Computing a Finite Size Representation of the Set of Approximate Solutions of an MOP

Recently, a framework for the approximation of the entire set of $\epsilon$-efficient solutions (denote by $E_\epsilon$) of a multi-objective optimization problem with stochastic search algorithms has been proposed. It was proven that such an algorithm produces -- under mild assumptions on the process to generate new candidate solutions --a sequence of archives which converges to $E_{\epsilon}$ in the limit and in the probabilistic sense. The result, though satisfactory for most discrete MOPs, is at least from the practical viewpoint not sufficient for continuous models: in this case, the set of approximate solutions typically forms an $n$-dimensional object, where $n$ denotes the dimension of the parameter space, and thus, it may come to perfomance problems since in practise one has to cope with a finite archive. Here we focus on obtaining finite and tight approximations of $E_\epsilon$, the latter measured by the Hausdorff distance. We propose and investigate a novel archiving strategy theoretically and empirically. For this, we analyze the convergence behavior of the algorithm, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting approximation, and present some numerical results

EXPERIMENTS WITH SOUNDS IN REPELLING MAMMALS

Since its introduction for use in repelling birds , a number of people have found that Av-Alarm is effective for control of certain mammals. This includes not only those familiar to North Americans (deer, elk , coyotes), but also various less familiar species, even anthropoids (baboons) and bats. A number of example cases are described. A concept theory is presented in order to explain why certain sounds are more effective than others, and why sounds originally meant for bird control are also effective with mammals. The theory helps to predict untested situations , and also suggests when complex repelling sounds can profitably be augmented by other sounds or by visual harassment

Landscape analysis in multi-objective combinatorial optimization

La majorité de problèmes réels d'optimisation (ex. gérer grandes infrastructures, planifier les ressources pour les communautés, villes ou entreprises, etc.) sont combinatoire par la nature et impliquent l'utilisation de plusieurs objectifs, souvent contradictoire ou différent par le type. Comme déterminé par la nature contradictoire des objectifs, une solution "idéale" n'existe pas, sur une base générale, le but étant fixée d’atteindre un ensemble des meilleures solutions de compromis. Les résultats de cette thèse font partie de l'effort d'améliorer les capacités de méthodes d'optimisation combinatoire multi-objectif (MOCO), pour des instances de grand taille. La thèse propose l'utilisation de l'analyse de paysage en tant qu'outil de guidage pour des méthodes d'optimisation, mais également en tant que moyen de mesurer la difficulté des problèmes en s'appuyant sur l'analyse topologique. L'étude est principalement basée sur les études d'analyse de paysage qui fournissent des informations au sujet de la distribution des solutions faisables dans l'espace objectif. Les approches d'analyse de paysage proposées traitent un aspect quelque peu nouvel des problèmes MOCO, c'est-à-dire les études topologiques réalisées au-dessus de l'ensemble de solutions faisables ou pour les ensembles spécifiques d'intérêts comme l'ensemble de Pareto (l'ensemble des meilleures solutions de compromis) ou l'ensemble de e-Pareto. En outre, les études de structuralité sont intégrées dans des techniques interactives afin d'aider le processus de recherche et fournir des garanties de performance même pour des recherches stochastiques dans le cas combinatoire à objectifs multiples.The majority of real-life optimization problems (e.g. managing large infrastructures, the planning of resources for communities, cities or enterprises, etc.) are combinatorial by nature and imply the use of several objectives, often conflicting or different by type. As determined by the conflicting nature of the objectives, there exists no single "ideal" best compromise solution, on a general basis, the goal being set on attaining a set of best compromise solutions. The results of this thesis are part of the effort of improving Multi-Objective Combinatorial Optimization (MOCO) methods capabilities, for large instances.The thesis proposes the use of landscape analysis as guiding tool for optimization methods, but also as mean of quantifying the difficulty of problems based on topological analysis. The present study is mainly based on landscape analysis studies that provide information about the distribution of feasible solutions in the objective space. The proposed landscape analysis approaches tackle a somewhat new aspect of MOCO problems, i.e. the topological studies performed over the set of feasible solutions or for specific sets of interests as the Pareto set (the set of best compromise solutions) or the e-Pareto set. These techniques are seen as a priori techniques, providing useful information for the design of approximation methods. Furthermore, the structurality studies are integrated in online interactive techniques in order to help the search process and to provide performance guarantees even for stochastic searches in the multi-objective combinatorial case

Asymmetric quadratic landscape approximation model

This work presents an asymmetric quadratic approximation model and an ε-archiving algorithm. The model allows to construct, under local convexity assumptions, descriptors for local optima points in continuous functions. A descriptor can be used to extract confidence radius information. The ε-archiving algorithm is designed to maintain and update a set of such asymmetric descriptors, spaced at some given threshold distance. An in-depth analysis is conducted on the stability and performance of the asymmetric model, comparing the results with the ones obtained by a quadratic polynomial approximation. A series of different applications are possible in areas such as dynamic and robust optimization. © 2014 ACM

On dynamic multi-objective optimization - classification and performance measures

In this work we focus on defining how dynamism can be modeled in the context of multi-objective optimization. Based on this, we construct a component oriented classification for dynamic multi-objective optimization problems. For each category we provide synthetic examples that depict in a more explicit way the defined model. We do this either by positioning existing synthetic benchmarks with respect to the proposed classification or through new problem formulations. In addition, an online dynamic MNK-landscape formulation is introduced together with a new comparative metric for the online dynamic multi-objective context

On the Foundations and the Applications of Evolutionary Computing

Genetic type particle methods are increasingly used to sample from complex high-dimensional distributions. They have found a wide range of applications in applied probability, Bayesian statistics, information theory, and engineering sciences. Understanding rigorously these new Monte Carlo simulation tools leads to fascinating mathematics related to Feynman-Kac path integral theory and their interacting particle interpretations. In this chapter, we provide an introduction to the stochastic modeling and the theoretical analysis of these particle algorithms. We also illustrate these methods through several applications

Sparse Antenna Array Optimization with the Cross-Entropy Method

The interest in sparse antenna arrays is growing, mainly due to cost concerns, array size limitations, etc. Formally, it can be shown that their design can be expressed as a constrained multidimensional nonlinear optimization problem. Generally, through lack of convex property, such a multiextrema problem is very tricky to solve by usual deterministic optimization methods. In this article, a recent stochastic approach, called Cross-Entropy method, is applied to the continuous constrained design problem. The method is able to construct a random sequence of solutions which converges probabilistically to the optimal or the near-optimal solution. Roughly speaking, it performs adaptive changes to probability density functions according to the Kullback-Leibler cross-entropy. The approach efficiency is illustrated in the design of a sparse antenna array with various requirements