A Model for Analysing the Collective Dynamic Behaviour and Characterising the Exploitation of Population-Based Algorithms

Several previous studies have focused on modelling and analysing the collective dynamic behaviour of population-based algorithms. However, an empirical approach for identifying and characterising such a behaviour is surprisingly lacking. In this paper, we present a new model to capture this collective behaviour, and to extract and quantify features associated with it. The proposed model studies the topological distribution of an algorithm's activity from both a genotypic and a phenotypic perspective, and represents population dynamics using multiple levels of abstraction. The model can have different instantiations. Here it has been implemented using a modified version of self-organising maps. These are used to represent and track the population motion in the fitness landscape as the algorithm operates on solving a problem. Based on this model, we developed a set of features that characterise the population's collective dynamic behaviour. By analysing them and revealing their dependency on fitness distributions, we were then able to define an indicator of the exploitation behaviour of an algorithm. This is an entropy-based measure that assesses the dependency on fitness distributions of different features of population dynamics. To test the proposed measures, evolutionary algorithms with different crossover operators, selection pressure levels and population handling techniques have been examined, which lead populations to exhibit a wide range of exploitation-exploration behaviours. </jats:p

A model for characterising the collective dynamic behaviour of evolutionary algorithms

Exploration and exploitation are considered essential notions in evolutionary algorithms. However, a precise interpretation of what constitutes exploration or exploitation is clearly lacking and so are specific measures for characterising such notions. In this paper, we start addressing this issue by presenting new measures that can be used as indicators of the exploitation behaviour of an algorithm. These work by characterising the extent to which available information guides the search. More precisely, they quantify the dependency of a population's activity on the observed fitness values and genetic material, utilising an empirical model that uses a coarse-grained representation of population dynamics and records information about it. The model uses the k-means clustering algorithm to identify the population's "basins of activity". The exploitation behaviour is then captured by an entropy-based measure based on the model that quantifies the strength of the association between a population's activity distribution and the observed fitness landscape information. In experiments, we analysed the effects of the search operators and their parameter settings on the collective dynamic behaviour of populations. We also analysed the effect of using different problems on algorithm behaviours.We define a behavioural landscape for each problem to identify the appropriate behaviour to achieve good results and point out possible applications for the proposed model

On Formal Methods for Collective Adaptive System Engineering. {Scalable Approximated, Spatial} Analysis Techniques. Extended Abstract

In this extended abstract a view on the role of Formal Methods in System Engineering is briefly presented. Then two examples of useful analysis techniques based on solid mathematical theories are discussed as well as the software tools which have been built for supporting such techniques. The first technique is Scalable Approximated Population DTMC Model-checking. The second one is Spatial Model-checking for Closure Spaces. Both techniques have been developed in the context of the EU funded project QUANTICOL.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200

A Model for Characterising the Collective Dynamic Behaviour of Evolutionary Algorithms

Abstract. Exploration and exploitation are considered essential notions in evolutionary algorithms. However, a precise interpretation of what constitutes exploration or exploitation is clearly lacking and so are specific measures for characterising such notions. In this paper, we start addressing this issue by presenting new measures that can be used as indicators of the exploitation behaviour of an algorithm. These work by characterising the extent to which available information guides the search. More precisely, they quantify the dependency of a population&apos;s activity on the observed fitness values and genetic material, utilising an empirical model that uses a coarse-grained representation of population dynamics and records information about it. The model uses the k-means clustering algorithm to identify the population&apos;s &quot;basins of activity&quot;. The exploitation behaviour is then captured by an entropy-based measure based on the model that quantifies the strength of the association between a population&apos;s activity distribution and the observed fitness landscape information. In experiments, we analysed the effects of the search operators and their parameter settings on the collective dynamic behaviour of populations. We also analysed the effect of using different problems on algorithm behaviours. We define a behavioural landscape for each problem to identify the appropriate behaviour to achieve good results and point out possible applications for the proposed model

French Roadmap for complex Systems 2008-2009

This second issue of the French Complex Systems Roadmap is the outcome of the Entretiens de Cargese 2008, an interdisciplinary brainstorming session organized over one week in 2008, jointly by RNSC, ISC-PIF and IXXI. It capitalizes on the first roadmap and gathers contributions of more than 70 scientists from major French institutions. The aim of this roadmap is to foster the coordination of the complex systems community on focused topics and questions, as well as to present contributions and challenges in the complex systems sciences and complexity science to the public, political and industrial spheres

Establishing norms with metanorms in distributed computational systems

Norms provide a valuable mechanism for establishing coherent cooperative behaviour in decentralised systems in which there is no central authority. One of the most influential formulations of norm emergence was proposed by Axelrod (Am Political Sci Rev 80(4):1095–1111, 1986). This paper provides an empirical analysis of aspects of Axelrod’s approach, by exploring some of the key assumptions made in previous evaluations of the model. We explore the dynamics of norm emergence and the occurrence of norm collapse when applying the model over extended durations . It is this phenomenon of norm collapse that can motivate the emergence of a central authority to enforce laws and so preserve the norms, rather than relying on individuals to punish defection. Our findings identify characteristics that significantly influence norm establishment using Axelrod’s formulation, but are likely to be of importance for norm establishment more generally. Moreover, Axelrod’s model suffers from significant limitations in assuming that private strategies of individuals are available to others, and that agents are omniscient in being aware of all norm violations and punishments. Because this is an unreasonable expectation , the approach does not lend itself to modelling real-world systems such as online networks or electronic markets. In response, the paper proposes alternatives to Axelrod’s model, by replacing the evolutionary approach, enabling agents to learn, and by restricting the metapunishment of agents to cases where the original defection is observed, in order to be able to apply the model to real-world domains . This work can also help explain the formation of a “social contract” to legitimate enforcement by a central authority

From modularity to emergence: a primer on the design and science of complex systems

Electrical networks, flocking birds, transportation hubs, weather patterns, commercial organisations, swarming robots... Increasingly, many of the systems that we want to engineer or understand are said to be ‘complex’. These systems are often considered to be intractable because of their unpredictability, non-linearity, interconnectivity, heterarchy and ‘emergence’. Such attributes are often framed as a problem, but can also be exploited to encourage systems to efficiently exhibit intelligent, robust, self-organising behaviours. But what does it mean to describe systems as complex? How do these complex systems differ from the more easily understood ‘modular’ systems that we are familiar with? What are the underlying similarities between different systems, whether modular or complex? Answering these questions is a first step in approaching the design and science of complexity. However, to do so, it is necessary to look beyond the specifics of any particular system or field of study. We need to consider the fundamental nature of systems, looking for a common way to view ostensibly different phenomena. This primer introduces a domain-neutral framework and diagrammatic scheme for characterising the ways in which systems are modular or complex. Rather than seeing modularity and complexity as inherent attributes of systems, we instead see them as ways in which those systems are characterised by those who are interested in them. The framework is not tied to any established mode of representation (e.g. networks, equations, formal modelling languages) nor to any domain-specific terminology (e.g. ‘vertex’, ‘eigenvector’, ‘entropy’). Instead, it consists of basic system constructs and three fundamental attributes of modular system architecture, namely structural encapsulation, function-structure mapping and interfacing. These constructs and attributes encourage more precise descriptions of different aspects of complexity (e.g. emergence, self-organisation, heterarchy). This allows researchers and practitioners from different disciplines to share methods, theories and findings related to the design and study of different systems, even when those systems appear superficially dissimilar