313 research outputs found
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 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
Local Optima Networks of NK Landscapes with Neutrality
In previous work we have introduced a network-based model that abstracts many
details of the underlying landscape and compresses the landscape information
into a weighted, oriented graph which we call the local optima network. The
vertices of this graph are the local optima of the given fitness landscape,
while the arcs are transition probabilities between local optima basins. Here
we extend this formalism to neutral fitness landscapes, which are common in
difficult combinatorial search spaces. By using two known neutral variants of
the NK family (i.e. NKp and NKq) in which the amount of neutrality can be tuned
by a parameter, we show that our new definitions of the optima networks and the
associated basins are consistent with the previous definitions for the
non-neutral case. Moreover, our empirical study and statistical analysis show
that the features of neutral landscapes interpolate smoothly between landscapes
with maximum neutrality and non-neutral ones. We found some unknown structural
differences between the two studied families of neutral landscapes. But
overall, the network features studied confirmed that neutrality, in landscapes
with percolating neutral networks, may enhance heuristic search. Our current
methodology requires the exhaustive enumeration of the underlying search space.
Therefore, sampling techniques should be developed before this analysis can
have practical implications. We argue, however, that the proposed model offers
a new perspective into the problem difficulty of combinatorial optimization
problems and may inspire the design of more effective search heuristics.Comment: IEEE Transactions on Evolutionary Computation volume 14, 6 (2010) to
appea
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
Multi-layer local optima networks for the analysis of advanced local search-based algorithms
A Local Optima Network (LON) is a graph model that compresses the fitness
landscape of a particular combinatorial optimization problem based on a
specific neighborhood operator and a local search algorithm. Determining which
and how landscape features affect the effectiveness of search algorithms is
relevant for both predicting their performance and improving the design
process. This paper proposes the concept of multi-layer LONs as well as a
methodology to explore these models aiming at extracting metrics for fitness
landscape analysis. Constructing such models, extracting and analyzing their
metrics are the preliminary steps into the direction of extending the study on
single neighborhood operator heuristics to more sophisticated ones that use
multiple operators. Therefore, in the present paper we investigate a twolayer
LON obtained from instances of a combinatorial problem using bitflip and swap
operators. First, we enumerate instances of NK-landscape model and use the hill
climbing heuristic to build the corresponding LONs. Then, using LON metrics, we
analyze how efficiently the search might be when combining both strategies. The
experiments show promising results and demonstrate the ability of multi-layer
LONs to provide useful information that could be used for in metaheuristics
based on multiple operators such as Variable Neighborhood Search.Comment: Accepted in GECCO202
Clustering of Local Optima in Combinatorial Fitness Landscapes
Using the recently proposed model of combinatorial landscapes: local optima
networks, we study the distribution of local optima in two classes of instances
of the quadratic assignment problem. Our results indicate that the two problem
instance classes give rise to very different configuration spaces. For the
so-called real-like class, the optima networks possess a clear modular
structure, while the networks belonging to the class of random uniform
instances are less well partitionable into clusters. We briefly discuss the
consequences of the findings for heuristically searching the corresponding
problem spaces.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
Set-based Multiobjective Fitness Landscapes: A Preliminary Study
Fitness landscape analysis aims to understand the geometry of a given
optimization problem in order to design more efficient search algorithms.
However, there is a very little knowledge on the landscape of multiobjective
problems. In this work, following a recent proposal by Zitzler et al. (2010),
we consider multiobjective optimization as a set problem. Then, we give a
general definition of set-based multiobjective fitness landscapes. An
experimental set-based fitness landscape analysis is conducted on the
multiobjective NK-landscapes with objective correlation. The aim is to adapt
and to enhance the comprehensive design of set-based multiobjective search
approaches, motivated by an a priori analysis of the corresponding set problem
properties
Coarse-Grained Barrier Trees of Fitness Landscapes
Recent literature suggests that local optima in fitness landscapes are clustered, which offers an explanation of why perturbation-based metaheuristics often fail to find the global optimum: they become trapped in a sub-optimal cluster. We introduce a method to extract and visualize the global organization of these clusters in form of a barrier tree. Barrier trees have been used to visualize the barriers between local optima basins in fitness landscapes. Our method computes a more coarsely grained tree to reveal the barriers between clusters of local optima. The core element is a new variant of the flooding algorithm, applicable to local optima networks, a compressed representation of fitness landscapes. To identify the clusters, we apply a community detection algorithm. A sample of 200 NK fitness landscapes suggests that the depth of their coarse-grained barrier tree is related to their search difficulty
PageRank centrality for performance prediction: the impact of the local optima network model
A local optima network (LON) compresses relevant features of fitness landscapes in a complex network, where nodes are local optima and edges represent transition probabilities between different basins of attraction. Previous work has found that the PageRank centrality of local optima can be used to predict the success rate and average fitness achieved by local search based metaheuristics. Results are available for LONs where edges describe either basin transition probabilities or escape edges. This paper studies the interplay between the type of LON edges and the ability of the PageRank centrality for the resulting LON to predict the performance of local search based metaheuristics. It finds that LONs are stochastic models of the search heuristic. Thus, to achieve an accurate prediction, the definition of the LON edges must properly reflect the type of diversification steps used in the metaheuristic. LONs with edges representing basin transition probabilities capture well the diversification mechanism of simulated annealing which sometimes also accepts worse solutions that allow the search process to pass between basins. In contrast, LONs with escape edges capture well the diversification step of iterated local search, which escapes from local optima by applying a larger perturbation step
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