Abstract
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.
Highlights
Findings in the continuous domain are not entirely conclusive [2], No Free Lunch Theorems [42] suggest that algorithms are designed to address specific optimisation problems.Many real-world problems can be formulated as blackbox optimisation problems [3]
In the tables a “+” indicates that the proposed algorithm (GPSRFLA/Adaptive Covariance Patter Search (ACPS)) significantly outperformed its competitor, a “−” indicates that the competitor significantly outperformed the proposed algorithm, and a “=” indicates that there is no significant difference in performance
These plots confirm the reports on Table 4; at higher dimensions, Covariance Matrix Adaptive Evolution Strategy (CMAES) and ACPS both appear to be inadequate at solving some problems but are very well suited for others
Summary
Another recent example of an algorithm designed on the basis of a fitness landscape analysis for the continuous domain is the Covariance Pattern Search (CPS) [30, 31] This algorithm characterises the geometry of the problem by sampling points whose objective function is below a certain threshold. F objective function candidate solution trial solution ns number of samples for the analysis f objective function kv since of the space where points are sampled data set for the analysis ( nv its number of rows) covariance of the points in eigenvector (basis) matrix of i eigenvalue of k generating matrix k pattern matrix radius. Algorithm 5 shows the pseudocode of the proposed GPS designed on the basis of the fitness landscape analysis
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