Angle modulated population based algorithms to solve binary problems

Recently, continuous-valued optimization problems have received a great amount of focus, resulting in optimization algorithms which are very efficient within the continuous-valued space. Many optimization problems are, however, defined within the binary-valued problem space. These continuous-valued optimization algorithms can not operate directly on a binary-valued problem representation, without algorithm adaptations because the mathematics used within these algorithms generally fails within a binary problem space. Unfortunately, such adaptations may alter the behavior of the algorithm, potentially degrading the performance of the original continuous-valued optimization algorithm. Additionally, binary representations present complications with respect to increasing problem dimensionality, interdependencies between dimensions, and a loss of precision. This research investigates the possibility of applying continuous-valued optimization algorithms to solve binary-valued problems, without requiring algorithm adaptation. This is achieved through the application of a mapping technique, known as angle modulation. Angle modulation effectively addresses most of the problems associated with the use of a binary representation by abstracting a binary problem into a four-dimensional continuous-valued space, from which a binary solution is then obtained. The abstraction is obtained as a bit-generating function produced by a continuous-valued algorithm. A binary solution is then obtained by sampling the bit-generating function. This thesis proposes a number of population-based angle-modulated continuous-valued algorithms to solve binary-valued problems. These algorithms are then compared to binary algorithm counterparts, using a suite of benchmark functions. Empirical analysis will show that the angle-modulated continuous-valued algorithms are viable alternatives to binary optimization algorithms. Copyright 2012, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Pamparà, G 2012, Angle modulated population based algorithms to solve binary problems, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd C12/4/188/gmDissertation (MSc)--University of Pretoria, 2012.Computer Scienceunrestricte

Geometric Particle Swarm Optimization for Multi-objective Optimization Using Decomposition

Multi-objective evolutionary algorithms (MOEAs) based on decomposition are aggregation-based algorithms which transform a multi-objective optimization problem (MOP) into several single-objective subproblems. Being effective, efficient, and easy to implement, Particle Swarm Optimization (PSO) has become one of the most popular single-objective optimizers for continuous problems, and recently it has been successfully extended to the multi-objective domain. However, no investigation on the application of PSO within a multi-objective decomposition framework exists in the context of combinatorial optimization. This is precisely the focus of the paper. More specifically, we study the incorporation of Geometric Particle Swarm Optimization (GPSO), a discrete generalization of PSO that has proven successful on a number of single-objective combinatorial problems, into a decomposition approach. We conduct experiments on manyobjective 1/0 knapsack problems i.e. problems with more than three objectives functions, substantially harder than multi-objective problems with fewer objectives. The results indicate that the proposed multi-objective GPSO based on decomposition is able to outperform two version of the wellknow MOEA based on decomposition (MOEA/D) and the most recent version of the non-dominated sorting genetic algorithm (NSGA-III), which are state-of-the-art multi-objective evolutionary approaches based on decomposition

Dynamic co-evolutionary algorithms for dynamic, constrained optimisation problems

Thesis (PhD)--Stellenbosch University, 2021.ENGLISH ABSTRACT: Dynamic, constrained optimisation problems (DCOPs) are a class of optimisa- tion problem where the problem landscape changes and problem constraints optionally change over time. Although DCOPs represent the super-set of op- timisation problems, relatively little is understood about these problems due to the complexity added to the optimisation process. However, unlike the available optimisation algorithms developed for changing problem landscapes, few algorithm variants exist for DCOPs. Optimisation algorithms for DCOPs are expected to not only adapt to the changing problem landscape but need to also consider the feasibility of solutions whilst adapting to any changes to the problem constraints over time. This thesis examines the constituent parts of the optimisation process by providing an in-depth review of the optimisation process. A substantial chal- lenge is created by DCOPs for optimisation algorithms and this thesis examines these problems in detail with a fitness landscape analysis (FLA), before propos- ing a DCOP benchmark generator capable of producing a truly comprehensive set of possible problem landscape and constraint combinations. Quantification of the performance of optimisation algorithms on these comprehensive DCOP instances is identified as being problematic. The behaviour of the algorithm during the entire optimisation process should provide a better indication of algorithm performance and this thesis proposes a new measurement capable of quantifying algorithm performance from the very beginning of the optimisation process. Generally, a constraint handling method is used to manage the optimisation problem constraints for the optimisation algorithm. The constraint handling method should also adapt to the changing optimisation problem. As a result, adaptive constraint handling methods are thought to be best. However, many of these methods introduce additional control parameters that require tuning which is not useful within DCOPs. This thesis provides evidence that a dy- namic co-evolutionary approach using the Lagrangian transformation of the optimisation problem can produce solutions to DCOPs. The co-evolutionary approach uses dynamic optimisation algorithms in order to adapt to both the changing problem landscape and changing problem constraints. This thesis also proposes a novel self-adaptive quantum particle swarm optimisation as one of these dynamic optimisation algorithms. Lastly, this thesis proposes a reproducible framework for computational intelligence allowing for the perfect replication of the experimental work of the aforementioned dynamic co-evolutionary algorithms.AFRIKAANSE OPSOMMING: Dinamiese, beperkte optimeringsprobleme (DCOPs) is ’n klas optimeringsprob- leem waar die probleemlandskap verander en probleembeperkings opsioneel ve- rander met die verloop van tyd. As gevolg van die addisionele kompleksiteit wat hierdie klas van optimeringsprobleem by die optimeringsproses byvoeg, word daar huidiglik relatief min verstaan omtrent dié superstel van optimeringsprob- leme. Daar is ’n klein aantal optimeringsalgoritmes wat tans beskikbaar is vir veranderende probleemlandskappe soos DCOPs. Dit word van optimer- ingsalgoritmes vir DCOPs verwag om nie net by die veranderende probleem- landskap aan te pas nie, maar ook om die haalbaarheid van oplossings te oorweeg. Terselfdertyd moet optimeringsalgoritmes ook by enige verandering in die probleembeperkings aanpas met tyd. Hierdie proefskrif ondersoek die dele van die optimeringsproses deur ’n diepgaande oorsig van die optimeringsproses te gee. Die uitdagings wat deur DCOPs aan optimeringsalgoritmes gestel word is groot, en hierdie proefskrif ondersoek hierdie probleme deur “fiksheidlandskapanalise” (FLA). Nadat die eienskappe van die probleme ondersoek is, word ’n funksie voorgestel wat DCOP probleme kan genereer. Hierdie funksie kan ’n reeks van moontlike probleemlandskap en beperkingskombinasies lewer. Die kwantifisering van optimeringsalgoritme oplossings wat vir die reeks probleme gevind word, kan as problematies geïdentifiseer word. Die versameling van resultate na elke iterasie van ’n algoritme gee ’n beter aanduiding van die kwalitiet van oplossings wat deur ’n algoritme gevind kan word. In hierdie proefskrif word ’n nuwe metingsproses voorgestel wat die kwalitiet van algoritme oplossings kan bepaal, vanaf die begin van die optimeringsproses tot en met die einde daarvan. Oor die algemeen word ’n beperkingshanteringmetode gebruik om die probeem beperkings vir die optimeringsalgoritme te bestuur. Die beperkinghanter- ingsmetode moet ook aanpas by enige verandering van die optimeringsprobleem. As gevolg hiervan word aanpasbare metodes vir die hantering van probleem- beperkings as die beste beskou. Ongelukkig benodig baie van die probleem- beperking metodes addisionele beheerparameters wat ingestel moet word, maar die instel van beheerparameters maak geen sin binne DCOPs nie. Hierdie proefskrif lewer bewys dat ’n dinamiese ko-evolusionêre benader- ing wat die Lagrangiaanse transformasie van die optimeringsprobleem gebruik, oplossings vir DCOPs kan lewer. Die ko-evolusionêre benadering gebruik dinamiese optimeringsalgoritmes om aan te pas by die veranderende probleem- landskap en veranderende probleembeperkings. Hierdie proefskrif stel ook ’n nuwe selfaanpassende “kwantum deeltjieswerm optimeringsalgoritme” voor as een van hierdie dinamiese optimeringsalgoritmes. Laastens stel hierdie proefskrif ’n raamwerk voor vir rekenaarintelligensie paradigmas wat die perfekte replikasie van die eksperimentele werk van die bogenoemde dinamiese ko-evolusionêre algoritmes moontlik maak.Doctora