Adaptive primal-dual genetic algorithms in dynamic environments

This article is placed here with permission of IEEE - Copyright @ 2010 IEEERecently, there has been an increasing interest in applying genetic algorithms (GAs) in dynamic environments. Inspired by the complementary and dominance mechanisms in nature, a primal-dual GA (PDGA) has been proposed for dynamic optimization problems (DOPs). In this paper, an important operator in PDGA, i.e., the primal-dual mapping (PDM) scheme, is further investigated to improve the robustness and adaptability of PDGA in dynamic environments. In the improved scheme, two different probability-based PDM operators, where the mapping probability of each allele in the chromosome string is calculated through the statistical information of the distribution of alleles in the corresponding gene locus over the population, are effectively combined according to an adaptive Lamarckian learning mechanism. In addition, an adaptive dominant replacement scheme, which can probabilistically accept inferior chromosomes, is also introduced into the proposed algorithm to enhance the diversity level of the population. Experimental results on a series of dynamic problems generated from several stationary benchmark problems show that the proposed algorithm is a good optimizer for DOPs.This work was supported in part by the National Nature Science Foundation of China (NSFC) under Grant 70431003 and Grant 70671020, by the National Innovation Research Community Science Foundation of China under Grant 60521003, by the National Support Plan of China under Grant 2006BAH02A09, by the Engineering and Physical Sciences Research Council (EPSRC) of U.K. under Grant EP/E060722/1, and by the Hong Kong Polytechnic University Research Grants under Grant G-YH60

Genetic algorithms with implicit memory

This thesis investigates the workings of genetic algorithms in dynamic optimisation problems where fitness landscapes materialise that are identical to, or resemble in some way, landscapes previously encountered. The objective is to appraise the performances of the various approaches offered by the GAs. Approaches specifically tailored for different kinds of dynamic environment lie outside the remit of the thesis. The main topics that are explored are: genetic redundancy, modularity, neutral evolution, explicit memory, and implicit memory. It is in the matter of implicit memory that the thesis makes the majority of its novel contributions. It is demonstrated via experimental analysis that the pre-existing techniques are deficient, and a new algorithm – the pointer genetic algorithm (pGA) – is expounded and assessed in an attempt to offer an improvement. It is shown that though it outperforms its rivals, it cannot attain the performance levels of an explicit memory algorithm (that is, an algorithm using an external memory bank). The main claims of the thesis are that with regard to memory, the pre-existing implicit-memory algorithms are deficient, the new pointer GA is superior, and that because all of the implicit approaches are inferior to explicit approaches, it is explicit approaches that should be used in real-world problem solving

The Effects of Population Size Histories on Estimates of Selection Coefficients from Time-Series Genetic Data.

Many approaches have been developed for inferring selection coefficients from time series data while accounting for genetic drift. These approaches have been motivated by the intuition that properly accounting for the population size history can significantly improve estimates of selective strengths. However, the improvement in inference accuracy that can be attained by modeling drift has not been characterized. Here, by comparing maximum likelihood estimates of selection coefficients that account for the true population size history with estimates that ignore drift by assuming allele frequencies evolve deterministically in a population of infinite size, we address the following questions: how much can modeling the population size history improve estimates of selection coefficients? How much can mis-inferred population sizes hurt inferences of selection coefficients? We conduct our analysis under the discrete Wright-Fisher model by deriving the exact probability of an allele frequency trajectory in a population of time-varying size and we replicate our results under the diffusion model. For both models, we find that ignoring drift leads to estimates of selection coefficients that are nearly as accurate as estimates that account for the true population history, even when population sizes are small and drift is high. This result is of interest because inference methods that ignore drift are widely used in evolutionary studies and can be many orders of magnitude faster than methods that account for population sizes

Fundamental Properties of the Evolution of Mutational Robustness

Evolution on neutral networks of genotypes has been found in models to concentrate on genotypes with high mutational robustness, to a degree determined by the topology of the network. Here analysis is generalized beyond neutral networks to arbitrary selection and parent-offspring transmission. In this larger realm, geometric features determine mutational robustness: the alignment of fitness with the orthogonalized eigenvectors of the mutation matrix weighted by their eigenvalues. "House of cards" mutation is found to preclude the evolution of mutational robustness. Genetic load is shown to increase with increasing mutation in arbitrary single and multiple locus fitness landscapes. The rate of decrease in population fitness can never grow as mutation rates get higher, showing that "error catastrophes" for genotype frequencies never cause precipitous losses of population fitness. The "inclusive inheritance" approach taken here naturally extends these results to a new concept of dispersal robustness.Comment: 17 pages, 1 figur

Modelling the dynamics of genetic algorithms using statistical mechanics

A formalism for modelling the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics, originally due to Prugel-Bennett and Shapiro, is reviewed, generalized and improved upon. This formalism can be used to predict the averaged trajectory of macroscopic statistics describing the GA's population. These macroscopics are chosen to average well between runs, so that fluctuations from mean behaviour can often be neglected. Where necessary, non-trivial terms are determined by assuming maximum entropy with constraints on known macroscopics. Problems of realistic size are described in compact form and finite population effects are included, often proving to be of fundamental importance. The macroscopics used here are cumulants of an appropriate quantity within the population and the mean correlation (Hamming distance) within the population. Including the correlation as an explicit macroscopic provides a significant improvement over the original formulation. The formalism is applied to a number of simple optimization problems in order to determine its predictive power and to gain insight into GA dynamics. Problems which are most amenable to analysis come from the class where alleles within the genotype contribute additively to the phenotype. This class can be treated with some generality, including problems with inhomogeneous contributions from each site, non-linear or noisy fitness measures, simple diploid representations and temporally varying fitness. The results can also be applied to a simple learning problem, generalization in a binary perceptron, and a limit is identified for which the optimal training batch size can be determined for this problem. The theory is compared to averaged results from a real GA in each case, showing excellent agreement if the maximum entropy principle holds. Some situations where this approximation brakes down are identified. In order to fully test the formalism, an attempt is made on the strong sc np-hard problem of storing random patterns in a binary perceptron. Here, the relationship between the genotype and phenotype (training error) is strongly non-linear. Mutation is modelled under the assumption that perceptron configurations are typical of perceptrons with a given training error. Unfortunately, this assumption does not provide a good approximation in general. It is conjectured that perceptron configurations would have to be constrained by other statistics in order to accurately model mutation for this problem. Issues arising from this study are discussed in conclusion and some possible areas of further research are outlined