Structural coherence of problem and algorithm: An analysis for EDAs on all 2-bit and 3-bit problems

Abstract

This is an author produced version of a paper published in IEEE Congress on Evolutionary Computation (CEC): Proceedings (ISBN 9781479974924)This version may not include final proof corrections and does not include published layout or pagination. Citation DetailsCitation for the version of the work held in 'OpenAIR@RGU': Copyright Items in 'OpenAIR@RGU', Robert Gordon University Open Access Institutional Repository, are protected by copyright and intellectual property law. If you believe that any material held in 'OpenAIR@RGU' infringes copyright, please contact openair-help@rgu.ac.uk with details. The item will be removed from the repository while the claim is investigated. Abstract-Metaheuristics assume some kind of coherence between decision and objective spaces. Estimation of Distribution algorithms approach this by constructing an explicit probabilistic model of high fitness solutions, the structure of which is intended to reflect the structure of the problem. In this context, "structure" means the dependencies or interactions between problem variables in a probabilistic graphical model. There are many approaches to discovering these dependencies, and existing work has already shown that often these approaches discover "unnecessary" elements of structure -that is, elements which are not needed to correctly rank solutions. This work performs an exhaustive analysis of all 2 and 3 bit problems, grouped into classes based on mononotic invariance. It is shown in [1] that each class has a minimal Walsh structure that can be used to solve the problem. We compare the structure discovered by different structure learning approaches to the minimal Walsh structure for each class, with summaries of which interactions are (in)correctly identified. Our analysis reveals a large number of symmetries that may be used to simplify problem solving. We show that negative selection can result in improved coherence between discovered and necessary structure, and conclude with some directions for a general programme of study building on this work.for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Generating Easy and Hard Problems using the Proximate Optimality Principle

“…More complex algorithms will operate on the representation in more complex ways and the concept of coherence will need to be generalised. One current line of active research [1,2] is to use probabilistic graphical models on representation space to structure fitness in ways coherent with the action of algorithm operators.…”

“…Examples include [1,4,5,[7][8][9][10][11]. POP is often stated in terms like "good solutions possess some similar structure" [5].…”

Evolutionary Algorithms with Linkage Information for Feature Selection in Brain Computer Interfaces

“…However, it has also been shown [1,4,13] that some aspects of linkage are inessential for fully ranking all solutions to a problem and locating the global optima. Indeed, including such inessential dependencies in the problem model used by the algorithm can hamper performance [2,19,23].…”

“…The sample data used was provided by the second Berlin BCI competition, in which dataset three was selected (motor-imagery) 1 as previous studies have shown it to be a clearly defined, yet challenging dataset. The recorded task involved having a participant utilize motor imagery of right and left hand movements to control an onscreen bar.…”

Structure discovery in mixed order hyper networks

“…McCall et al [19] use statistical tests of independence to discover second order connections between pairs of variables subject to a limit on the number of connections a node can have and follow this with a clique finding algorithm to infer higher order connections [20].…”