Angle modulated population based algorithms to solve binary problems

Abstract

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 < http://upetd.up.ac.za/thesis/available/etd-02242012-090312 / > C12/4/188/gm