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

Local Optima Networks: A New Model of Combinatorial Fitness Landscapes

This chapter overviews a recently introduced network-based model of combinatorial landscapes: Local Optima Networks (LON). The model compresses the information given by the whole search space into a smaller mathematical object that is a graph having as vertices the local optima and as edges the possible weighted transitions between them. Two definitions of edges have been proposed: basin-transition and escape-edges, which capture relevant topological features of the underlying search spaces. This network model brings a new set of metrics to characterize the structure of combinatorial landscapes, those associated with the science of complex networks. These metrics are described, and results are presented of local optima network extraction and analysis for two selected combinatorial landscapes: NK landscapes and the quadratic assignment problem. Network features are found to correlate with and even predict the performance of heuristic search algorithms operating on these problems