3,351 research outputs found
Playing Mastermind With Constant-Size Memory
We analyze the classic board game of Mastermind with holes and a constant
number of colors. A result of Chv\'atal (Combinatorica 3 (1983), 325-329)
states that the codebreaker can find the secret code with
questions. We show that this bound remains valid if the codebreaker may only
store a constant number of guesses and answers. In addition to an intrinsic
interest in this question, our result also disproves a conjecture of Droste,
Jansen, and Wegener (Theory of Computing Systems 39 (2006), 525-544) on the
memory-restricted black-box complexity of the OneMax function class.Comment: 23 page
OneMax in Black-Box Models with Several Restrictions
Black-box complexity studies lower bounds for the efficiency of
general-purpose black-box optimization algorithms such as evolutionary
algorithms and other search heuristics. Different models exist, each one being
designed to analyze a different aspect of typical heuristics such as the memory
size or the variation operators in use. While most of the previous works focus
on one particular such aspect, we consider in this work how the combination of
several algorithmic restrictions influence the black-box complexity. Our
testbed are so-called OneMax functions, a classical set of test functions that
is intimately related to classic coin-weighing problems and to the board game
Mastermind.
We analyze in particular the combined memory-restricted ranking-based
black-box complexity of OneMax for different memory sizes. While its isolated
memory-restricted as well as its ranking-based black-box complexity for bit
strings of length is only of order , the combined model does not
allow for algorithms being faster than linear in , as can be seen by
standard information-theoretic considerations. We show that this linear bound
is indeed asymptotically tight. Similar results are obtained for other memory-
and offspring-sizes. Our results also apply to the (Monte Carlo) complexity of
OneMax in the recently introduced elitist model, in which only the best-so-far
solution can be kept in the memory. Finally, we also provide improved lower
bounds for the complexity of OneMax in the regarded models.
Our result enlivens the quest for natural evolutionary algorithms optimizing
OneMax in iterations.Comment: This is the full version of a paper accepted to GECCO 201
Reducing the Arity in Unbiased Black-Box Complexity
We show that for all the -ary unbiased black-box
complexity of the -dimensional \onemax function class is . This
indicates that the power of higher arity operators is much stronger than what
the previous 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 -ary unbiased variation operators only, we may
simulate an unrestricted memory of size 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
Complexity Theory for Discrete Black-Box Optimization Heuristics
A predominant topic in the theory of evolutionary algorithms and, more
generally, theory of randomized black-box optimization techniques is running
time analysis. Running time analysis aims at understanding the performance of a
given heuristic on a given problem by bounding the number of function
evaluations that are needed by the heuristic to identify a solution of a
desired quality. As in general algorithms theory, this running time perspective
is most useful when it is complemented by a meaningful complexity theory that
studies the limits of algorithmic solutions.
In the context of discrete black-box optimization, several black-box
complexity models have been developed to analyze the best possible performance
that a black-box optimization algorithm can achieve on a given problem. The
models differ in the classes of algorithms to which these lower bounds apply.
This way, black-box complexity contributes to a better understanding of how
certain algorithmic choices (such as the amount of memory used by a heuristic,
its selective pressure, or properties of the strategies that it uses to create
new solution candidates) influences performance.
In this chapter we review the different black-box complexity models that have
been proposed in the literature, survey the bounds that have been obtained for
these models, and discuss how the interplay of running time analysis and
black-box complexity can inspire new algorithmic solutions to well-researched
problems in evolutionary computation. We also discuss in this chapter several
interesting open questions for future work.Comment: This survey article is to appear (in a slightly modified form) in the
book "Theory of Randomized Search Heuristics in Discrete Search Spaces",
which will be published by Springer in 2018. The book is edited by Benjamin
Doerr and Frank Neumann. Missing numbers of pointers to other chapters of
this book will be added as soon as possibl
On the Query Complexity of Black-Peg AB-Mastermind
Mastermind is a two players zero sum game of imperfect information. Starting with ErdËos and RĂ©nyi (1963), its combinatorics have been studied to date by several authors, e.g., Knuth (1977), ChvĂĄtal (1983), Goodrich (2009). The ïŹrst player, called âcodemakerâ, chooses a secret code and the second player, called âcodebreakerâ, tries to break the secret code by making as few guesses as possible, exploiting information that is given by the codemaker after each guess. For variants that allow color repetition, Doerr et al. (2016) showed optimal results. In this paper, we consider the so called Black-Peg variant of Mastermind, where the only information concerning a guess is the number of positions in which the guess coincides with the secret code. More precisely, we deal with a special version of the Black-Peg game with n holes and k â„ n colors where no repetition of colors is allowed. We present upper and lower bounds on the number of guesses necessary to break the secret code. For the case k = n, the secret code can be algorithmically identiïŹed within less than (n â 3)dlog 2 ne + 5 2 n â 1 queries. This result improves the result of Ker-I Ko and Shia-Chung Teng (1985) by almost a factor of 2. For the case k > n, we prove an upper bound of (n â 2)dlog 2 ne + k + 1. Furthermore, we prove a new lower bound of n for the case k = n, which improves the recent n â log log(n) bound of Berger et al. (2016). We then generalize this lower bound to k queries for the case k â„ n
âLike Following a Mirageâ: Memory and Empowerment in Alice Munroâs âThe Bear Came Over the Mountainâ
La nouvelle âThe Bear Came Over the Mountainâ dâAlice Munro est une Ă©tude sur la douleur, la perte, la trahison et, en premier lieu, une rĂ©flexion sur le principe fĂ©minin. La nouvelle a attirĂ© lâattention dâautres Ă©crivains â en particulier celle de Jonathan Franzen qui la classe parmi les plus belles rĂ©ussites de Munro ; ou Sarah Polly qui a rĂ©alisĂ© Away from Her, lâadaptation dâun texte fort ambigu. Le prĂ©sent article souhaite revenir sur cette ambigĂŒitĂ©. Ă premiĂšre vue, la nouvelle dĂ©crit la tragĂ©die dâune femme qui sombre peu Ă peu dans la maladie dâAlzheimer : Fiona doit apprendre Ă vivre avec ses dĂ©faillances mĂ©morielles et accepter de quitter son foyer. Munro ne se satisfait jamais de prĂ©senter le point de vue limitĂ© dâun personnage. Elle laisse entrevoir, par le biais de subtiles suggestions, que le choix de Fiona de sâĂ©carter du monde social relĂšve dâun dĂ©sir de se venger de mari volage. En dâautres termes, cet article suggĂšre que Fiona joue la malade pour reprendre sa vie en main et ainsi Ă©chapper Ă lâamour hypocrite de son Ă©poux. De cette maniĂšre, la nouvelle devient lâune des illustrations rĂ©centes les plus fortes de lâambition de Munro de dĂ©crire les femmes dans leur vie de tous les jours et dâexplorer les moyens mis en Ćuvre pour en amĂ©liorer les conditions
Affective states during problem solving : The role of feedback, individual performance, and motivation.
Individuals who perform a task to achieve a goal undergo different affective states, depending on whether they advance towards their goal or not. Those individuals who are able to perform well are confronted with significantly more goal-advancing situations and more positive affective contexts accordingly than individuals who perform poorly. The main contribution of this thesis is a novel experimental task, namely Luckless Mastermind, that allows computer-aided empirical investigation of affective states during problem solving by providing the same goal-advancing situation to any individual, regardless of actual performance. The robustness of resulting game courses is proven via an extensive-search algorithm. The task paradigm enables analysis of different affective states in terms of peripheral physiological response. Skin conductance response is utilized as physiological signal. Based on Luckless Mastermind, an experimental setup has been developed and implemented to investigate three different hypotheses on affective states during problem solving targeted on objective valence, individual evaluation, and ambition
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