Abstract
This paper explores a novel approach aimed at overcoming existing challenges in the realm of local search algorithms. The main objective is to better manage information within these algorithms, while retaining simplicity and generality in their core components. Our goal is to equip a neural network with the same information as the basic local search and, after a training phase, use the neural network as the fundamental move component within a straightforward local search process. To assess the efficiency of this approach, we develop an experimental setup centered around NK landscape problems, offering the flexibility to adjust problem size and ruggedness. This approach offers a promising avenue for the emergence of new local search algorithms and the improvement of their problem-solving capabilities for black-box problems.
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Notes
- 1.
The program source code, benchmark instances and result files are available at the url https://github.com/Salim-AMRI/NK_Landscape_Project.git.
- 2.
For this evaluation test, we only perform one restart per instance, to avoid any dependency between the different executions that might take place on the same instance. It allows to obtain a distribution of 100 independently and identically distributed scores for each strategy and for each NK configuration.
- 3.
The normality condition required for this test was first confirmed using a Shapiro statistical test on the empirical distributions of 100 iid scores obtained by each strategy.
References
Basseur, M., Goëffon, A.: Hill-climbing strategies on various landscapes: an empirical comparison. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, pp. 479–486 (2013)
Basseur, M., Goëffon, A.: Climbing combinatorial fitness landscapes. Appl. Soft Comput. 30, 688–704 (2015)
Beyer, H.G.: The Theory of Evolution Strategies. Springer, Berlin, Heidelberg (2001). https://doi.org/10.1007/978-3-662-04378-3
Cappart, Q., Chételat, D., Khalil, E.B., Lodi, A., Morris, C., Velickovic, P.: Combinatorial optimization and reasoning with graph neural networks. J. Mach. Learn. Res. 24, 130:1–130:61 (2023)
Falkner, J.K., Thyssens, D., Bdeir, A., Schmidt-Thieme, L.: Learning to control local search for combinatorial optimization. In: Amini, MR., Canu, S., Fischer, A., Guns, T., Kralj Novak, P., Tsoumakas, G. (eds.) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2022. LNCS, vol. 13717, pp. 361–376. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-26419-1_22
Glover, F.: Tabu search-part i. ORSA J. Comput. 1(3), 190–206 (1989)
Hansen, N., Akimoto, Y., Baudis, P.: CMA-ES/pycma on Github. Zenodo (2019). https://doi.org/10.5281/zenodo.2559634
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)
Hoos, H.H.: Programming by optimization. Commun. ACM 55(2), 70–80 (2012)
Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Elsevier, Amsterdam (2004)
Hopfield, J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. U.S.A. 79, 2554–8 (1982)
Hudson, B., Li, Q., Malencia, M., Prorok, A.: Graph neural network guided local search for the traveling salesperson problem. In: The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, 25–29 April 2022. OpenReview.net (2022)
Jones, T., Forrest, S., et al.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: ICGA, vol. 95, pp. 184–192 (1995)
Kauffman, S.A., Weinberger, E.D.: The NK model of rugged fitness landscapes and its application to maturation of the immune response. J. Theor. Biol. 141(2), 211–245 (1989)
Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics. International Series in Operations Research and Management Science, LNCS, vol. 57, pp. 320–353. Springer, Boston, MA (2003). https://doi.org/10.1007/0-306-48056-5_11
Malan, K.M.: A survey of advances in landscape analysis for optimisation. Algorithms 14(2), 40 (2021)
Mamaghan, M.K., Mohammadi, M., Meyer, P., Karimi-Mamaghan, A.M., Talbi, E.: Machine learning at the service of meta-heuristics for solving combinatorial optimization problems: a state-of-the-art. Eur. J. Oper. Res. 296(2), 393–422 (2022)
Müller, N., Glasmachers, T.: Challenges in high-dimensional reinforcement learning with evolution strategies. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11102, pp. 411–423. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99259-4_33
Ochoa, G., Verel, S., Tomassini, M.: First-improvement vs. best-improvement local optima networks of NK landscapes. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 104–113. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15844-5_11
Özcan, E., Bilgin, B., Korkmaz, E.E.: A comprehensive analysis of hyper-heuristics. Intell. Data Anal. 12(1), 3–23 (2008)
Santana, Í., Lodi, A., Vidal, T.: Neural networks for local search and crossover in vehicle routing: a possible overkill? In: Cire, A.A. (eds.) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. LNCS, vol. 13884, pp. 184–199. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-33271-5_13
Schiavinotto, T., Stützle, T.: A review of metrics on permutations for search landscape analysis. Comput. Oper. Res. 34(10), 3143–3153 (2007)
Sörensen, K., Glover, F.: Metaheuristics. Encycl. Oper. Res. Manag. Sci. 62, 960–970 (2013)
Talbi, E.: Machine learning into metaheuristics: a survey and taxonomy. ACM Comput. Surv. 54(6), 129:1–129:32 (2022)
Tari, S., Basseur, M., Goëffon, A.: On the use of (1, \(\lambda \))-evolution strategy as efficient local search mechanism for discrete optimization: a behavioral analysis. Nat. Comput. 20, 345–361 (2021)
Trafalis, T.B., Kasap, S.: Neural networks for combinatorial optimization. In: Floudas, C., Pardalos, P. (eds.) Encyclopedia of Optimization, Second Edition, pp. 2547–2555. Springer, Boston, MA (2008). https://doi.org/10.1007/978-0-387-74759-0_439
Veerapen, N., Hamadi, Y., Saubion, F.: Using local search with adaptive operator selection to solve the progressive party problem. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2013, Cancun, Mexico, 20–23 June 2013, pp. 554–561. IEEE (2013)
Vuculescu, O., Pedersen, M.K., Sherson, J.F., Bergenholtz, C.: Human search in a fitness landscape: how to assess the difficulty of a search problem. Complexity 2020 (2020)
Whitley, D.: MK landscapes, NK landscapes, MAX-kSAT: a proof that the only challenging problems are deceptive. In: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, pp. 927–934 (2015)
Willmes, L., Bäck, T., Jin, Y., Sendhoff, B.: Comparing neural networks and kriging for fitness approximation in evolutionary optimization. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2003, Canberra, Australia, 8–12 December 2003, pp. 663–670. IEEE (2003)
Zaheer, M., Kottur, S., Ravanbakhsh, S., Poczos, B., Salakhutdinov, R.R., Smola, A.J.: Deep sets. Adv. Neural Inf. Process. Syst. 30 (2017)
Acknowledgment
This work was granted access to the HPC resources of IDRIS (Grant No. AD010611887R1) from GENCI. The authors would like to thank the Pays de la Loire region for its financiel support for the Deep Meta project (Etoiles Montantes en Pays de la Loire). The authors also acknowledge ANR - FRANCE (French National Research Agency) for its financial support of the COMBO project (PRC - AAPG 2023 - Axe E.2 - CE23). We are grateful to the reviewers for their comments.
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Goudet, O., Amri Sakhri, M.S., Goëffon, A., Saubion, F. (2024). Emergence of New Local Search Algorithms with Neuro-Evolution. In: Stützle, T., Wagner, M. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2024. Lecture Notes in Computer Science, vol 14632. Springer, Cham. https://doi.org/10.1007/978-3-031-57712-3_3
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