Critical considerations on angle modulated particle swarm optimisers

This article investigates various aspects of angle modulated particle swarm optimisers (AMPSO). Previous attempts at improving the algorithm have only been able to produce better results in a handful of test cases. With no clear understanding of when and why the algorithm fails, improving the algorithm’s performance has proved to be a difficult and sometimes blind undertaking. Therefore, the aim of this study is to identify the circumstances under which the algorithm might fail, and to understand and provide evidence for such cases. It is shown that the general assumption that good solutions are grouped together in the search space does not hold for the standard AMPSO algorithm or any of its existing variants. The problem is explained by specific characteristics of the generating function used in AMPSO. Furthermore, it is shown that the generating function also prevents particle velocities from decreasing, hindering the algorithm’s ability to exploit the binary solution space. Methods are proposed to both confirm and potentially solve the problems found in this study. In particular, this study addresses the problem of finding suitable generating functions for the first time. It is shown that the potential of a generating function to solve arbitrary binary optimisation problems can be quantified. It is further shown that a novel generating function with a single coefficient is able to generate solutions to binary optimisation problems with fewer than four dimensions. The use of ensemble generating functions is proposed as a method to solve binary optimisation problems with more than 16 dimensions.http://link.springer.com/journal/117212016-12-31hb201

Algorithms for Exact Structure Discovery in Bayesian Networks

Bayesian networks are compact, flexible, and interpretable representations of a joint distribution. When the network structure is unknown but there are observational data at hand, one can try to learn the network structure. This is called structure discovery. This thesis contributes to two areas of structure discovery in Bayesian networks: space--time tradeoffs and learning ancestor relations. The fastest exact algorithms for structure discovery in Bayesian networks are based on dynamic programming and use excessive amounts of space. Motivated by the space usage, several schemes for trading space against time are presented. These schemes are presented in a general setting for a class of computational problems called permutation problems; structure discovery in Bayesian networks is seen as a challenging variant of the permutation problems. The main contribution in the area of the space--time tradeoffs is the partial order approach, in which the standard dynamic programming algorithm is extended to run over partial orders. In particular, a certain family of partial orders called parallel bucket orders is considered. A partial order scheme that provably yields an optimal space--time tradeoff within parallel bucket orders is presented. Also practical issues concerning parallel bucket orders are discussed. Learning ancestor relations, that is, directed paths between nodes, is motivated by the need for robust summaries of the network structures when there are unobserved nodes at work. Ancestor relations are nonmodular features and hence learning them is more difficult than modular features. A dynamic programming algorithm is presented for computing posterior probabilities of ancestor relations exactly. Empirical tests suggest that ancestor relations can be learned from observational data almost as accurately as arcs even in the presence of unobserved nodes.Algoritmeja Bayes-verkkojen rakenteen tarkkaan oppimiseen Bayes-verkot ovat todennäköisyysmalleja, joiden avulla voidaan kuvata muuttujien välisiä suhteita. Bayes-verkko koostuu kahdesta osasta: rakenteesta ja kuhunkin muuttujaan liittyvästä ehdollisesta todennäköisyysjakaumasta. Rakenteen puolestaan muodostaa muuttujien välisiä riippuvuuksia kuvaava suunnattu syklitön verkko. Kun tarkasteltavaa ilmiötä hyvin kuvaavaa Bayes-verkkoa ei tunneta ennalta, mutta ilmiöön liittyvistä muuttujista on kerätty havaintoaineistoa, voidaan sopivia algoritmeja käyttäen yrittää löytää verkkorakenne, joka sovittuu aineistoon mahdollisimman hyvin. Nopeimmat tarkat rakenteenoppimisalgoritmit perustuvat niin kutsuttuun dynaamiseen ohjelmointiin, eli ne pitävät välituloksia muistissa ja näin välttävät suorittamasta samoja laskuja useaan kertaan. Vaikka tällaiset menetelmät ovat suhteellisen nopeita, niiden haittapuolena on suuri muistinkäyttö, joka estää suurten verkkojen rakenteen oppimisen. Väitöskirjan alkuosa käsittelee rakenteenoppimisalgoritmeja, jotka tasapainottelevat ajan- ja muistinkäytön välillä. Kirjassa esitellään menetelmiä, joilla verkon rakenne voidaan oppia tehokkaasti käyttäen hyväksi kaikki käytössä oleva tila. Uusi menetelmä mahdollistaa entistä suurempien verkkojen rakenteen oppimisen. Edellä mainittu menetelmä yleistetään ratkaisemaan Bayes-verkkojen rakenteenoppimisen lisäksi myös niin kutsuttuja permutaatio-ongelmia, joista tunnetuin lienee kauppamatkustajan ongelma. Väitöskirjan loppuosa käsittelee muuttujien välisien esi-isäsuhteiden oppimista. Kyseiset suhteet ovat kiinnostavia, sillä ne antavat lisätietoa muuttujien sekä suorista että epäsuorista syy-seuraussuhteista. Väitöskirjassa esitetään algoritmi esi-isäsuhteiden todennäköisyyksien laskemiseen. Algoritmin toimintaa tutkitaan käytännössä ja todetaan, että esi-isäsuhteita pystytään oppimaan melko hyvin jopa silloin, kun useat havaitsemattomat muuttujat vaikuttavat aineiston muuttujiin

