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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…

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…

Local Optima Networks (LONs) have been recently proposed as an alternative model of combinatorial fitness landscapes. The model compresses the information given by the whole search space into a smaller mathematical object that is the graph…

This study investigates the use of local optima network (LON) analysis, a derivative of the fitness landscape of candidate solutions, to characterise and visualise the neural architecture space. The search space of feedforward neural…

Morpho-evolution (ME) refers to the simultaneous optimisation of a robot's design and controller to maximise performance given a task and environment. Many genetic encodings have been proposed which are capable of representing design and…

We propose Local Optima Networks (LONs) as a formal framework for modeling innovation dynamics. A LON is a directed weighted graph in which nodes represent locally stable technological configurations and edges encode transition…

We propose a new way of looking at local optima networks (LONs). LONs represent fitness landscapes; the nodes are local optima, and the edges are search transitions between them. Many metrics computed on LONs have been proposed and shown to…

Local Optima Networks (LONs) represent the global structure of search spaces as graphs, but their construction requires iterative execution of a search algorithm to find local optima and approximate transitions between Basins of Attraction…

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…

One of the most common problem-solving heuristics is by analogy. For a given problem, a solver can be viewed as a strategic walk on its fitness landscape. Thus if a solver works for one problem instance, we expect it will also be effective…

The local optima network model has proved useful in the past in connection with combinatorial optimization problems. Here we examine its extension to the real continuous function domain. Through a sampling process, the model builds a…

Using a recently proposed model for combinatorial landscapes, Local Optima Networks (LON), we conduct a thorough analysis of two types of instances of the Quadratic Assignment Problem (QAP). This network model is a reduction of the…

There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High…

Modern machine learning often relies on optimizing a neural network's parameters using a loss function to learn complex features. Beyond training, examining the loss function with respect to a network's parameters (i.e., as a loss…

Network-based representations of fitness landscapes have grown in popularity in the past decade; this is probably because of growing interest in explainability for optimisation algorithms. Local optima networks (LONs) have been especially…

We present Locally Orderless Networks (LON) and its theoretic foundation which links it to Convolutional Neural Networks (CNN), to Scale-space histograms, and measurement theory. The key elements are a regular sampling of the bias and the…

Viewing neural network models in terms of their loss landscapes has a long history in the statistical mechanics approach to learning, and in recent years it has received attention within machine learning proper. Among other things, local…

This paper extends a recently proposed model for combinatorial landscapes: Local Optima Networks (LON), to incorporate a first-improvement (greedy-ascent) hill-climbing algorithm, instead of a best-improvement (steepest-ascent) one, for the…

Optimization of high-dimensional black-box functions is an extremely challenging problem. While Bayesian optimization has emerged as a popular approach for optimizing black-box functions, its applicability has been limited to…

Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but…