L. Cruz-Filipe, T. Ehlers, M. Muller, and P. Schneider-Kamp. 2016. Sorting networks: To the end and back again. Journal of Computer and System Sciences.

    Google Scholar 

  9. C. A. C. Coello, G. B. Lamont, and D. A. Van Veldhuizen. 2007. Evolutionary algorithms for solving multi-objective problems. Vol. 5. Springer.

    Google Scholar 

  10. I. Contreras, J.I. Hidalgo, L. Nunez-Letamendia, J.M. Velasco. 2017. A meta-grammatical evolutionary process for portfolio selection and trading. Genetic Programming and Evolvable Machines 18(4), 411–431.

    CrossRef  Google Scholar 

  11. G. Cuccu and F Gomez. 2011. When Novelty is Not Enough. In Evostar. 234–243.

    Google Scholar 

  12. W. Cui, A. Brabazon, M. O’Neill. 2011. Adaptive trade execution using a grammatical evolution approach. International Journal of Financial Markets and Derivatives 2(1/2), 4–3.

    CrossRef  Google Scholar 

  13. A. Cully, J. Clune, D. Tarapore, and J-B. Mouret. 2015. Robots that can adapt like animals. Nature 521, 7553 (2015), 503–507.

    Google Scholar 

  14. K. Deb, A. Pratap, S. Agarwal, and T. A. Meyarivan. 2002. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6, 2 (2002), 182–197.

    Google Scholar 

  15. K. Deb, and H. Jain. 2014. An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints. In IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, 577–601.

    CrossRef  Google Scholar 

  16. K. Deb, K. Sindhya, and J. Hakanen. 2016. Multi-objective optimization. In Decision Sciences: Theory and Practice. 145–184.

    Google Scholar 

  17. J. Gomes, P. Mariano, and A. L. Christensen. 2015. Devising effective novelty search algorithms: A comprehensive empirical study. In Proc. of GECCO. 943–950.

    Google Scholar 

  18. F. Gomez, and R. Miikkulainen. 1997. Incremental evolution of complex general behavior. Adaptive Behavior 5(3–4), pp.317–342.

    CrossRef  Google Scholar 

  19. J. Gomes, P. Urbano, and A. L. Christensen. 2013. Evolution of swarm robotics systems with novelty search. Swarm Intelligence, 7:115–144.

    CrossRef  Google Scholar 

  20. F. J. Gomez. 2009. Sustaining diversity using behavioral information distance. In Proc. of GECCO. 113–120.

    Google Scholar 

  21. I. Gonçalves, S. Silva. 2013. Balancing Learning and Overfitting in Genetic Programming with Interleaved Sampling of Training Data. In: Krawiec K., Moraglio A., Hu T., Etaner-Uyar A., Hu B. (eds) Genetic Programming. EuroGP 2013. Lecture Notes in Computer Science, vol 7831. Springer, Berlin, Heidelberg.

    Google Scholar 

  22. B. Hodjat, H. Shahrzad, and R. Miikkulainen. 2016. Distributed Age-Layered Novelty Search. In Proc. of ALIFE. 131–138.

    Google Scholar 

  23. H. Jain, and K. Deb. 2014. An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach. In IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, 602–622.

    CrossRef  Google Scholar 

  24. P. Kipfer, M. Segal, and R. Westermann. 2004. Uberflow: A gpu-based particle engine. In HWWS 2004: Proc. of the ACM SIGGRAPH/EUROGRAPHICS, 115–122.

    Google Scholar 

  25. D. E. Knuth. 1998. Art of Computer Programming: Sorting and Searching, volume 3. Addison-Wesley Professional, 2 edition.

    Google Scholar 

  26. P. Krcah, and D. Toropila. 2010. Combination of novelty search and fitness-based search applied to robot body-brain coevolution. In Proc. of 13th Czech-Japan Seminar on Data Analysis and Decision Making in Service Science.

    Google Scholar 

  27. J. Lehman, S. Risi, and J. Clune. 2016. Creative Generation of 3D Objects with Deep Learning and Innovation Engines. In Proc. of ICCC. 180–187.

