Analysis of the (μ/μI,λ)(\mu/\mu_I,\lambda)-CSA-ES with Repair by Projection Applied to a Conically Constrained Problem

Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a theoretical analysis of a multi-recombinative evolution strategy with cumulative step size adaptation applied to a conically constrained linear optimization problem. The state of the strategy is modeled by random variables and a stochastic iterative mapping is introduced. For the analytical treatment, fluctuations are neglected and the mean value iterative system is considered. Non-linear difference equations are derived based on one-generation progress rates. Based on that, expressions for the steady state of the mean value iterative system are derived. By comparison with real algorithm runs, it is shown that for the considered assumptions, the theoretical derivations are able to predict the dynamics and the steady state values of the real runs.Comment: This is a PREPRINT of an article that has been accepted for publication in the journal MIT Press Evolutionary Computation (ECJ). 25 pages + supplementary material. The work was supported by the Austrian Science Fund FWF under grant P29651-N3

On the performance of (1,l)-Evolution Strategies at the ridge function class

This paper presents the N-dependent analysis of the (1, l) Evolution Strategy (ES) with isotropic mutations at the ridge functions including the special cases sharp and parabolic ridge. The new approach presented allows for the prediction of the dynamics in ridge direction as well as in radial direction. The central quantities are the corresponding progress rates which are determined in terms of analytical expressions. Its predictive quality is evaluated by ES simulations and the steady state behavior is discussed in detail

Quantifying excitations of quasinormal mode systems

Computations of the strong field generation of gravitational waves by black hole processes produce waveforms that are dominated by quasinormal (QN) ringing, a damped oscillation characteristic of the black hole. We describe here the mathematical problem of quantifying the QN content of the waveforms generated. This is done in several steps: (i) We develop the mathematics of QN systems that are complete (in a sense to be defined) and show that there is a quantity, the ``excitation coefficient,'' that appears to have the properties needed to quantify QN content. (ii) We show that incomplete systems can (at least sometimes) be converted to physically equivalent complete systems. Most notably, we give a rigorous proof of completeness for a specific modified model problem. (iii) We evaluate the excitation coefficient for the model problem, and demonstrate that the excitation coefficient is of limited utility. We finish by discussing the general question of quantification of QN excitations, and offer a few speculations about unavoidable differences between normal mode and QN systems.Comment: 27 pages, 14 figures. To be published in: J. Math. Phys. (1999

A multistate model for early decision making in oncology

The development of oncology drugs progresses through multiple phases, where after each phase a decision is made about whether to move a molecule forward. Early phase efficacy decisions are often made on the basis of single arm studies based on RECIST tumor response as endpoint. This decision rules are implicitly assuming some form of surrogacy between tumor response and long-term endpoints like progression-free survival (PFS) or overall survival (OS). The surrogacy is most often assessed as weak, but sufficient to allow a rapid decision making as early phase studies lack the survival follow up and number of patients to properly assess PFS or OS. With the emergence of therapies with new mechanisms of action, for which the link between RECIST tumor response and long-term endpoints is either not accessible yet because not enough data is available to perform a meta-regression, or the link is weaker than with classical chemotherapies, tumor response based rules may not be optimal. In this paper, we explore the use of a multistate model for decision making based on single-arm early phase trials. The multistate model allows to account for more information than the simple RECIST response status, namely, the time to get to response, the duration of response, the PFS time and time to death. We propose to base the decision on efficacy on the OS hazard ratio (HR), predicted from a multistate model based on early phase data with limited survival follow-up, combined with historical control data. Using three case studies and simulations, we illustrate the feasibility of the estimation of the OS HR using a multistate model based on limited data from early phase studies. We argue that, in the presence of limited follow up and small sample size, and on assumptions within the multistate model, the OS prediction is acceptable and may lead to better decisions for continuing the development of a drug

Self-Adaptive Genetic Algorithms with Simulated Binary Crossover

Self-adaptation is an essential feature of natural evolution. However, in the context of function optimization, self-adaptation features of evolutionary search algorithms have been explored only with evolution strategy (ES) and evolutionary programming (EP). In this paper, we demonstrate the self-adaptive feature of real-parameter genetic algorithms (GAs) using simulated binary crossover (SBX) operator and without any mutation operator. The connection between the working of self-adaptive ESs and real-parameter GAs with SBX operator is also discussed. Thereafter, the self-adaptive behavior of real-parameter GAs is demonstrated on a number of test problems commonly-used in the ES literature. The remarkable similarity in the working principle of real-parameter GAs and self-adaptive ESs shown in this study suggests the need of emphasizing further studies on self-adaptive GAs

On the Analysis of Self-Adaptive Evolutionary Algorithms

Due to the exibility in adapting to different fitness landscapes, self-adaptive evolutionary algorithms (SA-EAs) have been gaining popularity in the recent past. In this paper, we postulate the properties that SA-EA operators should have for successful applications. Specifically, population mean and variance of a number of SA-EA operators, such as various real-parameter crossover operators and self-adaptive evolution strategies, are calculated for this purpose. In every case, simulation results are shown to verify the theoretical calculations. The postulations and population variance calculations explain why self-adaptive GAs and ESs have shown similar performance in the past and also suggest appropriate strategy parameter values which must be chosen while applying and comparing different SA-EAs

Benchmarking Evolutionary Algorithms For Single Objective Real-valued Constrained Optimization - A Critical Review

Benchmarking plays an important role in the development of novel search algorithms as well as for the assessment and comparison of contemporary algorithmic ideas. This paper presents common principles that need to be taken into account when considering benchmarking problems for constrained optimization. Current benchmark environments for testing Evolutionary Algorithms are reviewed in the light of these principles. Along with this line, the reader is provided with an overview of the available problem domains in the field of constrained benchmarking. Hence, the review supports algorithms developers with information about the merits and demerits of the available frameworks.Comment: This manuscript is a preprint version of an article published in Swarm and Evolutionary Computation, Elsevier, 2018. Number of pages: 4

Optimum Tracking with Evolution Strategies

Evolutionary algorithms are frequently applied to dynamic optimization problems in which the objective varies with time. It is desirable to gain an improved understanding of the influence of different genetic operators and of the parameters of a strategy on its tracking performance. An approach that has proven useful in the past is to mathematically analyze the strategy's behavior in simple, idealized environments. The present paper investigates the performance of a multiparent evolution strategy that employs cumulative step length adaptation for an optimization task in which the target moves linearly with uniform speed. Scaling laws that quite accurately describe the behavior of the strategy and that greatly contribute to its understanding are derived. It is shown that in contrast to previously obtained results for a randomly moving target, cumulative step length adaptation fails to achieve optimal step lengths if the target moves in a linear fashion. Implications for the choice of population size parameters are discussed