Scalability Problems of Simple Genetic Algorithms

1999 ◽  
Vol 7 (4) ◽  
pp. 331-352 ◽  
Author(s):  
Dirk Thierens
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Evolutionary Computation ◽  
Building Block ◽  
Building Blocks ◽  
Research Topic ◽  
Problem Size ◽  
Clear Insight ◽  
Simple Genetic Algorithms ◽  
Algorithmic Design

Scalable evolutionary computation has. become an intensively studied research topic in recent years. The issue of scalability is predominant in any field of algorithmic design, but it became particularly relevant for the design of competent genetic algorithms once the scalability problems of simple genetic algorithms were understood. Here we present some of the work that has aided in getting a clear insight in the scalability problems of simple genetic algorithms. Particularly, we discuss the important issue of building block mixing. We show how the need for mixing places a boundary in the GA parameter space that, together with the boundary from the schema theorem, delimits the region where the GA converges reliably to the optimum in problems of bounded difficulty. This region shrinks rapidly with increasing problem size unless the building blocks are tightly linked in the problem coding structure. In addition, we look at how straightforward extensions of the simple genetic algorithm—namely elitism, niching, and restricted mating are not significantly improving the scalability problems.

A Comparison of the Fixed and Floating Building Block Representation in the Genetic Algorithm

1996 ◽  
Vol 4 (2) ◽  
pp. 169-193 ◽  
Author(s):  
Annie S. Wu ◽  
Robert K. Lindsay
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Building Block ◽  
Deoxyribonucleic Acid ◽  
Evolutionary Process ◽  
Building Blocks ◽  
Problem Representation ◽  
Parallel Search ◽  
Diverse Population ◽  
Significant Difference

This article compares the traditional, fixed problem representation style of a genetic algorithm (GA) with a new floating representation in which the building blocks of a problem are not fixed at specific locations on the individuals of the population. In addition, the effects of noncoding segments on both of these representations is studied. Noncoding segments are a computational model of noncoding deoxyribonucleic acid, and floating building blocks mimic the location independence of genes. The fact that these structures are prevalent in natural genetic systems suggests that they may provide some advantages to the evolutionary process. Our results show that there is a significant difference in how GAs solve a problem in the fixed and floating representations. Genetic algorithms are able to maintain a more diverse population with the floating representation. The combination of noncoding segments and floating building blocks appears to encourage a GA to take advantage of its parallel search and recombination abilities.

scholarly journals How Crossover Speeds up Building Block Assembly in Genetic Algorithms

2017 ◽  
Vol 25 (2) ◽  
pp. 237-274 ◽  
Author(s):  
Dirk Sudholt
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Evolutionary Algorithms ◽  
Building Block ◽  
Broad Class ◽  
Statistical Tests ◽  
Building Blocks ◽  
Fundamental Question ◽  
Royal Road ◽  
Crossover Experiments

We reinvestigate a fundamental question: How effective is crossover in genetic algorithms in combining building blocks of good solutions? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter, we show that using crossover makes every ([Formula: see text]+[Formula: see text]) genetic algorithm at least twice as fast as the fastest evolutionary algorithm using only standard bit mutation, up to small-order terms and for moderate [Formula: see text] and [Formula: see text]. Crossover is beneficial because it can capitalize on mutations that have both beneficial and disruptive effects on building blocks: crossover is able to repair the disruptive effects of mutation in later generations. Compared to mutation-based evolutionary algorithms, this makes multibit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from [Formula: see text] to [Formula: see text]. This holds both for uniform crossover and k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building block functions.

