Characterising the rankings produced by combinatorial optimisation problems and finding their intersections

The aim of this paper is to introduce the concept of intersection between combinatorial optimisation problems. We take into account that most algorithms, in their machinery, do not consider the exact objective function values of the solutions, but only a comparison between them. In this sense, if the solutions of an instance of a combinatorial optimisation problem are sorted into their objective function values, we can see the instances as (partial) rankings of the solutions of the search space. Working with specific problems, particularly, the linear ordering problem and the symmetric and asymmetric traveling salesman problem, we show that they can not generate the whole set of (partial) rankings of the solutions of the search space, but just a subset. First, we characterise the set of (partial) rankings each problem can generate. Secondly, we study the intersections between these problems: those rankings which can be generated by both the linear ordering problem and the symmetric/asymmetric traveling salesman problem, respectively. The fact of finding large intersections between problems can be useful in order to transfer heuristics from one problem to another, or to define heuristics that can be useful for more than one problem

Clarifying the Difference in Local Optima Network Sampling Algorithms

We conduct the first ever statistical comparison between two Local Optima Network (LON) sampling algorithms. These methodologies attempt to capture the connectivity in the local optima space of a fitness landscape. One sampling algorithm is based on a random-walk snowballing procedure, while the other is centred around multiple traced runs of an Iterated Local Search. Both of these are proposed for the Quadratic Assignment Problem (QAP), making this the focus of our study. It is important to note the sampling algorithm frameworks could easily be modified for other domains. In our study descriptive statistics for the obtained search space samples are contrasted and commented on. The LON features are also used in linear mixed models and random forest regression for predicting heuristic optimisation performance of two prominent heuristics for the QAP on the underlying combinatorial problems. The model results are then used to make deductions about the sampling algorithms’ utility. We also propose a specific set of LON metrics for use in future predictive models alongside previously-proposed network metrics, demonstrating the payoff in doing so

Prescriptive formalism for constructing domain-specific evolutionary algorithms

It has been widely recognised in the computational intelligence and machine learning communities that the key to understanding the behaviour of learning algorithms is to understand what representation is employed to capture and manipulate knowledge acquired during the learning process. However, traditional evolutionary algorithms have tended to employ a fixed representation space (binary strings), in order to allow the use of standardised genetic operators. This approach leads to complications for many problem domains, as it forces a somewhat artificial mapping between the problem variables and the canonical binary representation, especially when there are dependencies between problem variables (e.g. problems naturally defined over permutations). This often obscures the relationship between genetic structure and problem features, making it difficult to understand the actions of the standard genetic operators with reference to problem-specific structures. This thesis instead advocates m..

Anatomy of the Local Optima Level in Combinatorial Optimisation

Many situations in daily life represent complex combinatorial optimisation problems. These include issues such as efficient fuel consumption, nurse scheduling, or distribution of humanitarian aid. There are many algorithms that attempt to solve these problems but the ability to understand their likely performance on a given problem is still lacking. Fitness landscape analysis identifies some of the reasons why metaheuristic algorithms behave in a particular way. The Local Optima Network (LON) model, proposed in 2008, encodes local optima connectivity in fitness landscapes. In this approach, nodes are local optima and edges encode transitions between these optima. A LON provides a static image of the dynamics of algorithm-problem inter- play. Analysing these structures provides insights into the reactions between optimisation problems and metaheuristic search algorithms. This thesis proposes that analysis of the local optima space of combinatorial fitness landscapes encoded using a LON provides important information concerning potential search algorithm performance. It considers the question as to whether or not features of LONs can contribute to explaining or predicting the outcome of trying to optimise an associated combinatorial problem. Topological landscape features of LONs are proposed, analysed and compared. Benchmark and novel problem instances are studied; both types of problem are sampled and in some cases exhaustively-enumerated such that LONs can be extracted for analysis. Investigations into the nature and biases of LON construction algorithms are conducted and compared. Contributions include aligning fractal geometry to the study of LONs; proposals for novel ways to compute fractal dimension from these structures; comparing the power of different LON construction algorithms for explaining algorithm performances; and analysing the interplay between algorithmic operations and infeasible regions in the local optima space using LONs as a tool. Throughout the thesis, large scale structural patterns in fitness landscapes are shown to be strongly linked with metaheuristic algorithm performance. This includes arrangements of local optima funnel structures; spatial and geometric complexity in the LON (measured by their fractal dimensionality) and fitness levels in the space of local optima. These features are demonstrated to have explanatory or predictive ability with respect to algorithm performance for the underlying combinatorial problems. The results presented here indicate that large topological patterns in fitness landscapes are important during metaheuristic search algorithm design. In many cases they are incontrovertibly linked to the success of the algorithm. These results indicate that use of the suggested fitness landscape measures would be highly beneficial when considering the design of search algorithms for a given problem domain

