A Local Optima Network View of Real Function Fitness Landscapes

TL;DR

This paper extends the local optima network model to real continuous functions, providing a graph-based framework that helps analyze and visualize function landscapes and their difficulty for optimization algorithms.

Contribution

It introduces a method to construct local optima networks for real functions, linking graph properties to problem hardness and aiding in problem classification and algorithm design.

Findings

Function hardness correlates with graph properties of local optima networks.

The model facilitates analysis and visualization of high-dimensional function landscapes.

Potential for improved metaheuristic strategies based on network analysis.

Abstract

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 weighted directed graph which captures the function's minima basin structure and its interconnection and which can be easily manipulated with the help of complex networks metrics. We show that the model provides a complementary view of function spaces that is easier to analyze and visualize, especially at higher dimension. In particular, we show that function hardness as represented by algorithm performance, is strongly related to several graph properties of the corresponding local optima network, opening the way for a classification of problem difficulty according to the corresponding graph structure and with possible extensions in the design of better metaheuristic approaches.