Hyperplane Elimination for Quickly Enumerating Local Optima

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9595)


Examining the properties of local optima is a common method for understanding combinatorial-problem landscapes. Unfortunately, exhaustive algorithms for finding local optima are limited to very small problem sizes. We propose a method for exploiting problem structure to skip hyperplanes that cannot contain local optima, allowing runtime to scale with the number of local optima instead of with the landscape size. We prove optimality for linear functions and Concatenated Traps, and we provide empirical evidence of optimality on NKq Landscapes and Ising Spin Glasses. We further refine this method to find solutions that cannot be improved by flipping r or fewer bits, which counterintuitively can reduce total runtime. While previous methods were limited to landscapes with at most \(2^{34}\) binary strings, hyperplane elimination can enumerate the same problems with \(2^{77}\) binary strings, and find all 4-bit local optima of problems with \(2^{200}\) binary strings.


Landscape understanding Gray-Box Mk Landscapes 



This material is based in part upon work supported by the National Science Foundation under Cooperative Agreement No. DBI-0939454. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.BEACON Center for the Study of Evolution in ActionMichigan State UniversityEast LansingUSA

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