Darryn J Reid

Enhanced genetic operators for the resolution of discrete constrained optimization problems

Abstract The behavior of the Crossover and Mutation Operators on candidate solutions to any discrete and constrained optimization problem is investigated in some detail, affording new understanding in the construction of Evolutionary and Genetic Algorithms for the effective resolution of problems of this kind. The important case in which some or all of the constraints are linear exemplifies the potential usefulness of these insights, by guiding the design and application of operators guaranteed to preserve feasibility. The computational challenge posed by numerous optimization problems has lead to the exploration of algorithms based on adaption observed in biological systems, as an alternative means of illation. Ideally suited to difficult conditions, in accordance with their inspiration, these methods have been successfully exploited in many problems that have defied adequate resolution by more traditional means. Despite their undeniable attraction, the applicability of Genetic Algorithms has been limited by the lack of general techniques to manage systems of constraints, a feature of many optimization tasks, and this is compounded when some proportion of the decision variables are discrete. In response, the fundamental behavior of the genetic operators with respect to any system of constraints has been investigated; this discussion summarizes and extends the results of earlier work. [ Math. Comp. Modelling , 1996, 23 (5), 87–111]. By investigating theoretically the behavior of the crossover operator on viable solutions of an entirely general system of constraints, the limitations of restricting attention to solely to feasible points become apparent. A relaxation of the crossover operator is also proposed to avoid calamitous performance degradation otherwise experienced in solving highly constrained problems, and its effective utilization suggests a modification in the overall algorithm in which the population is permitted to transiently increase in size.

Dynamics of confined crowds modelled using Entropic Stochastic Resonance and Quantum Neural Networks

We present a new approach to modelling dynamics of confined crowds driven by Entropic Stochastic Resonance (ESR). The standard approach is to model confined Brownian particles using overdamped Langevin equations and corresponding linear, real-time, Fokker-Planck equations for Probability Density Functions (PDFs). Instead, we propose a new approach based on a set of (weakly or strongly) coupled Quantum Neural Networks (QNNs), which are self-organised, complex-valued nonlinear Schrodinger equations with unsupervised Hebbian-type learning. Utilising the full power of nonlinear analysis in the complex-plane, the new approach promises to be ideal for any kind of two-dimensional terrains. Besides, instead of over-simplistic Brownian particles, the new approach allows us to model crowds consisting of rigid-body-type agents.

Complexity and control : towards a rigorous behavioral theory of complex dynamical systems

The book Complexity and Control: Towards a Rigorous Behavioral Theory of Complex Dynamical Systems is a graduate-level monographic textbook, intended to be a novel and rigorous contribution to modern Complexity Theory.This book contains 11 chapters and is designed as a one-semester course for engineers, applied and pure mathematicians, theoretical and experimental physicists, computer and economic scientists, theoretical chemists and biologists, as well as all mathematically educated scientists and students, both in industry and academia, interested in predicting and controlling complex dynamical systems of arbitrary nature.

Action-Amplitude Approach to Controlled Entropic Self-Organization

Motivated by the notion of perceptual error, as a core concept of the perceptual control theory, we propose an action-amplitude model for controlled entropic self-organization (CESO). We present several aspects of this development that illustrate its explanatory power: (i) a physical view of partition functions and path integrals, as well as entropy and phase transitions; (ii) a global view of functional compositions and commutative diagrams; (iii) a local geometric view of the Kahler–Ricci flow and time-evolution of entropic action; and (iv) a computational view using various path-integral approximations.

Entropic Geometry of Crowd Dynamics

We propose an entropic geometrical model of psycho-physical crowd dynamics (with dissipative crowd kinematics), using Feynman action-amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to explain the dynamics of crowds simultaneously and consistently across these three levels, in order to characterize their geometrical properties particularly with respect to behavior regimes and the state changes between them. Its most natural statistical descriptor is crowd entropy

Foundations of Trusted Autonomy: An Introduction

S

Tensor-Centric Warfare I: Tensor Lanchester Equations

that satisfies the Prigogines extended second law of thermodynamics,

Tensor-Centric Warfare II: Entropic Uncertainty Modeling

\partial_tS\geq 0

Formal-Language-Oriented Foundation of Dynamics of Human Crowds Using Topos-Theory

(for any nonisolated multi-component system). Qualitative similarities and superpositions between individual and crowd configuration manifolds motivate our claim that goal-directed crowd movement operates under entropy conservation,

Crowd behavior dynamics: entropic path-integral model

\partial_tS = 0