Approximation of reachable sets using optimal control algorithms

To appearInternational audienceNumerical experiences with a method for the approximation of reachable sets of nonlinear control systems are reported. The method is based on the formulation of suitable optimal control problems with varying objective functions, whose discretization by Euler's method lead to finite dimensional non-convex nonlinear programs. These are solved by a sequential quadratic programming method. An efficient adjoint method for gradient computation is used to reduce the computational costs. The discretization of the state space is more efficiently than by usual sequential realization of Euler's method and allows adaptive calculations or refinements. The method is illustrated for two test examples. Both examples have non-linear dynamics, the first one has a convex reachable set, whereas the second one has a non-convex reachable set

Advances in Artificial Intelligence: Models, Optimization, and Machine Learning

The present book contains all the articles accepted and published in the Special Issue “Advances in Artificial Intelligence: Models, Optimization, and Machine Learning” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of artificial intelligence and its subfields. These topics include, among others, deep learning and classic machine learning algorithms, neural modelling, architectures and learning algorithms, biologically inspired optimization algorithms, algorithms for autonomous driving, probabilistic models and Bayesian reasoning, intelligent agents and multiagent systems. We hope that the scientific results presented in this book will serve as valuable sources of documentation and inspiration for anyone willing to pursue research in artificial intelligence, machine learning and their widespread applications

Towards a more efficient use of computational budget in large-scale black-box optimization

Evolutionary algorithms are general purpose optimizers that have been shown effective in solving a variety of challenging optimization problems. In contrast to mathematical programming models, evolutionary algorithms do not require derivative information and are still effective when the algebraic formula of the given problem is unavailable. Nevertheless, the rapid advances in science and technology have witnessed the emergence of more complex optimization problems than ever, which pose significant challenges to traditional optimization methods. The dimensionality of the search space of an optimization problem when the available computational budget is limited is one of the main contributors to its difficulty and complexity. This so-called curse of dimensionality can significantly affect the efficiency and effectiveness of optimization methods including evolutionary algorithms. This research aims to study two topics related to a more efficient use of computational budget in evolutionary algorithms when solving large-scale black-box optimization problems. More specifically, we study the role of population initializers in saving the computational resource, and computational budget allocation in cooperative coevolutionary algorithms. Consequently, this dissertation consists of two major parts, each of which relates to one of these research directions. In the first part, we review several population initialization techniques that have been used in evolutionary algorithms. Then, we categorize them from different perspectives. The contribution of each category to improving evolutionary algorithms in solving large-scale problems is measured. We also study the mutual effect of population size and initialization technique on the performance of evolutionary techniques when dealing with large-scale problems. Finally, assuming uniformity of initial population as a key contributor in saving a significant part of the computational budget, we investigate whether achieving a high-level of uniformity in high-dimensional spaces is feasible given the practical restriction in computational resources. In the second part of the thesis, we study the large-scale imbalanced problems. In many real world applications, a large problem may consist of subproblems with different degrees of difficulty and importance. In addition, the solution to each subproblem may contribute differently to the overall objective value of the final solution. When the computational budget is restricted, which is the case in many practical problems, investing the same portion of resources in optimizing each of these imbalanced subproblems is not the most efficient strategy. Therefore, we examine several ways to learn the contribution of each subproblem, and then, dynamically allocate the limited computational resources in solving each of them according to its contribution to the overall objective value of the final solution. To demonstrate the effectiveness of the proposed framework, we design a new set of 40 large-scale imbalanced problems and study the performance of some possible instances of the framework