Convergence estimates for crude approximations of a Pareto set
نویسندگان
چکیده
منابع مشابه
Quality Assessment of Pareto Set Approximations
This chapter reviews methods for the assessment and comparison of Pareto set approximations. Existing set quality measures from the literature are critically evaluated based on a number of orthogonal criteria, including invariance to scaling, monotonicity and computational effort. Statistical aspects of quality assessment are also considered in the chapter. Three main methods for the statistica...
متن کاملStochastic convergence of random search to fixed size Pareto set approximations
This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality ǫ. The core of the algorithm is a new selection criterion based on a hypothetical multilevel grid on the objective space. It is shown that, when using this criterion for accepting new search points, the sequence of solution ...
متن کاملOn convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations
H. Neidhardt, A. Stephan, V. A. Zagrebnov WIAS Berlin, Mohrenstr. 39, D-10117 Berlin, Germany Humboldt Universität zu Berlin, Institut für Mathematik Unter den Linden 6, D-10099 Berlin, Germany Université d’Aix-Marseille and Institut de Mathématiques de Marseille (I2M) UMR 7373, CMI – Technopôle Château-Gombert, 13453 Marseille, France [email protected], [email protected], ...
متن کاملImpact of selection methods on the diversity of many-objective Pareto set approximations
Selection methods are a key component of all multi-objective and, consequently, many-objective optimisation evolutionary algorithms. They must perform two main tasks simultaneously. First of all, they must select individuals that are as close as possible to the Pareto optimal front (convergence). Second, but not less important, they must help the evolutionary approach to provide a diverse popul...
متن کاملOn a Multi–Objective Evolutionary Algorithm and Its Convergence to the Pareto Set
Although there are many versions of evolutionary algorithms that are tailored to multi–criteria optimization, theoretical results are apparently not yet available. Here, it is shown that results known from the theory of evolutionary algorithms in case of single criterion optimization do not carry over to the multi–criterion case. At first, three different step size rules are investigated numeri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2002
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(02)00200-6