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Abstract
The search landscape is a common metaphor to describe the structure of computational search spaces. Different landscape metrics can be computed and used to predict search difficulty. Yet, the metaphor falls short in visualisation terms because it is hard to represent complex landscapes, both in terms of size and dimensionality. This paper combines local optima networks, as a compact representation of the global structure of a search space, and dimensionality reduction, using the t-distributed stochastic neighbour embedding algorithm, in order to both bring the metaphor to life and convey new insight into the search process. As a case study, two benchmark programs, under a genetic improvement bug-fixing scenario, are analysed and visualised using the proposed method. Local optima networks for both iterated local search and a hybrid genetic algorithm, across different neighbourhoods, are compared, highlighting the differences in how the landscape is explored.
Highlights
Fitness landscapes have their roots in theoretical biology, and are nowadays widely used to describe the dynamics of both evolutionary and local search algorithms
The main contributions are: 1. Combining local optima networks and dimensionality reduction through the t-SNE algorithm to visualise the global structure of search landscapes
Since our objective is to visualise the global structure of fitness landscapes, we want to be able to display a large number of local optima and the connections between them
Summary
Fitness landscapes have their roots in theoretical biology, and are nowadays widely used to describe the dynamics of both evolutionary and local search algorithms (where they are referred to as search landscapes). Constructed barrier trees for MAX-SAT problems with up to 40 variables using branchand-bound to find only the best local optima in the space It is not the intention of this paper to propose a fully fledged standalone solution for visualising search landscapes and networks. Its purpose is to highlight that existing visualisation techniques can be added to the researcher’s or the practitioner’s toolkit when analysing and communicating results of a local optima network analysis Applying those techniques to a number of genetic improvement scenarios demonstrates the applicability of the techniques to a broader range of problems beyond traditional combinatorial optimisation benchmark problems such as the Travelling Salesman Problem. Combining local optima networks and dimensionality reduction through the t-SNE algorithm to visualise the global structure of search landscapes.
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