Natural Evolution Strategies

Editor: Una-May O’Reilly This paper presents Natural Evolution Strategies (NES), a recent family of black-box opti-mization algorithms that use the natural gradient to update a parameterized search distri-bution in the direction of higher expected fitness. We introduce a collection of techniques that address issues of convergence, robustness, sample complexity, computational complex-ity and sensitivity to hyperparameters. This paper explores a number of implementations of the NES family, such as general-purpose multi-variate normal distributions and separa-ble distributions tailored towards search in high dimensional spaces. Experimental results show best published performance on various standard benchmarks, as well as competitive performance on others

Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms

Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a multi-objective evolutionary algorithm called GSEMO until it has obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints we show that GSEMO achieves a (1 - 1/e)-approximation in expected time O(n2 (log n + k)), where k is the value of the given constraint. For the case of non-monotone submodular functions with k matroid intersection constraints, we show that GSEMO achieves a 1/(k +2+1/k + epsilon)-approximation in expected time O(nk+5 log(n)/epsilon).Tobias Friedrich and Frank Neuman

Maximizing submodular functions under matroid constraints by evolutionary algorithms

Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a simple single objective evolutionary algorithm called (1 + 1) EA and a multiobjective evolutionary algorithm called GSEMO until they have obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints, we show that the GSEMO achieves a (1 - 1/e)-approximation in expected polynomial time. For the case of monotone functions where the constraints are given by the intersection of K ≥ 2 matroids, we show that the (1 + 1) EA achieves a (1/k + δ)-approximation in expected polynomial time for any constant δ > 0. Turning to nonmonotone symmetric submodular functions with k ≥ 1 matroid intersection constraints, we show that the GSEMO achieves a 1/((k + 2)(1 + ε))-approximation in expected time O(n(k + 6)log(n)/ε.Tobias Friedrich, Frank Neuman

Leistungsarmes Ionenspektrometer fuer hohe Zaehlraten Abschlussbericht. Abschlussdatum: Maerz 1980

Technische Informationsbibliothek Hannover: RA 674 (80-019) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman