Dynamical modelling of a genetic algorithm

This work addresses the signal propagation and the fractional-order dynamics during the evolution of a genetic algorithm (GA). In order to investigate the phenomena involved in the GA population evolution, the mutation is exposed to excitation perturbations during some generations and the corresponding fitness variations are evaluated. Three distinct fitness functions are used to study their influence in the GA dynamics. The input and output signals are studied revealing a fractional-order dynamic evolution, characteristic of a long-term system memory

Fractional dynamics in genetic algorithms

This paper investigate the fractional-order dynamics during the evolution of a Genetic Algorithm (GA). In order to study the phenomena involved in the GA population evolution, themutation is exposed to excitation perturbations during some generations and the corresponding fitness variations are evaluated. Three similar functions are tested to measure its influence in GA dynamics. The input and output signals are studied revealing a fractional-order dynamic evolution.N/

Knowledge Creation as a Square Dance on the Hilbert Cube

This paper presents a micro-model of knowledge creation and transfer in a small group of people. It is intended to contribute eventually to the development of microfoundations for aggregate models of knowledge externalities used in various literatures, such as those pertaining to endogenous growth theory, urban agglomeration and growth, organizational R&D and knowledge creation, and human capital accumulation. Our model incorporates two key aspects of the cooperative process of knowledge creation: (i) heterogeneity of people in their state of knowledge is essential for successful cooperation in the joint creation of new ideas, while (ii) the very process of cooperative knowledge creation affects the heterogeneity of people through the accumulation of knowledge in common. In the two person case, we show that the equilibrium process tends to result in the accumulation of too much knowledge in common compared to the most productive state. Unlike the two-person case, in the four person case we show that under certain conditions, the equilibrium process of knowledge creation by four persons may converge to the most productive state. Extensions of the basic model are discussedknowledge creation, knowledge transfer, knowledge externalities, microfoundations of endogenous growth

Fractional dynamics of genetic algorithms using hexagonal space tessellation

The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions

Analysing the visual dynamics of spatial morphology

Recently there has been a revival of interest in visibility analysis of architectural configurations. The new analyses rely heavily on computing power and statistical analysis, two factors which, according to the postpositivist school of geography, should immediately cause us to be wary. Thedanger, they would suggest, is in the application of a reductionist formal mathematical description in order to `explain' multilayered sociospatial phenomena. The author presents an attempt to rationalise how we can use visibility analysis to explore architecture in this multilayered context by considering the dynamics that lead to the visual experience. In particular, it is recommended that we assess the visualprocess of inhabitation, rather than assess the visibility in vacuo. In order to investigate the possibilities and limitations of the methodology, an urban environment is analysed by means of an agent-based model of visual actors within the configuration. The results obtained from the model are compared with actual pedestrian movement and other analytic measurements of the area: the agents correlate well both with human movement patterns and with configurational relationship as analysed by space-syntax methods. The application of both methods in combination improves on the correlation with observed movement of either, which in turn implies that an understanding of both the process of inhabitation and the principles of configuration may play a crucial role in determining the social usage of space

SciTech News Volume 71, No. 2 (2017)

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Particle Swarm Optimization: Dynamical Analysis through Fractional Calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions

Aquaculture-Fisheries Interactions

In this paper, I investigate aquaculture externalities on fisheries, affecting either habitat, wild fish stock genetics, or fishing efficiency under open-access and rent-maximising fisheries. This is done with a Verhulst-Schaefer model of fish population-dynamics and production, coupled with a simple aquaculture production model. Externalities are modelled by letting carrying capacity, the stock’s intrinsic growth rate, or catchability coefficient in the fishery depend on aquaculture production. The different externalities can give totally opposite results on steady-state fishing effort, yield, and stock, even for only negative externalities. With a catchability externality, increased unit cost of fishing effort implies reduced aquaculture production to maximise benefits to society under reasonable assumptions. Resource allocation between the industries is analysed under three different coastal management regimes: 1) aquaculture has a primary right of use; 2) joint management of aquaculture and fishery; 3) fishers have a primary right of use, including the right to sell marine farming rights.Aquaculture, fisheries, externality, interactions, carrying capacity, intrinsic growth rate, catchability coefficient, habitat, genetics., Environmental Economics and Policy, International Relations/Trade, Public Economics, Q22, R52,

Fractional Dynamics in Particle Swarm Optimization

This paper studies the fractional dynamics during the evolution of a Particle Swarm Optimization (PSO). Some swarm particles of the initial population are randomly changed for stimulating the system response. After the result is compared with a reference situation. The perturbation effect in the PSO evolution is observed in the perspective of the time behavior of the fitness of the best individual position visited by the replaced particles. The dynamics is investigated through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence of the PSO parameters upon the global dynamics is also analyzed by performing several experiments for distinct values.N/