Lenka Skanderova

Evolutionary Dynamics as The Structure of Complex Networks

This chapter presents a novel method for visualizing the dynamics of evolutionary algorithms in the form of complex networks. The analogy between individuals in populations in an arbitrary evolutionary algorithm and vertices of a complex network is discussed, as well as between edges in a complex network and communication between individuals in a population. The possibility of visualizing the dynamics of a complex network using the coupled map lattices method and control by means of chaos control techniques are also discussed.

Differential evolution dynamics analysis by complex networks

Differential evolution is a simple yet efficient heuristic originally designed for global optimization over continuous spaces that has been used in many research areas. The question how to improve its performance is still popular and during the years, many successful methods dealing with optimal setting or hybridization of the control parameters were proposed. In this paper, we propose a novel approach based on modeling of the differential evolution dynamics by complex networks. In each generation, the individuals are mapped to the nodes and the relationships between them are modeled by the edges of the graph. Thanks to this simple visualization, the interconnection between the differential evolution convergence speed and the weighted clustering coefficients has been revealed. As a consequence, we have focused on the parents selection in the mutation step where the individuals are not selected randomly as usual but on the basis of their weighted clustering coefficients. Our enhancement has been incorporated in the classical differential evolution, self-adaptive differential evolution (jDE) and differential evolution with composite trial vector generation strategies and control parameters. Finally, a set of well-known benchmark functions (including 21 functions) has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithms perform better or at least comparable to their original versions and the analysis of the differential evolution dynamics with the aim of the complex network might be an effective tool to improve the differential evolution convergence in the future.

Chaos Powered Selected Evolutionary Algorithms

It is well known that the evolution algorithms use pseudo-random numbers generators for example to generate random individuals in the space of possible solutions, crossing etc. In this paper we are dealing with the effect of different pseudo-random numbers generators on the course of evolution and the speed of their convergence to the global minimum. From evolution algorithms the differential evolution and self organizing migrating algorithm have been chosen because they have different strategies. As the random generators Mersenne Twister and chaotic system - logistic map have been used.

Differential Evolution Enhanced by the Closeness Centrality: Initial Study

The closeness centrality can be considered as the natural distance metric between pairs of nodes in connected graphs. This paper is the initial study of the influence of the closeness centrality of the graph built on the basis of the differential evolution dynamics to the differential evolution convergence rate. Our algorithm is based on the principle that the differential evolution creates graph for each generation, where nodes represent the individuals and edges the relationships between them. For each individual the closeness centrality is computed and on the basis of its value the individuals are selected in the mutation step of the algorithm. The higher value of the closeness centrality means the higher probability to become the parent in the mutation step. This enhancement has been incorporated in the classical differential evolution and a set of 21 well-known benchmark functions has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithm performs better or at least comparable to its original version.

Hidden Complexity of Evolutionary Dynamics: Analysis

This chapter presents a method for visualization of the dynamics of evolutionary algorithms in the form of complex networks and is continuation of our previous research. The analogy between individuals of populations in an arbitrary evolutionary algorithm and vertices of a complex network is mentioned, as well as between edges in a complex network and communication between individuals in a population. Visualization of various attributes of network based on differential algorithm is presented here.

Visualization of complex networks dynamics: case study

In this article is discussed novel method of the so-called complex networks dynamics and its visualization by means of so called coupled map lattices method. The main aim of this research is to demonstrate possibility to visualize complex network dynamics by means of the same method, that is used spatiotemporal chaos modeling. It is suggested here to use coupled map lattices system to simulate complex network so that each site is equal to one vertex of complex network. Interaction between network vertices is in coupled map lattices equal to the strength of mutual influence between system sites. Also another results from previous experiments, where dynamics of evolutionary algorithms has been converted to complex network and consequently to CML, are mentioned at the end. All results has been properly visualized and explained.

Differential evolution based on the node degree of its complex network: Initial study

In this paper is reported our progress in the synthesis of two partially different areas of research: complex networks and evolutionary computation. Ideas and results reported and mentioned here are based on our previous results and experiments. The main core of our participation is an evolutionary algorithm performance improvement by means of complex network use. Complex network is related to the evolutionary dynamics and reflect it. We report here our latest results as well as propositions on further research that is in process in our group (http://navy.cs.vsb.cz/). Only the main ideas and results are reported here, for more details it is recommended to read related literature of our previous research and results.

Differential Evolution Dynamics Modeled by Longitudinal Social Network

Abstract Differential evolution (DE) is a population-based algorithm using Darwinian and Mendel principles to find out an optimal solution to difficult problems. In this work, the dynamics of the DE algorithm are modeled by using a longitudinal social network. Because a population of the DE algorithm is improved in generations, each generation of DE algorithm is represented by one short-interval network. Each short-interval network is created by individuals contributing to population improvement. On the basis of this model, a new parent selection in the mutation operation is presented and a well-known benchmark set CEC 2013 Special Session on Real-Parameter Optimization (including 28 functions) is used to evaluate the performance of the proposed algorithm.

Small-world hidden in differential evolution

Differential evolution is an effective population-based global optimizer which is used in many areas of research. The population consists of individuals, which are mutated, crossed and better of them survive to the next generation. In this paper, we look at this process as at the communication between individuals which can be modeled by the network where the individuals are represented by the nodes and the edges between them reflect the dynamics in the population, i.e. interactions between individuals. The main goal of this work is to find out if the differential evolution algorithm is able to create the networks where the small-world phenomenon (known as six degrees of separation) is observed. The secondary objective was to investigate the dependency between the type of the selected test function and the extent of this phenomenon. To evaluate the performance of the algorithm eleven test functions from the benchmark set CEC 2015 have been used. The analysis of the generated networks indicates that the differential evolution is able to create small-world networks in majority of test functions. As the result, the selected test functions can be classified into three categories which binds to the degree of cooperation between the individuals in the population.

Comparison of Pseudorandom Numbers Generators and Chaotic Numbers Generators used in Differential Evolution

Differential evolution is one of the great family of evolutionary algorithms. As well as all evolutionary algorithms differential evolution uses pseudorandom numbers generators in many steps of algorithm. In this paper we will compare pseudorandom numbers generators as Mersenne Twister, Crypto Random, Random number generator in Microsoft .NET System.Random class, Visual Studio 2010, Multiply-with-carry, Xorshift and chaotic numbers generators as Logistic map, Arnold Cat Map and Sinai. The main goal of this paper is compare these pseudorandom numbers generators and chaotic numbers generators from the view of differential evolution convergence’s speed to the global minimum.