The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations

1999 ◽  
Vol 7 (3) ◽  
pp. 231-253 ◽  
Author(s):  
George Harik ◽  
Erick Cantú-Paz ◽  
David E. Goldberg ◽  
Brad L. Miller
Keyword(s):  
Genetic Algorithms ◽  
Building Blocks ◽  
Correct Selection ◽  
Problem Size ◽  
One Dimensional ◽  
Fitness Evaluation ◽  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Selection Of

This paper presents a model to predict the convergence quality of genetic algorithms based on the size of the population. The model is based on an analogy between selection in GAs and one-dimensional random walks. Using the solution to a classic random walk problem—the gambler's ruin—the model naturally incorporates previous knowledge about the initial supply of building blocks (BBs) and correct selection of the best BB over its competitors. The result is an equation that relates the size of the population with the desired quality of the solution, as well as the problem size and difficulty. The accuracy of the model is verified with experiments using additively decomposable functions of varying difficulty. The paper demonstrates how to adjust the model to account for noise present in the fitness evaluation and for different tournament sizes.

scholarly journals Schemata Evolution and Building Blocks

1999 ◽  
Vol 7 (2) ◽  
pp. 109-124 ◽  
Author(s):  
Chris Stephens ◽  
Henri Waelbroeck
Keyword(s):  
Genetic Algorithms ◽  
Evolution Equation ◽  
Building Block ◽  
Building Blocks ◽  
Effective Fitness ◽  
Over Time ◽  
Low Order

In the light of a recently derived evolution equation for genetic algorithms we consider the schema theorem and the building block hypothesis. We derive a schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The equation makes manifest the content of the building block hypothesis showing how fit schemata are constructed from fit sub-schemata. However, we show that, generically, there is no preference for short, low-order schemata. In the case where schema reconstruction is favored over schema destruction, large schemata tend to be favored. As a corollary of the evolution equation we prove Geiringer's theorem.

Designing Genetic Algorithms to Solve GIS Problems

2001 ◽  
Author(s):  
Dirk Thierens ◽  
Mark De Berg
Keyword(s):  
Genetic Algorithms ◽  
Building Block ◽  
Domain Knowledge ◽  
Geographical Information Systems ◽  
Optimal Solution ◽  
Building Blocks ◽  
Geographical Information ◽  
Specific Class ◽  
Map Labeling ◽  
Linkage Learning

What makes a problem hard for a genetic algorithm (GA)? How does one need to design a GA to solve a problem satisfactorily? How does the designer include domain knowledge in the GA? When is a GA suitable to use for solving a problem? These are all legitimate questions. This chapter will offer a view on genetic algorithms that stresses the role of the so-called linkage. Linkage relates to the fact that between the variables of the solution dependencies exist that cause a need to treat those variables as one “block,” since the best setting of each individual variable can only be determined by looking at the other variables as well. The genes that represent these variables will then have to be transferred together. When these genes are set to their optimal values, they constitute a building block. Building blocks will be transferred as a whole during recombination and the building blocks of all the genes make up the optimal solution. As will become apparent, knowing the linkage of a building block is a big advantage and will allow one to design efficient GAs. Sadly, in the majority of problems, the linkage is unknown. This observation has given rise to a lot of development in linkage learning algorithms (for an example, see Kargupta 1996). However, there is a specific class of problems that allows for relatively easy determination of linkage: spatial problems. This is because in these problems, the linkage is geometrically defined. We will focus in this chapter on certain hard problems that arise in the context of geographical information systems and for which the linkage can be easily found. Specifically, we will fully detail the design of a GA for the problem of map labeling, which is an important problem in automated cartography. The map labeling problem for point features is to find a placement for the labels of a set of points such that the number of labels that do not intersect other labels is maximized.

