3 research outputs found
Clustering of Local Optima in Combinatorial Fitness Landscapes
Using the recently proposed model of combinatorial landscapes: local optima
networks, we study the distribution of local optima in two classes of instances
of the quadratic assignment problem. Our results indicate that the two problem
instance classes give rise to very different configuration spaces. For the
so-called real-like class, the optima networks possess a clear modular
structure, while the networks belonging to the class of random uniform
instances are less well partitionable into clusters. We briefly discuss the
consequences of the findings for heuristically searching the corresponding
problem spaces.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
Information flow and Laplacian dynamics on local optima networks
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 be linked to metaheuristic search difficulty. These have
typically considered LONs as describing static structures. In contrast to this,
Laplacian dynamics (LD) is an approach to consider the information flow across
a network as a dynamical process. We adapt and apply LD to the context of LONs.
As a testbed, we consider instances from the quadratic assignment problem (QAP)
library. Metrics related to LD are proposed and these are compared with
existing LON metrics. The results show that certain LD metrics are strong
predictors of metaheuristic performance for iterated local search and tabu
search
Generalised Pattern Search with Restarting Fitness Landscape Analysis
Fitness landscape analysis for optimisation is a technique that involves analysing black-box optimisation problems to extract pieces of information about the problem, which can beneficially inform the design of the optimiser. Thus, the design of the algorithm aims to address the specific features detected during the analysis of the problem. Similarly, the designer aims to understand the behaviour of the algorithm, even though the problem is unknown and the optimisation is performed via a metaheuristic method. Thus, the algorithmic design made using fitness landscape analysis can be seen as an example of explainable AI in the optimisation domain. The present paper proposes a framework that performs fitness landscape analysis and designs a Pattern Search (PS) algorithm on the basis of the results of the analysis. The algorithm is implemented in a restarting fashion: at each restart, the fitness landscape analysis refines the analysis of the problem and updates the pattern matrix used by PS. A computationally efficient implementation is also presented in this study. Numerical results show that the proposed framework clearly outperforms standard PS and another PS implementation based on fitness landscape analysis. Furthermore, the two instances of the proposed framework considered in this study are competitive with popular algorithms present in the literature