Contributions to the mathematical modeling of estimation of distribution algorithms and pseudo-boolean functions

134 p.Maximice o minimice una función objetivo definida sobre un espacio discreto. Dado que la mayoría de dichos problemas no pueden ser resueltos mediante una búsqueda exhaustiva, su resolución se aproxima frecuentemente mediante algoritmos heurísticos. Sin embargo, no existe ningún algoritmo que se comporte mejor que el resto de algoritmos para resolver todas las instancias de cualquier problema. Por ello, el objetivo ideal es, dado una instancia de un problema, saber cuál es el algoritmo cuya resoluciones más eficiente. Las dos líneas principales de investigación para lograr dicho objetivo son estudiar las definiciones de los problemas y las posibles instancias que cada problema puede generar y el estudio delos diseños y características de los algoritmos. En esta tesis, se han tratado ambas lineas. Por un lado,hemos estudiado las funciones pseudo-Booleanas y varios problemas binarios específicos. Por otro lado,se ha presentado un modelado matemático para estudiar Algoritmos de Estimación de Distribuciones diseñados para resolver problemas basados en permutaciones. La principal motivación ha sido seguir progresando en este campo para comprender mejor las relaciones entre los Problemas de Optimización Combinatoria y los algoritmos de optimización

INTELLIGENT TECHNIQUES FOR HANDLING UNCERTAINTY IN THE ASSESSMENT OF NEONATAL OUTCOME

Objective assessment of the neonatal outcome of labour is important, but it is a difficult and challenging problem. It is an invaluable source of information which can be used to provide feedback to clinicians, to audit a unit's overall performance, and can guide subsequent neonatal care. Current methods are inadequate as they fail to distinguish damage that occurred during labour from damage that occurred before or after labour. Analysis of the chemical acid-base status of blood taken from the umbilical cord of an infant immediately after delivery provides information on any damage suffered by the infant due to lack of oxygen during labour. However, this process is complex and error prone, and requires expertise which is not always available on labour wards. A model of clinical expertise required for the accurate interpretation of umbilical acid-base status was developed, and encapsulated in a rule-based expert system. This expert system checks results to ensure their consistency, identifies whether the results come from arterial or venous vessels, and then produces an interpretation of their meaning. This 'crisp' expert system was validated, verified and commercially released, and has since been installed at twenty two hospitals all around the United Kingdom. The assessment of umbilical acid-base status is characterised by uncertainty in both the basic data and the knowledge required for its interpretation. Fuzzy logic provides a technique for representing both these forms of uncertainty in a single framework. A 'preliminary' fuzzy-logic based expert system to interpret error-free results was developed, based on the knowledge embedded in the crisp expert system. Its performance was compared against clinicians in a validation test, but initially its performance was found to be poor in comparison with the clinicians and inferior to the crisp expert system. An automatic tuning algorithm was developed to modify the behaviour of the fuzzy model utilised in the expert system. Sub-normal membership functions were used to weight terms in the fuzzy expert system in a novel manner. This resulted in an improvement in the performance of the fuzzy expert system to a level comparable to the clinicians, and superior to the crisp expert system. Experimental work was carried out to evaluate the imprecision in umbilical cord acid-base parameters. This information, in conjunction with fresh knowledge elicitation sessions, allowed the creation of a more comprehensive fuzzy expert system, to validate and interpret all acid-base data. This 'integrated' fuzzy expert system was tuned using the comparison data obtained previously, and incorporated vessel identification rules and interpretation rules, with numeric and linguistic outputs for each. The performance of each of the outputs was evaluated in a rigorous validation study. This demonstrated excellent agreement with the experts for the numeric outputs, and agreement on a par with the experts for the linguistic outputs. The numeric interpretation produced by the fuzzy expert system is a novel single dimensional measure that accurately represents the severity of acid-base results. The development of the crisp and fuzzy expert systems represents a major achievement and constitutes a significant contribution to the assessment of neonatal outcome.Plymouth Postgraduate Medical Schoo

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order