Self-Organized Modularization in Evolutionary Algorithms

2005 ◽  
Vol 13 (3) ◽  
pp. 303-328 ◽  
Author(s):  
Peter Dauscher ◽  
Thomas Uthmann
Keyword(s):  
Evolutionary Computation ◽  
Building Blocks ◽  
Search Space ◽  
Equivalence Classes ◽  
Self Organized ◽  
Wide Range ◽  
Simple Genetic Algorithms ◽  
Evolutionary Operators ◽  
Selection Factor

The principle of modularization has proven to be extremely successful in the field of technical applications and particularly for Software Engineering purposes. The question to be answered within the present article is whether mechanisms can also be identified within the framework of Evolutionary Computation that cause a modularization of solutions. We will concentrate on processes, where modularization results only from the typical evolutionary operators, i.e. selection and variation by recombination and mutation (and not, e.g., from special modularization operators). This is what we call Self-Organized Modularization. Based on a combination of two formalizations by Radcliffe and Altenberg, some quantitative measures of modularity are introduced. Particularly, we distinguish Built-in Modularityas an inherent property of a genotype and Effective Modularity, which depends on the rest of the population. These measures can easily be applied to a wide range of present Evolutionary Computation models. It will be shown, both theoretically and by simulation, that under certain conditions, Effective Modularity (as defined within this paper) can be a selection factor. This causes Self-Organized Modularization to take place. The experimental observations emphasize the importance of Effective Modularityin comparison with Built-in Modularity. Although the experimental results have been obtained using a minimalist toy model, they can lead to a number of consequences for existing models as well as for future approaches. Furthermore, the results suggest a complex self-amplification of highly modular equivalence classes in the case of respected relations. Since the well-known Holland schemata are just the equivalence classes of respected relations in most Simple Genetic Algorithms, this observation emphasizes the role of schemata as Building Blocks (in comparison with arbitrary subsets of the search space).

Modeling Simple Genetic Algorithms

1995 ◽  
Vol 3 (4) ◽  
pp. 453-472 ◽  
Author(s):  
Michael D. Vose
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Asymptotic Behavior ◽  
Finite Population ◽  
Large Population ◽  
Population Models ◽  
Genetic Search ◽  
Simple Genetic Algorithm ◽  
Simple Genetic Algorithms

The infinite- and finite-population models of the simple genetic algorithm are extended and unified, The result incorporates both transient and asymptotic GA behavior. This leads to an interpretation of genetic search that partially explains population trajectories. In particular, the asymptotic behavior of the large-population simple genetic algorithm is analyzed.

scholarly journals Improving Initial Population for Genetic Algorithm using the Multi Linear Regression Based Technique

2020 ◽  
Vol 23 (1) ◽  
pp. E1-E10
Author(s):  
Esra'a Alkafaween ◽  
Ahmad B. A. Hassanat ◽  
Sakher Tarawneh
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Linear Regression ◽  
Heuristic Search ◽  
Large Scale ◽  
Travelling Salesman Problem ◽  
Initial Population ◽  
Problem Size ◽  
Travelling Salesman ◽  
Multi Linear Regression

Genetic algorithms (GAs) are powerful heuristic search techniques that are used successfully to solve problems for many different applications. Seeding the initial population is considered as the first step of the GAs. In this work, a new method is proposed, for the initial population seeding called the Multi Linear Regression Based Technique (MLRBT). That method divides a given large scale TSP problem into smaller sub-problems and the technique works frequently until the sub-problem size is very small, four cities or less. Experiments were carried out using the well-known Travelling Salesman Problem (TSP) instances and they showed promising results in improving the GAs' performance to solve the TSP.

Evolutionary Computation and Genetic Algorithms

2011 ◽  
pp. 477-481
Author(s):  
William H. Hsu
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Natural Selection ◽  
Genetic Programming ◽  
Sexual Reproduction ◽  
Evolutionary Computation ◽  
Evolutionary Biology ◽  
Approximate Solutions ◽  
Biologically Inspired ◽  
Genetic Inheritance

A genetic algorithm (GA) is a procedure used to find approximate solutions to search problems through the application of the principles of evolutionary biology. Genetic algorithms use biologically inspired techniques, such as genetic inheritance, natural selection, mutation, and sexual reproduction (recombination, or crossover). Along with genetic programming (GP), they are one of the main classes of genetic and evolutionary computation (GEC) methodologies.

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