Measurements, Models, Systems and Design

531 s.

Critical analysis of angle modulated particle swarm optimisers

This dissertation presents an analysis of the angle modulated particle swarm optimisation (AMPSO) algorithm. AMPSO is a technique that enables one to solve binary optimisation problems with particle swarm optimisation (PSO), without any modifications to the PSO algorithm. While AMPSO has been successfully applied to a range of optimisation problems, there is little to no understanding of how and why the algorithm might fail. The work presented here includes in-depth theoretical and emprical analyses of the AMPSO algorithm in an attempt to understand it better. Where problems are identified, they are supported by theoretical and/or empirical evidence. Furthermore, suggestions are made as to how the identified issues could be overcome. In particular, the generating function is identified as the main cause for concern. The generating function in AMPSO is responsible for generating binary solutions. However, it is shown that the increasing frequency of the generating function hinders the algorithm’s ability to effectively exploit the search space. The problem is addressed by introducing methods to construct different generating functions, and to quantify the quality of arbitrary generating functions. In addition to this, a number of other problems are identified and addressed in various ways. The work concludes with an empirical analysis that aims to identify which of the various suggestions made throughout this dissertatioin hold substantial promise for further research.Dissertation (MSc)--University of Pretoria, 2017.Computer ScienceMScUnrestricte

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

Models, solution methods and threshold behaviour for the teaching space allocation problem

Universities have to manage their teaching space, and plan future needs. Their efforts are frequently hampered by, capital and maintenance costs, on one hand, pedagogical and teaching services on the other. The efficiency of space usage, can be measured by the utilisation: the percentage of available seat-hours actually used. The observed utilisation, in many institutions, is unacceptably low, and this provides our main underlying motivation: To address and assess some of the major factors that affect teaching space usage in the hope of improving it in practise. Also, when performing space management, managers operate within a limited number and capacity of lecture theatres, tutorial rooms, etc. Hence, some teaching activities require splitting into different groups. For example, lectures being too large to fit in any one room and seminars/tutorials being taught in small groups for good teaching practise. This thesis forms the cornerstone of ongoing research to illuminate issues stemming from poorly utilised space and studies the nature of constraints that underlies those low levels of utilisation. We give quantitative evidence that constraints related to timetabling are major players in pushing down utilisation levels and also, devise "Dynamic Splitting" algorithms to illustrate the effects of splitting on utilisation levels. We showed the existence of threshold between phases where splitting and allocation is "always possible" to ones where "it's never possible", hence, introducing a practical application of Phase Transition to space planning and management. We have also worked on the long-term planning aspect of teaching space and proposed methods to improve the future expected utilisation