    Google Scholar 

  28. J. Lehman, and R. Miikkulainen. 2014. Overcoming deception in evolution of cognitive behaviors. In Proc. of GECCO.

    Google Scholar 

  29. J. Lehman and K. O. Stanley. 2012. Beyond open-endedness: Quantifying impressiveness. In Proc. of ALIFE. 75–82.

    Google Scholar 

  30. J. Lehman and K. O. Stanley. 2011. Evolving a diversity of virtual creatures through novelty search and local competition. In Proc. of GECCO. 211–218.

    Google Scholar 

  31. J. Lehman and K. O. Stanley. 2011. Abandoning objectives: Evolution through the search for novelty alone. Evolutionary Computation 19, 2 (2011), 189–223.

    Google Scholar 

  32. J. Lehman and K. O. Stanley. 2010. Efficiently evolving programs through the search for novelty. In Proc. of GECCO. 836–844.

    Google Scholar 

  33. J. Lehman and K. O. Stanley. 2008. Exploiting Open-Endedness to Solve Problems Through the Search for Novelty. In Proc. of ALIFE. 329–336.

    Google Scholar 

  34. E. Meyerson, and R. Miikkulainen. 2017. Discovering evolutionary stepping stones through behavior domination. In Proc. of GECCO, 139–146. ACM.

    Google Scholar 

  35. E. Meyerson, J. Lehman, and R. Miikkulainen. 2016. Learning behavior characterizations for novelty search. In Proc. of GECCO. 149–156.

    Google Scholar 

  36. J-B. Mouret and J. Clune. 2015. Illuminating search spaces by mapping elites. CoRR abs/1504.04909 (2015).

    Google Scholar 

  37. J-B. Mouret and S. Doncieux. 2012. Encouraging behavioral diversity in evolutionary robotics: An empirical study. Evolutionary Computation 20, 1 (2012), 91–133.

    Google Scholar 

  38. J. K. Pugh, L. B. Soros, P. A. Szerlip, and K. O. Stanley. 2015. Confronting the Challenge of Quality Diversity. In Proc. of GECCO. 967–974.

    Google Scholar 

  39. H. Shahrzad, D. Fink, and R. Miikkulainen. 2018. Enhanced Optimization with Composite Objectives and Novelty Selection. In Proc. of ALIFE. 616–622.

    Google Scholar 

  40. V. K. Valsalam, and R. Miikkulainen. 2013. Using symmetry and evolutionary search to minimize sorting networks. Journal of Machine Learning Research 14(Feb):303–331.

    MathSciNet  MATH  Google Scholar 

  41. H. White. 2000. A reality check for data snooping. Econometrica Sep. 2000; 68(5):1097–126.

    Google Scholar 

  42. D. Whitley, K. Mathias, P. Fitzhorn. 1991. Delta coding: An iterative search strategy for genetic algorithms. In ICGA (Vol. 91, pp. 77–84).

    Google Scholar 

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Correspondence to Hormoz Shahrzad .

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Appendix

Appendix

The graph of the new world record for 20-line sorting network, which moved the previous record of 92 comparators also discovered by evolution [40] down to 91.

One of the nice properties of Novelty Pulsation Method is the ability to converge with a very small pool size (like only 30 individuals in case of sorting networks). However, it still took almost 2 months to break the world record on the 20-line network running on a single machine (Fig. 14.11). Interestingly, even if it takes the same number of generations for the other methods to get there with a normal pool size of a thousand, those runs will take almost 5 years to converge!

Fig. 14.11
figure 11

The new 20-line sorting network with 91 comparators, discovered by novelty pulsation

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Shahrzad, H. et al. (2020). Enhanced Optimization with Composite Objectives and Novelty Pulsation. In: Banzhaf, W., Goodman, E., Sheneman, L., Trujillo, L., Worzel, B. (eds) Genetic Programming Theory and Practice XVII. Genetic and Evolutionary Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-39958-0_14

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  • DOI: https://doi.org/10.1007/978-3-030-39958-0_14

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