The performance of (==;)-ESs (Evolution Strategies) in the asymptotic limit for N ! 1 and ! 1 is investigated. The conjecture made by Schwefel that the maximum performance of such strategies scales like ln(==) will be proved. Furthermore, it will be shown that an optimally tuned (==;)-ES performs exactly times faster than an optimally tuned (1+1)-ES, if the hyper-sphere is taken as the tness mo...

Orthogonal term rewriting systems (also known as regular systems) provide an elegant framework for programming in equational logic. O'Donnell showed that the parallel-outermost strategy, which replaces all outermost redexes in each step, is complete for such systems. Many of the reductions performed by this strategy could be wasteful in general. A lazy normalization algorithm that completely el...

Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction sequences converge to a limit. Strong Convergence requires in addition that redex positions in a reduction sequence move...

We lift the theory of optimal reduction to a decomposition of the lambda calculus known as the Linear Substitution Calculus (LSC). LSC decomposes β-reduction into finer steps that manipulate substitutions in two distinctive ways: it uses context rules that allow substitutions to act “at a distance” and rewrites modulo a set of equations that allow substitutions to “float” in a term. We propose ...

one of the most important problems in the system reliability optimization is redundancy allocation problem that has been studied in different system configurations. k-out-of-n structure is a general system configuration and offers enhanced capabilities for analyzing more design problems. hence, in this paper, the redundancy allocation problem of k-out-of-n systems is studied. in the most previo...

Randomized direct-search methods for the optimization of a function f : R → R given by a black box for f -evaluations are investigated. We consider the cumulative step-size adaptation (CSA) for the variance of multivariate zero-mean normal distributions. Those are commonly used to sample new candidate solutions within metaheuristics, in particular within the CMA Evolution Strategy (CMA-ES), a s...

This document presents a proposal to incorporate a fitness inheritance mechanism into an Evolution Strategy used to solve the general nonlinear programming problem. The aim is to find a trade-off between a lower number of evaluations of each solution and a good performance of the approach. A set of test problems taken from the specialized literature was used to test the capabilities of the prop...

Simulated annealing and and single trial versions of evolution strategies possess a close relationship when they are designed for optimization over continuous variables. Analytical investigations of their diierences and similarities lead to a cross-fertilization of both approaches, resulting in new theoretical results, new parallel population based algorithms, and a better understanding of the ...

The performance of the evolutionary algorithms depends strongly upon the combined eeect of the operators (e.g. mutation) and the mappings from genotype to phenotype space and phenotype to t-ness space. We demonstrate, with the example of the canonical Genetic Algorithm (cGA) for parameter optimization, that the right choice of the mutation operator should depend on the genom position and we sho...