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

Recherche locale multi-objectif basée sur les ensembles

Date du colloque : 04/2012National audienc

On the Neutrality of Flowshop Scheduling Fitness Landscapes

Solving efficiently complex problems using metaheuristics, and in particular local searches, requires incorporating knowledge about the problem to solve. In this paper, the permutation flowshop problem is studied. It is well known that in such problems, several solutions may have the same fitness value. As this neutrality property is an important one, it should be taken into account during the design of optimization methods. Then in the context of the permutation flowshop, a deep landscape analysis focused on the neutrality property is driven and propositions on the way to use this neutrality to guide efficiently the search are given.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Tunnelling Crossover Networks for the Asymmetric TSP

Local optima networks are a compact representation of fitness landscapes that can be used for analysis and visualisation. This paper provides the first analysis of the Asymmetric Travelling Salesman Problem using local optima networks. These are generated by sampling the search space by recording the progress of an existing evolutionary algorithm based on the Generalised Asymmetric Partition Crossover. They are compared to networks sampled through the Chained Lin-Kernighan heuristic across 25 instances. Structural differences and similarities are identified, as well as examples where crossover smooths the landscape

Insights into the feature selection problem using local optima networks

The binary feature selection problem is investigated in this paper. Feature selection fitness landscape analysis is done, which allows for a better understanding of the behaviour of feature selection algorithms. Local optima networks are employed as a tool to visualise and characterise the fitness landscapes of the feature selection problem in the context of classification. An analysis of the fitness landscape global structure is provided, based on seven real-world datasets with up to 17 features. Formation of neutral global optima plateaus are shown to indicate the existence of irrelevant features in the datasets. Removal of irrelevant features resulted in a reduction of neutrality and the ratio of local optima to the size of the search space, resulting in improved performance of genetic algorithm search in finding the global optimum

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

Global Landscape Structure and the Random MAX-SAT Phase Transition

We revisit the fitness landscape structure of random MAX-SAT instances, and address the question: what structural features change when we go from easy underconstrained instances to hard overconstrained ones? Some standard techniques such as autocorrelation analysis fail to explain what makes instances hard to solve for stochastic local search algorithms, indicating that deeper landscape features are required to explain the observed performance differences. We address this question by means of local optima network (LON) analysis and visualisation. Our results reveal that the number, size, and, most importantly, the connectivity pattern of local and global optima change significantly over the easy-hard transition. Our empirical results suggests that the landscape of hard MAX-SAT instances may feature sub-optimal funnels, that is, clusters of sub-optimal solutions where stochastic local search methods can get trapped

The Connectivity of NK Landscapes' Basins: A Network Analysis

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 where the 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 small NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties can be related to the search difficulty on the underlying NK landscapes with varying values of K.Comment: Artificial Life XI, Winchester : France (2008