Upper and Lower Bounds on Unrestricted Black-Box Complexity of Jump\(_{n,\ell }\)

  • Maxim Buzdalov
  • Mikhail Kever
  • Benjamin Doerr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9026)


We analyse the unrestricted black-box complexity of \(\textsc {Jump}_{n,\ell }\) functions. For upper bounds, we present three algorithms for small, medium and extreme values of \(\ell \). We present a matrix lower bound theorem which is capable of giving better lower bounds than a general information theory approach if one is able to assign different types to queries and define relationships between them. Using this theorem, we prove lower bounds for Jump separately for odd and even values of \(n\). For several cases, notably for extreme Jump, the first terms of lower and upper bounds coincide.


Lower Bound Search Heuristic Fitness Evaluation Underlying Idea Popular Class 
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  1. 1.
    Doerr, B., Doerr, C., Ebel, F.: Lessons from the black-box: fast crossover-based genetic algorithms. In: Proceedings of Genetic and Evolutionary Computation Conference, pp. 781–788 (2014)Google Scholar
  2. 2.
    Doerr, B., Doerr, C., Kötzing, T.: Unbiased black-box complexities of jump functions.
  3. 3.
    Doerr, B., Johannsen, D., Kötzing, T., Lehre, P.K., Wagner, M., Winzen, C.: Faster black-box algorithms through higher arity operators. In: Proceedings of Foundations of Genetic Algorithms, pp. 163–172 (2011)Google Scholar
  4. 4.
    Droste, S., Jansen, T., Wegener, I.: Upper and lower bounds for randomized search heuristics in black-box optimization. Theory Comput. Syst. 39(4), 525–544 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58(301), 13–30 (1963)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Yao, A.C.C.: Probabilistic computations: toward a unified measure of complexity. In: 18th Annual Symposium on Foundations of Computer Science, pp. 222–227 (1977)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.ITMO UniversitySaint-PetersburgRussia
  2. 2.LIXÉcole PolytechniquePalaiseau CedexFrance

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