The role of Walsh structure and ordinal linkage in the optimisation of pseudo-Boolean functions under monotonicity invariance.

Optimisation heuristics rely on implicit or explicit assumptions about the structure of the black-box fitness function they optimise. A review of the literature shows that understanding of structure and linkage is helpful to the design and analysis of heuristics. The aim of this thesis is to investigate the role that problem structure plays in heuristic optimisation. Many heuristics use ordinal operators; which are those that are invariant under monotonic transformations of the fitness function. In this thesis we develop a classification of pseudo-Boolean functions based on rank-invariance. This approach classifies functions which are monotonic transformations of one another as equivalent, and so partitions an infinite set of functions into a finite set of classes. Reasoning about heuristics composed of ordinal operators is, by construction, invariant over these classes. We perform a complete analysis of 2-bit and 3-bit pseudo-Boolean functions. We use Walsh analysis to define concepts of necessary, unnecessary, and conditionally necessary interactions, and of Walsh families. This helps to make precise some existing ideas in the literature such as benign interactions. Many algorithms are invariant under the classes we define, which allows us to examine the difficulty of pseudo-Boolean functions in terms of function classes. We analyse a range of ordinal selection operators for an EDA. Using a concept of directed ordinal linkage, we define precedence networks and precedence profiles to represent key algorithmic steps and their interdependency in terms of problem structure. The precedence profiles provide a measure of problem difficulty. This corresponds to problem difficulty and algorithmic steps for optimisation. This work develops insight into the relationship between function structure and problem difficulty for optimisation, which may be used to direct the development of novel algorithms. Concepts of structure are also used to construct easy and hard problems for a hill-climber

Substructural local search in discrete estimation of distribution algorithms

Tese dout., Engenharia Electrónica e Computação, Universidade do Algarve, 2009SFRH/BD/16980/2004The last decade has seen the rise and consolidation of a new trend of stochastic optimizers known as estimation of distribution algorithms (EDAs). In essence, EDAs build probabilistic models of promising solutions and sample from the corresponding probability distributions to obtain new solutions. This approach has brought a new view to evolutionary computation because, while solving a given problem with an EDA, the user has access to a set of models that reveal probabilistic dependencies between variables, an important source of information about the problem. This dissertation proposes the integration of substructural local search (SLS) in EDAs to speedup the convergence to optimal solutions. Substructural neighborhoods are de ned by the structure of the probabilistic models used in EDAs, generating adaptive neighborhoods capable of automatic discovery and exploitation of problem regularities. Speci cally, the thesis focuses on the extended compact genetic algorithm and the Bayesian optimization algorithm. The utility of SLS in EDAs is investigated for a number of boundedly di cult problems with modularity, overlapping, and hierarchy, while considering important aspects such as scaling and noise. The results show that SLS can substantially reduce the number of function evaluations required to solve some of these problems. More importantly, the speedups obtained can scale up to the square root of the problem size O( p `).Fundação para a Ciência e Tecnologia (FCT

Adaptive algorithms for history matching and uncertainty quantification

Numerical reservoir simulation models are the basis for many decisions in regard to predicting, optimising, and improving production performance of oil and gas reservoirs. History matching is required to calibrate models to the dynamic behaviour of the reservoir, due to the existence of uncertainty in model parameters. Finally a set of history matched models are used for reservoir performance prediction and economic and risk assessment of different development scenarios. Various algorithms are employed to search and sample parameter space in history matching and uncertainty quantification problems. The algorithm choice and implementation, as done through a number of control parameters, have a significant impact on effectiveness and efficiency of the algorithm and thus, the quality of results and the speed of the process. This thesis is concerned with investigation, development, and implementation of improved and adaptive algorithms for reservoir history matching and uncertainty quantification problems. A set of evolutionary algorithms are considered and applied to history matching. The shared characteristic of applied algorithms is adaptation by balancing exploration and exploitation of the search space, which can lead to improved convergence and diversity. This includes the use of estimation of distribution algorithms, which implicitly adapt their search mechanism to the characteristics of the problem. Hybridising them with genetic algorithms, multiobjective sorting algorithms, and real-coded, multi-model and multivariate Gaussian-based models can help these algorithms to adapt even more and improve their performance. Finally diversity measures are used to develop an explicit, adaptive algorithm and control the algorithm’s performance, based on the structure of the problem. Uncertainty quantification in a Bayesian framework can be carried out by resampling of the search space using Markov chain Monte-Carlo sampling algorithms. Common critiques of these are low efficiency and their need for control parameter tuning. A Metropolis-Hastings sampling algorithm with an adaptive multivariate Gaussian proposal distribution and a K-nearest neighbour approximation has been developed and applied

Using Prior Knowledge and Learning from Experience in Estimation of Distribution Algorithms

Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. One of the primary advantages of EDAs over many other stochastic optimization techniques is that after each run they leave behind a sequence of probabilistic models describing useful decompositions of the problem. This sequence of models can be seen as a roadmap of how the EDA solves the problem. While this roadmap holds a great deal of information about the problem, until recently this information has largely been ignored. My thesis is that it is possible to exploit this information to speed up problem solving in EDAs in a principled way. The main contribution of this dissertation will be to show that there are multiple ways to exploit this problem-specific knowledge. Most importantly, it can be done in a principled way such that these methods lead to substantial speedups without requiring parameter tuning or hand-inspection of models

Algorithms and Methods for Designing and Scheduling Smart Manufacturing Systems

This book, as a Special Issue, is a collection of some of the latest advancements in designing and scheduling smart manufacturing systems. The smart manufacturing concept is undoubtedly considered a paradigm shift in manufacturing technology. This conception is part of the Industry 4.0 strategy, or equivalent national policies, and brings new challenges and opportunities for the companies that are facing tough global competition. Industry 4.0 should not only be perceived as one of many possible strategies for manufacturing companies, but also as an important practice within organizations. The main focus of Industry 4.0 implementation is to combine production, information technology, and the internet. The presented Special Issue consists of ten research papers presenting the latest works in the field. The papers include various topics, which can be divided into three categories—(i) designing and scheduling manufacturing systems (seven articles), (ii) machining process optimization (two articles), (iii) digital insurance platforms (one article). Most of the mentioned research problems are solved in these articles by using genetic algorithms, the harmony search algorithm, the hybrid bat algorithm, the combined whale optimization algorithm, and other optimization and decision-making methods. The above-mentioned groups of articles are briefly described in this order in this book