Estimating attraction basin sizes

The performance of local search algorithms is influenced by the properties that the neighborhood imposes on the search space. Among these properties, the number of local optima has been traditionally considered as a complexity measure of the instance, and different methods for its estimation have been developed. The accuracy of these estimators depends on properties such as the relative attraction basin sizes. As calculating the exact attraction basin sizes becomes unaffordable for moderate problem sizes, their estimations are required. The lack of techniques achieving this purpose encourages us to propose two methods that estimate the attraction basin size of a given local optimum. The first method takes uniformly at random solutions from the whole search space, while the second one takes into account the structure defined by the neighborhood. They are tested on different instances of problems in the permutation space, considering the swap and the adjacent swap neighborhoods

Potentials and Limits to Basin Stability Estimation

Acknowledgments The authors gratefully acknowledge the support of BMBF, CoNDyNet, FK. 03SF0472A.Peer reviewedPublisher PD

A Study of NK Landscapes' Basins and Local Optima Networks

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the inherent network is the graph where the vertices are all the local maxima and edges mean basin adjacency between two maxima. We exhaustively extract such networks on representative small NK landscape instances, and show that they are 'small-worlds'. However, the maxima graphs are not random, since their clustering coefficients are much larger than those of corresponding random graphs. Furthermore, the degree distributions are close to exponential instead of Poissonian. We also describe the nature of the basins of attraction and their relationship with the local maxima network.Comment: best paper nominatio

Complex-network analysis of combinatorial spaces: The NK landscape case

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph whose vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties are related to the search difficulty on the underlying NK landscapes with varying values of K.Comment: arXiv admin note: substantial text overlap with arXiv:0810.3492, arXiv:0810.348

Delineation of the Native Basin in Continuum Models of Proteins

We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the basin size can be determined by monitoring random distortions in the shape of the protein around the native state. Both techniques yield the similar results. As a byproduct, a simple method to determine the folding temperature is obtained.Comment: REVTeX, 6 pages, 5 EPS figure

Setting Fees in Competing Double Auction Marketplaces: An Equilibrium Analysis

In this paper, we analyse competing double auction marketplaces that vie for traders and need to set appropriate fees to make a profit. Specifically, we show how competing marketplaces should set their fees by analysing the equilibrium behaviour of two competing marketplaces. In doing so, we focus on two different types of market fees: registration fees charged to traders when they enter the marketplace, and profit fees charged to traders when they make transactions. In more detail, given the market fees, we first derive equations to calculate the marketplaces' expected profits. Then we analyse the equilibrium charging behaviour of marketplaces in two different cases: where competing marketplaces can only charge the same type of fees and where competing marketplaces can charge different types of fees. This analysis provides insights which can be used to guide the charging behaviour of competing marketplaces. We also analyse whether two marketplaces can co-exist in equilibrium. We find that, when both marketplaces are limited to charging the same type of fees, traders will eventually converge to one marketplace. However, when different types of fees are allowed, traders may converge to different marketplaces (i.e. multiple marketplaces can co-exist)

Basins of attraction in forced systems with time-varying dissipation

We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final value. First, we consider situations where one is interested in the basins of attraction for damping coefficients varying linearly between two given values over many different time intervals: we outline a method to reduce the computation time required to estimate numerically the relative areas of the basins and discuss its range of applicability. Second, we observe that sometimes very slight changes in the time interval may produce abrupt large variations in the relative areas of the basins of attraction of the surviving attractors: we show how comparing the contracted phase space at a time after the final value of dissipation has been reached with the basins of attraction corresponding to that value of constant dissipation can explain the presence of such variations. Both procedures are illustrated by application to a pendulum with periodically oscillating support.Comment: 16 pages, 13 figures, 7 table

Instances of combinatorial optimization problems: complexity and generation

138 p.La optimización combinatoria considera problemas donde el objetivo es hallar el punto que maximiza o minimiza una función y donde el espacio de búsqueda es nito o innito numerable. La resolución de estos problemas es de gran importancia, ya que aparecen de forma natural en diferentes ámbitos como el mundo de la ciencia y de la ingeniería, la industria o la gestión

Controlling basins of attraction in a neural network-based telemetry monitor

The size of the basins of attraction around fixed points in recurrent neural nets (NNs) can be modified by a training process. Controlling these attractive regions by presenting training data with various amount of noise added to the prototype signal vectors is discussed. Application of this technique to signal processing results in a classification system whose sensitivity can be controlled. This new technique is applied to the classification of temporal sequences in telemetry data