Black-Box Complexity of the Binary Value Function

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 $\lceil \log_2 n \rceil + 2$, where $n$ is the problem size. We augment it with an upper bound of $\log_2 n + 2.42141558 - o(1)$, which is more precise for many values of $n$. We also present a lower bound of $\log_2 n + 1.1186406 - o(1)$. 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

Better Fixed-Arity Unbiased Black-Box Algorithms

In their GECCO'12 paper, Doerr and Doerr proved that the $k$-ary unbiased black-box complexity of OneMax on $n$ bits is $O(n/k)$ for $2\le k\le O(\log n)$. We propose an alternative strategy for achieving this unbiased black-box complexity when $3\le k\le\log_2 n$. While it is based on the same idea of block-wise optimization, it uses $k$-ary unbiased operators in a different way. For each block of size $2^{k-1}-1$ we set up, in $O(k)$ queries, a virtual coordinate system, which enables us to use an arbitrary unrestricted algorithm to optimize this block. This is possible because this coordinate system introduces a bijection between unrestricted queries and a subset of $k$-ary unbiased operators. We note that this technique does not depend on OneMax being solved and can be used in more general contexts. This together constitutes an algorithm which is conceptually simpler than the one by Doerr and Doerr, and at the same time achieves better constant factors in the asymptotic notation. Our algorithm works in $(2+o(1))\cdot n/(k-1)$, where $o(1)$ relates to $k$. Our experimental evaluation of this algorithm shows its efficiency already for $3\le k\le6$.Comment: An extended abstract will appear at GECCO'1

Better Fixed-Arity Unbiased Black-Box Algorithms

In their GECCO'12 paper, Doerr and Doerr proved that the $k$-ary unbiased black-box complexity of OneMax on $n$ bits is $O(n/k)$ for $2\le k\le O(\log n)$. We propose an alternative strategy for achieving this unbiased black-box complexity when $3\le k\le\log_2 n$. While it is based on the same idea of block-wise optimization, it uses $k$-ary unbiased operators in a different way. For each block of size $2^{k-1}-1$ we set up, in $O(k)$ queries, a virtual coordinate system, which enables us to use an arbitrary unrestricted algorithm to optimize this block. This is possible because this coordinate system introduces a bijection between unrestricted queries and a subset of $k$-ary unbiased operators. We note that this technique does not depend on OneMax being solved and can be used in more general contexts. This together constitutes an algorithm which is conceptually simpler than the one by Doerr and Doerr, and at the same time achieves better constant factors in the asymptotic notation. Our algorithm works in $(2+o(1))\cdot n/(k-1)$, where $o(1)$ relates to $k$. Our experimental evaluation of this algorithm shows its efficiency already for $3\le k\le6$.Comment: An extended abstract will appear at GECCO'1

Modeling of craton stability using a viscoelastic rheology

Archean cratons belong to the most remarkable features of our planet since they represent continental crust that has avoided reworking for several billions of years. Even more, it has become evident from both geophysical and petrological studies that cratons exhibit deep lithospheric keels which equally remained stable ever since the formation of the cratons in the Archean. Dating of inclusions in diamonds from kimberlite pipes gives Archean ages, suggesting that the Archean lithosphere must have been cold soon after its formation in the Archean (in order to allow for the existence of diamonds) and must have stayed in that state ever since. Yet, although strong evidence for the thermal stability of Archean cratonic lithosphere for billions of years is provided by diamond dating, the long-term thermal stability of cratonic keels was questioned on the basis of numerical modeling results. We devised a viscoelastic mantle convection model for exploring cratonic stability in the stagnant lid regime. Our modeling results indicate that within the limitations of the stagnant lid approach, the application of a sufficiently high temperature-dependent viscosity ratio can provide for thermal craton stability for billions of years. The comparison between simulations with viscous and viscoelastic rheology indicates no significant influence of elasticity on craton stability. Yet, a viscoelastic rheology provides a physical transition from viscously to elastically dominated regimes within the keel, thus rendering introduction of arbitrary viscosity cutoffs, as employed in viscous models, unnecessary

Chronicle of the XII Colloquium of Romanists of Central and Eastern Europe and Asia, Irkutsk, 2009

В статье описан ход работы XII Коллоквиума романистов Центрально-Восточной Европы и Азии, состоявшегося в Юридическом институте Иркутского государственного университета 14-17 октября 2009 г. This article describes the progress of work of the XII Colloquium of Romanists of Central and Eastern Europe and Asia, held at the Law Institute of Irkutsk State University, 14-17 October 2009

Fast Re-Optimization of LeadingOnes with Frequent Changes

International audienceIn real-world optimization scenarios, the problem instance that we are asked to solve may change during the optimization process, e.g., when new information becomes available or when the environmental conditions change. In such situations, one could hope to achieve reasonable performance by continuing the search from the best solution found for the original problem. Likewise, one may hope that when solving several problem instances that are similar to each other, it can be beneficial to "warm-start" the optimization process of the second instance by the best solution found for the first. However, it was shown in [Doerr et al., GECCO 2019] that even when initialized with structurally good solutions, evolutionary algorithms can have a tendency to replace these good solutions by structurally worse ones, resulting in optimization times that have no advantage over the same algorithms started from scratch. Doerr et al. also proposed a diversity mechanism to overcome this problem. Their approach balances greedy search around a best-so-far solution for the current problem with search in the neighborhood around the best-found solution for the previous instance. In this work, we first show that the re-optimization approach suggested by Doerr et al. reaches a limit when the problem instances are prone to more frequent changes. More precisely, we show that they get stuck on the dynamic LeadingOnes problem in which the target string changes periodically. We then propose a modification of their algorithm which interpolates between greedy search around the previous-best and the current-best solution. We empirically evaluate our smoothed re-optimization algorithm on LeadingOnes instances with various frequencies of change and with different perturbation factors and show that it outperforms both a fully restarted (1+1) Evolutionary Algorithm and the re-optimization approach by Doerr et al

Discovery of Novel Highly Potent Hepatitis C Virus NS5A Inhibitor (AV4025)

A series of next in class small-molecule hepatitis C virus (HCV) NS5A inhibitors with picomolar potency containing 2-pyrrolidin-2-yl-5-{4-[4-(2-pyrrolidin-2-yl-1<i>H</i>-imidazol-5-yl)­buta-1,3-diynyl]­phenyl}-1<i>H</i>-imidazole cores was designed based on the SAR studies available for the reported NS5A inhibitors. Compound <b>13a</b> (AV4025), with (<i>S</i>,<i>S</i>,<i>S</i>,<i>S</i>)-stereochemistry (EC₅₀ = 3.4 ± 0.2 pM, HCV replicon genotype 1b), was dramatically more active than were the compounds with two (<i>S</i>)- and two (<i>R</i>)-chiral centers. Human serum did not significantly reduce the antiviral activity (<4-fold). Relatively favorable pharmacokinetic features and good oral bioavailability were observed during animal studies. Compound <b>13a</b> was well tolerated in rodents (in mice, LD₅₀ = 2326 mg/kg or higher), providing a relatively high therapeutic index. During safety, pharmacology and subchronic toxicity studies in rats and dogs, it was not associated with any significant pathological or clinical findings. This compound is currently being evaluated in phase I/II clinical trials for the treatment of HCV infection