A new genetic algorithm based on primal-dual chromosomes for royal road functions

Copyright @ 2001 University of LeicesterGenetic algorithms (GAs) have been broadly studied by a huge amount of researchers and there are many variations developed based on Holland’s simple genetic algorithm (SGA). Inspired by the idea of diploid genotype and dominance mechanisms that broadly exists in nature, we propose a primal-dual genetic algorithm (PDGA). PDGA operates on a pair of chromosomes that are primal-dual to each other in the sense of Hamming distance in genotype. We compare the performance of PDGA over SGA based on the Royal Road functions, which are specially designed for testing GA's performance. The experiment results show that PDGA outperforms SGA on the Royal Road functions for different performance measures.This work was supported by the University of Leicester Research Fund 2001 under Grant FP15004, UK

Dominance learning in diploid genetic algorithms for dynamic optimization problems

Copyright @ 2006 YangThis paper proposes an adaptive dominance mechanism for diploidy genetic algorithms in dynamic environments. In this scheme, the genotype to phenotype mapping in each gene locus is controlled by a dominance probability, which is learned adaptively during the searching progress and hence is adapted to the dynamic environment. Using a series of dynamic test problems, the proposed dominance scheme is compared to two other dominance schemes for diploidy genetic algorithms. The experimental results validate the efficiency of the proposed dominance learning scheme

Evolutionary algorithms for dynamic optimization problems: workshop preface

Copyright @ 2005 AC

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

Population-based incremental learning with associative memory for dynamic environments

Copyright © 2007 IEEE. Reprinted from IEEE Transactions on Evolutionary Computation. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In recent years there has been a growing interest in studying evolutionary algorithms (EAs) for dynamic optimization problems (DOPs) due to its importance in real world applications. Several approaches, such as the memory and multiple population schemes, have been developed for EAs to address dynamic problems. This paper investigates the application of the memory scheme for population-based incremental learning (PBIL) algorithms, a class of EAs, for DOPss. A PBIL-specific associative memory scheme, which stores best solutions as well as corresponding environmental information in the memory, is investigated to improve its adaptability in dynamic environments. In this paper, the interactions between the memory scheme and random immigrants, multi-population, and restart schemes for PBILs in dynamic environments are investigated. In order to better test the performance of memory schemes for PBILs and other EAs in dynamic environments, this paper also proposes a dynamic environment generator that can systematically generate dynamic environments of different difficulty with respect to memory schemes. Using this generator a series of dynamic environments are generated and experiments are carried out to compare the performance of investigated algorithms. The experimental results show that the proposed memory scheme is efficient for PBILs in dynamic environments and also indicate that different interactions exist between the memory scheme and random immigrants, multi-population schemes for PBILs in different dynamic environments

Non-stationary problem optimization using the primal-dual genetic algorithm

This article is posted here with permission from IEEE - Copyright @ 2003 IEEEGenetic algorithms (GAs) have been widely used for stationary optimization problems where the fitness landscape does not change during the computation. However, the environments of real world problems may change over time, which puts forward serious challenge to traditional GAs. In this paper, we introduce the application of a new variation of GA called the primal-dual genetic algorithm (PDGA) for problem optimization in nonstationary environments. Inspired by the complementarity and dominance mechanisms in nature, PDGA operates on a pair of chromosomes that are primal-dual to each other in the sense of maximum distance in genotype in a given distance space. This paper investigates an important aspect of PDGA, its adaptability to dynamic environments. A set of dynamic problems are generated from a set of stationary benchmark problems using a dynamic problem generating technique proposed in this paper. Experimental study over these dynamic problems suggests that PDGA can solve complex dynamic problems more efficiently than traditional GA and a peer GA, the dual genetic algorithm. The experimental results show that PDGA has strong viability and robustness in dynamic environments

Evolutionary algorithms in dynamic environments

The file attached to this record is the author's final peer reviewed version.Evolutionary algorithms (EAs) are widely and often used for solving stationary optimization problems where the fitness landscape or objective function does not change during the course of computation. However, the environments of real world optimization problems may fluctuate or change sharply. If the optimization problem is dynamic, the goal is no longer to find the extrema, but to track their progression through the search space as closely as possible. All kinds of approaches that have been proposed to make EAs suitable for the dynamic environments are surveyed, such as increasing diversity, maintaining diversity, memory based approaches, multi-population approaches and so on

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