Local optima networks of hard combinatorial landscapes

Combinatorial optimization involves finding an optimal solution in a finite set of options; many everyday life problems are of this kind. However, the number of options grows exponentially with the size of the problem, such that an exhaustive search for the best solution is practically infeasible beyond a certain problem size. When efficient algorithms are not available, a practical approach to obtain an approximate solution to the problem at hand, is to start with an educated guess and gradually refine it until we have a good-enough solution. Roughly speaking, this is how local search heuristics work. These stochastic algorithms navigate the problem search space by iteratively turning the current solution into new candidate solutions, guiding the search towards better solutions. The search performance, therefore, depends on structural aspects of the search space, which in turn depend on the move operator being used to modify solutions. A common way to characterize the search space of a problem is through the study of its fitness landscape, a mathematical object comprising the space of all possible solutions, their value with respect to the optimization objective, and a relationship of neighborhood defined by the move operator. The landscape metaphor is used to explain the search dynamics as a sort of potential function. The concept is indeed similar to that of potential energy surfaces in physical chemistry. Borrowing ideas from that field, we propose to extend to combinatorial landscapes the notion of the inherent network formed by energy minima in energy landscapes. In our case, energy minima are the local optima of the combinatorial problem, and we explore several definitions for the network edges. At first, we perform an exhaustive sampling of local optima basins of attraction, and define weighted transitions between basins by accounting for all the possible ways of crossing the basins frontier via one random move. Then, we reduce the computational burden by only counting the chances of escaping a given basin via random kick moves that start at the local optimum. Finally, we approximate network edges from the search trajectory of simple search heuristics, mining the frequency and inter-arrival time with which the heuristic visits local optima. Through these methodologies, we build a weighted directed graph that provides a synthetic view of the whole landscape, and that we can characterize using the tools of complex networks science. We argue that the network characterization can advance our understanding of the structural and dynamical properties of hard combinatorial landscapes. We apply our approach to prototypical problems such as the Quadratic Assignment Problem, the NK model of rugged landscapes, and the Permutation Flow-shop Scheduling Problem. We show that some network metrics can differentiate problem classes, correlate with problem non-linearity, and predict problem hardness as measured from the performances of trajectory-based local search heuristics.

Advances in MRI-based computational neuroanatomy: from morphometry to in-vivo histology.

PURPOSE OF REVIEW: Current computational neuroanatomy based on MRI focuses on morphological measures of the brain. We present recent methodological developments in quantitative MRI (qMRI) that provide standardized measures of the brain, which go beyond morphology. We show how biophysical modelling of qMRI data can provide quantitative histological measures of brain tissue, leading to the emerging field of in-vivo histology using MRI (hMRI). RECENT FINDINGS: qMRI has greatly improved the sensitivity and specificity of computational neuroanatomy studies. qMRI metrics can also be used as direct indicators of the mechanisms driving observed morphological findings. For hMRI, biophysical models of the MRI signal are being developed to directly access histological information such as cortical myelination, axonal diameters or axonal g-ratio in white matter. Emerging results indicate promising prospects for the combined study of brain microstructure and function. SUMMARY: Non-invasive brain tissue characterization using qMRI or hMRI has significant implications for both research and clinics. Both approaches improve comparability across sites and time points, facilitating multicentre/longitudinal studies and standardized diagnostics. hMRI is expected to shed new light on the relationship between brain microstructure, function and behaviour, both in health and disease, and become an indispensable addition to computational neuroanatomy.

Development of a systematic computer vision-based method to analyse and compare images of false identity documents for forensic intelligence purposes-Part I: acquisition, calibration and validation issues

Following their detection and seizure by police and border guard authorities, false identity and travel documents are usually scanned, producing digital images. This research investigates the potential of these images to classify false identity documents, highlight links between documents produced by a same modus operandi or same source, and thus support forensic intelligence efforts. Inspired by previous research work about digital images of Ecstasy tablets, a systematic and complete method has been developed to acquire, collect, process and compare images of false identity documents. This first part of the article highlights the critical steps of the method and the development of a prototype that processes regions of interest extracted from images. Acquisition conditions have been fine-tuned in order to optimise reproducibility and comparability of images. Different filters and comparison metrics have been evaluated and the performance of the method has been assessed using two calibration and validation sets of documents, made up of 101 Italian driving licenses and 96 Portuguese passports seized in Switzerland, among which some were known to come from common sources. Results indicate that the use of Hue and Edge filters or their combination to extract profiles from images, and then the comparison of profiles with a Canberra distance-based metric provides the most accurate classification of documents. The method appears also to be quick, efficient and inexpensive. It can be easily operated from remote locations and shared amongst different organisations, which makes it very convenient for future operational applications. The method could serve as a first fast triage method that may help target more resource-intensive profiling methods (based on a visual, physical or chemical examination of documents for instance). Its contribution to forensic intelligence and its application to several sets of false identity documents seized by police and border guards will be developed in a forthcoming article (part II).