1,629 research outputs found

    Enhancing partition crossover with articulation points analysis

    Get PDF
    Partition Crossover is a recombination operator for pseudo-Boolean optimization with the ability to explore an exponential number of solutions in linear or square time. It decomposes the objective function as a sum of subfunctions, each one depending on a different set of variables. The decomposition makes it possible to select the best parent for each subfunction independently, and the operator provides the best out of 2q2^q solutions, where qq is the number of subfunctions in the decomposition. These subfunctions are defined over the connected components of the recombination graph: a subgraph of the objective function variable interaction graph containing only the differing variables in the two parents. In this paper, we advance further and propose a new way to increase the number of linearly independent subfunctions by analyzing the articulation points of the recombination graph. These points correspond to variables that, once flipped, increase the number of connected components. The presence of a connected component with an articulation point increases the number of explored solutions by a factor of, at least, 4. We evaluate the new operator using Iterated Local Search combined with Partition Crossover to solve NK Landscapes and MAX-SAT.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Funding was provided by the Fulbright program, the Spanish Ministry of Education, Culture and Sport (CAS12/00274), the Spanish Ministry of Economy and Competitiveness and FEDER (TIN2014-57341-R and TIN2017-88213-R), the Air Force Office of Scientific Research, (FA9550-11-1-0088), the Leverhulme Trust (RPG-2015-395), the FAPESP (2015/06462-1) and CNPq (304400/2014-9)

    Reducing the Arity in Unbiased Black-Box Complexity

    Full text link
    We show that for all 1<klogn1<k \leq \log n the kk-ary unbiased black-box complexity of the nn-dimensional \onemax function class is O(n/k)O(n/k). This indicates that the power of higher arity operators is much stronger than what the previous O(n/logk)O(n/\log k) bound by Doerr et al. (Faster black-box algorithms through higher arity operators, Proc. of FOGA 2011, pp. 163--172, ACM, 2011) suggests. The key to this result is an encoding strategy, which might be of independent interest. We show that, using kk-ary unbiased variation operators only, we may simulate an unrestricted memory of size O(2k)O(2^k) bits.Comment: An extended abstract of this paper has been accepted for inclusion in the proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2012

    Black-Box Complexity of the Binary Value Function

    Full text link
    The binary value function, or BinVal, has appeared in several studies in theory of evolutionary computation as one of the extreme examples of linear pseudo-Boolean functions. Its unbiased black-box complexity was previously shown to be at most log2n+2\lceil \log_2 n \rceil + 2, where nn is the problem size. We augment it with an upper bound of log2n+2.42141558o(1)\log_2 n + 2.42141558 - o(1), which is more precise for many values of nn. We also present a lower bound of log2n+1.1186406o(1)\log_2 n + 1.1186406 - o(1). Additionally, we prove that BinVal is an easiest function among all unimodal pseudo-Boolean functions at least for unbiased algorithms.Comment: 24 pages, one figure. An extended two-page abstract of this work will appear in proceedings of the Genetic and Evolutionary Computation Conference, GECCO'1

    10361 Abstracts Collection and Executive Summary -- Theory of Evolutionary Algorithms

    Get PDF
    From September 5 to 10, the Dagstuhl Seminar 10361 ``Theory of Evolutionary Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general

    Unbiased Black-Box Complexities of Jump Functions

    Full text link
    We analyze the unbiased black-box complexity of jump functions with small, medium, and large sizes of the fitness plateau surrounding the optimal solution. Among other results, we show that when the jump size is (1/2ε)n(1/2 - \varepsilon)n, that is, only a small constant fraction of the fitness values is visible, then the unbiased black-box complexities for arities 33 and higher are of the same order as those for the simple \textsc{OneMax} function. Even for the extreme jump function, in which all but the two fitness values n/2n/2 and nn are blanked out, polynomial-time mutation-based (i.e., unary unbiased) black-box optimization algorithms exist. This is quite surprising given that for the extreme jump function almost the whole search space (all but a Θ(n1/2)\Theta(n^{-1/2}) fraction) is a plateau of constant fitness. To prove these results, we introduce new tools for the analysis of unbiased black-box complexities, for example, selecting the new parent individual not by comparing the fitnesses of the competing search points, but also by taking into account the (empirical) expected fitnesses of their offspring.Comment: This paper is based on results presented in the conference versions [GECCO 2011] and [GECCO 2014
    corecore