scholarly journals Motif Difficulty (MD): A Predictive Measure of Problem Difficulty for Evolutionary Algorithms Using Network Motifs

2012 ◽  
Vol 20 (3) ◽  
pp. 321-347 ◽  
Author(s):  
Jing Liu ◽  
Hussein A. Abbass ◽  
David G. Green ◽  
Weicai Zhong
Keyword(s):  
Evolutionary Algorithms ◽  
Fitness Landscape ◽  
Sampling Technique ◽  
Binary Search ◽  
Knapsack Problems ◽  
Network Motifs ◽  
Problem Difficulty ◽  
Search Spaces ◽  
Multidimensional Knapsack

One of the major challenges in the field of evolutionary algorithms (EAs) is to characterise which kinds of problems are easy and which are not. Researchers have been attracted to predict the behaviour of EAs in different domains. We introduce fitness landscape networks (FLNs) that are formed using operators satisfying specific conditions and define a new predictive measure that we call motif difficulty (MD) for comparison-based EAs. Because it is impractical to exhaustively search the whole network, we propose a sampling technique for calculating an approximate MD measure. Extensive experiments on binary search spaces are conducted to show both the advantages and limitations of MD. Multidimensional knapsack problems (MKPs) are also used to validate the performance of approximate MD on FLNs with different topologies. The effect of two representations, namely binary and permutation, on the difficulty of MKPs is analysed.

scholarly journals A Note on Problem Difficulty Measures in Black-Box Optimization: Classification, Realizations and Predictability

2007 ◽  
Vol 15 (4) ◽  
pp. 435-443 ◽  
Author(s):  
Jun He ◽  
Colin Reeves ◽  
Carsten Witt ◽  
Xin Yao
Keyword(s):  
Evolutionary Algorithms ◽  
Polynomial Time ◽  
Fitness Landscape ◽  
Fitness Function ◽  
Black Box ◽  
Landscape Analysis ◽  
Problem Difficulty ◽  
Fitness Landscape Analysis ◽  
Theoretical Assumptions ◽  
Different Types

Various methods have been defined to measure the hardness of a fitness function for evolutionary algorithms and other black-box heuristics. Examples include fitness landscape analysis, epistasis, fitness-distance correlations etc., all of which are relatively easy to describe. However, they do not always correctly specify the hardness of the function. Some measures are easy to implement, others are more intuitive and hard to formalize. This paper rigorously defines difficulty measures in black-box optimization and proposes a classification. Different types of realizations of such measures are studied, namely exact and approximate ones. For both types of realizations, it is proven that predictive versions that run in polynomial time in general do not exist unless certain complexity-theoretical assumptions are wrong.

A New Method for Modeling the Behavior of Finite Population Evolutionary Algorithms

2010 ◽  
Vol 18 (3) ◽  
pp. 451-489 ◽  
Author(s):  
Tatsuya Motoki
Keyword(s):  
Markov Chain ◽  
Evolutionary Algorithms ◽  
Finite Population ◽  
Fitness Landscape ◽  
Markov Chain Model ◽  
Search Space ◽  
Chain Model ◽  
Transition Matrices ◽  
Memory Space ◽  
Exact Model

As practitioners we are interested in the likelihood of the population containing a copy of the optimum. The dynamic systems approach, however, does not help us to calculate that quantity. Markov chain analysis can be used in principle to calculate the quantity. However, since the associated transition matrices are enormous even for modest problems, it follows that in practice these calculations are usually computationally infeasible. Therefore, some improvements on this situation are desirable. In this paper, we present a method for modeling the behavior of finite population evolutionary algorithms (EAs), and show that if the population size is greater than 1 and much less than the cardinality of the search space, the resulting exact model requires considerably less memory space for theoretically running the stochastic search process of the original EA than the Nix and Vose-style Markov chain model. We also present some approximate models that use still less memory space than the exact model. Furthermore, based on our models, we examine the selection pressure by fitness-proportionate selection, and observe that on average over all population trajectories, there is no such strong bias toward selecting the higher fitness individuals as the fitness landscape suggests.

Parallel Evolutionary Computation in R

2013 ◽  
pp. 105-129 ◽  
Author(s):  
Cedric Gondro ◽  
Paul Kwan
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Computation ◽  
Genome Wide Association Study ◽  
Optimization Methods ◽  
Large Field ◽  
Search Spaces ◽  
Parallel Evolutionary Algorithms ◽  
Genome Wide ◽  
Statistical Programming ◽  
Candidate Regions

Evolutionary Computation (EC) is a branch of Artificial Intelligence which encompasses heuristic optimization methods loosely based on biological evolutionary processes. These methods are efficient in finding optimal or near-optimal solutions in large, complex non-linear search spaces. While evolutionary algorithms (EAs) are comparatively slow in comparison to deterministic or sampling approaches, they are also inherently parallelizable. As technology shifts towards multicore and cloud computing, this overhead becomes less relevant, provided a parallel framework is used. In this chapter the authors discuss how to implement and run parallel evolutionary algorithms in the popular statistical programming language R. R has become the de facto language for statistical programming and it is widely used in biostatistics and bioinformatics due to the availability of thousands of packages to manipulate and analyze data. It is also extremely easy to parallelize routines within R, which makes it a perfect environment for evolutionary algorithms. EC is a large field of research, and many different algorithms have been proposed. While there is no single silver bullet that can handle all classes of problems, an algorithm that is extremely simple, efficient, and with good generalization properties is Differential Evolution (DE). Herein the authors discuss step-by-step how to implement DE in R and how to parallelize it. They then illustrate with a toy genome-wide association study (GWAS) how to identify candidate regions associated with a quantitative trait of interest.

Sign in / Sign up

Export Citation Format

Share Document