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

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

Local Optima Networks, Landscape Autocorrelation and Heuristic Search Performance

Chicano, F., Daolio F., Ochoa G., Vérel S., Tomassini M., & Alba E. (2012). Local Optima Networks, Landscape Autocorrelation and Heuristic Search Performance. (Coello, C. A. Coello, Cutello V., Deb K., Forrest S., Nicosia G., & Pavone M., Ed.).Parallel Problem Solving from Nature - PPSN XII - 12th International Conference, Taormina, Italy, September 1-5, 2012, Proceedings, Part II. 337–347.Recent developments in fitness landscape analysis include the study of Local Optima Networks (LON) and applications of the Elementary Landscapes theory. This paper represents a first step at combining these two tools to explore their ability to forecast the performance of search algorithms. We base our analysis on the Quadratic Assignment Problem (QAP) and conduct a large statistical study over 600 generated instances of different types. Our results reveal interesting links between the network measures, the autocorrelation measures and the performance of heuristic search algorithms.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Spanish Ministry of Science and Innovation and FEDER under contract TIN2011-28194. Andalusian Government under contract P07-TIC-03044. Swiss National Science Foundation for financial support under grant number 200021-124578

Communities of Minima in Local Optima Networks of Combinatorial Spaces

In this work we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted oriented transitions between their basins of attraction. We apply the approach to the detection of communities in the optima networks produced by two different classes of instances of a hard combinatorial optimization problem: the quadratic assignment problem (QAP). We provide evidence indicating that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the networks possess a clear modular structure, while the optima networks belonging to the class of random uniform instances are less well partitionable into clusters. This is convincingly supported by using several statistical tests. Finally, we shortly discuss the consequences of the findings for heuristically searching the corresponding problem spaces

Negative Slope Coefficient: A Measure to Characterize Genetic Programming Fitness Landscapes

Negative slope coefficient has been recently introduced and empirically proven a suitable hardness indicator for some well known genetic programming benchmarks, such as the even parity problem, the binomial-3 and the artificial ant on the Santa Fe trail. Nevertheless, the original definition of this measure contains several limitations. This paper points out some of those limitations, presents a new and more relevant definition of the negative slope coefficient and empirically shows the suitability of this new definition as a hardness measure for some genetic programming benchmarks, including the multiplexer, the intertwined spirals problem and the royal trees

Cost-vs-accuracy of sampling in multi-objective combinatorial exploratory landscape analysis

International audienceThe design of effective features enabling the development of automated landscape-aware techniques requires to address a number of inter-dependent issues. In this paper, we are interested in contrasting the amount of budget devoted to the computation of features with respect to: (i) the effectiveness of the features in grasping the characteristics of the landscape, and (ii) the gain in accuracy when solving an unknown problem instance by means of a feature-informed automated algorithm selection approach. We consider multi-objective combinatorial landscapes where, to the best of our knowledge, no in depth investigations have been conducted so far. We study simple cost-adjustable sampling strategies for extracting different state-of-the-art features. Based on extensive experiments, we report a comprehensive analysis on the impact of sampling on landscape feature values, and the subsequent automated algorithm selection task. In particular, we identify different global trends of feature values leading to non-trivial cost-vs-accuracy trade-off(s). Besides, we provide evidence that the sampling strategy can improve the prediction accuracy of automated algorithm selection. Interestingly, this holds independently of whether the sampling cost is taken into account or not in the overall solving budget

Cost-vs-accuracy of sampling in multi-objective combinatorial exploratory landscape analysis

International audienceThe design of effective features enabling the development of automated landscape-aware techniques requires to address a number of inter-dependent issues. In this paper, we are interested in contrasting the amount of budget devoted to the computation of features with respect to: (i) the effectiveness of the features in grasping the characteristics of the landscape, and (ii) the gain in accuracy when solving an unknown problem instance by means of a feature-informed automated algorithm selection approach. We consider multi-objective combinatorial landscapes where, to the best of our knowledge, no in depth investigations have been conducted so far. We study simple cost-adjustable sampling strategies for extracting different state-of-the-art features. Based on extensive experiments, we report a comprehensive analysis on the impact of sampling on landscape feature values, and the subsequent automated algorithm selection task. In particular, we identify different global trends of feature values leading to non-trivial cost-vs-accuracy trade-off(s). Besides, we provide evidence that the sampling strategy can improve the prediction accuracy of automated algorithm selection. Interestingly, this holds independently of whether the sampling cost is taken into account or not in the overall solving budget