An Evolutionary Algorithm for the Estimation of Threshold Vector Error Correction Models

We develop an evolutionary algorithm to estimate Threshold Vector Error Correction models (TVECM) with more than two cointegrated variables. Since disregarding a threshold in cointegration models renders standard approaches to the estimation of the cointegration vectors inefficient, TVECM necessitate a simultaneous estimation of the cointegration vector(s) and the threshold. As far as two cointegrated variables are considered this is commonly achieved by a grid search. However, grid search quickly becomes computationally unfeasible if more than two variables are cointegrated. Therefore, the likelihood function has to be maximized using heuristic approaches. Depending on the precise problem structure the evolutionary approach developed in the present paper for this purpose saves 90 to 99 per cent of the computation time of a grid search.evolutionary strategy, genetic algorithm, TVECM

First Steps Towards a Runtime Comparison of Natural and Artificial Evolution

Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse their runtime on many illustrative problems. Here we apply this theory to a simple model of natural evolution. In the Strong Selection Weak Mutation (SSWM) evolutionary regime the time between occurrence of new mutations is much longer than the time it takes for a new beneficial mutation to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a (1+1)-type process where the probability of accepting a new genotype (improvements or worsenings) depends on the change in fitness. We present an initial runtime analysis of SSWM, quantifying its performance for various parameters and investigating differences to the (1+1)EA. We show that SSWM can have a moderate advantage over the (1+1)EA at crossing fitness valleys and study an example where SSWM outperforms the (1+1)EA by taking advantage of information on the fitness gradient

On the limitations of the univariate marginal distribution algorithm to deception and where bivariate EDAs might help

We introduce a new benchmark problem called Deceptive Leading Blocks (DLB) to rigorously study the runtime of the Univariate Marginal Distribution Algorithm (UMDA) in the presence of epistasis and deception. We show that simple Evolutionary Algorithms (EAs) outperform the UMDA unless the selective pressure $\mu/\lambda$ is extremely high, where $\mu$ and $\lambda$ are the parent and offspring population sizes, respectively. More precisely, we show that the UMDA with a parent population size of $\mu=\Omega(\log n)$ has an expected runtime of $e^{\Omega(\mu)}$ on the DLB problem assuming any selective pressure $\frac{\mu}{\lambda} \geq \frac{14}{1000}$, as opposed to the expected runtime of $\mathcal{O}(n\lambda\log \lambda+n^3)$ for the non-elitist $(\mu,\lambda)~\text{EA}$ with $\mu/\lambda\leq 1/e$. These results illustrate inherent limitations of univariate EDAs against deception and epistasis, which are common characteristics of real-world problems. In contrast, empirical evidence reveals the efficiency of the bi-variate MIMIC algorithm on the DLB problem. Our results suggest that one should consider EDAs with more complex probabilistic models when optimising problems with some degree of epistasis and deception.Comment: To appear in the 15th ACM/SIGEVO Workshop on Foundations of Genetic Algorithms (FOGA XV), Potsdam, German