A convergence proof for the particle swarm optimiser

The Particle Swarm Optimiser (PSO) is a population based stochastic optimisation algorithm, empirically shown to be efficient and robust. This paper provides a proof to show that the original PSO does not have guaranteed convergence to a local optimum. A flaw in the original PSO is identified which causes stagnation of the swarm. Correction of this flaw results in a PSO algorithm with guaranteed convergence to a local minimum. Further extensions with provable global convergence are also described. Experimental results are provided to elucidate the behavior of the modified PSO as well as PSO variations with global convergence.http://www.iospress.nl/loadtop/load.php?isbn=0169296

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Chaotic Quantum Double Delta Swarm Algorithm using Chebyshev Maps: Theoretical Foundations, Performance Analyses and Convergence Issues

Quantum Double Delta Swarm (QDDS) Algorithm is a new metaheuristic algorithm inspired by the convergence mechanism to the center of potential generated within a single well of a spatially co-located double-delta well setup. It mimics the wave nature of candidate positions in solution spaces and draws upon quantum mechanical interpretations much like other quantum-inspired computational intelligence paradigms. In this work, we introduce a Chebyshev map driven chaotic perturbation in the optimization phase of the algorithm to diversify weights placed on contemporary and historical, socially-optimal agents' solutions. We follow this up with a characterization of solution quality on a suite of 23 single-objective functions and carry out a comparative analysis with eight other related nature-inspired approaches. By comparing solution quality and successful runs over dynamic solution ranges, insights about the nature of convergence are obtained. A two-tailed t-test establishes the statistical significance of the solution data whereas Cohen's d and Hedge's g values provide a measure of effect sizes. We trace the trajectory of the fittest pseudo-agent over all function evaluations to comment on the dynamics of the system and prove that the proposed algorithm is theoretically globally convergent under the assumptions adopted for proofs of other closely-related random search algorithms.Comment: 27 pages, 4 figures, 19 table

Artificial intelligence to enhance aerodynamic shape optimisation of the Aegis UAV

This article presents an optimisation framework that uses stochastic multi-objective optimisation, combined with an Artificial Neural Network (ANN), and describes its application to the aerodynamic design of aircraft shapes. The framework uses the Multi-Objective Particle Swarm Optimisation (MOPSO) algorithm and the obtained results confirm that the proposed technique provides highly optimal solutions in less computational time than other approaches to the same design problem. The main idea was to focus computational effort on worthwhile design solutions rather than exploring and evaluating all possible solutions in the design space. It is shown that the number of valid solutions obtained using ANN-MOPSO compared to MOPSO for 3000 evaluations grew from 529 to 1006 (90% improvement) with a penalty of only 8.3% (11 min) in computational time. It is demonstrated that including an ANN, the ANN-MOPSO with 3000 evaluations produced a larger number of valid solutions than the MOPSO with 5500 evaluations, and in 33% less computational time (64 min). This is taken as confirmation of the potential power of ANNs when applied to this type of design problem

Global Trajectory Optimisation : Can We Prune the Solution Space When Considering Deep Space Manoeuvres? [Final Report]

This document contains a report on the work done under the ESA/Ariadna study 06/4101 on the global optimization of space trajectories with multiple gravity assist (GA) and deep space manoeuvres (DSM). The study was performed by a joint team of scientists from the University of Reading and the University of Glasgow