On the selection of fitness landscape analysis metrics for continuous optimization problems

Selecting the best algorithm for a given optimization problem is non-trivial due to large number of existing algorithms and high complexity of problems. A possible way to tackle this challenge is to attempt to understand the problem complexity. Fitness Landscape Analysis (FLA) metrics are widely used techniques to extract characteristics from problems. Based on the extracted characteristics, machine learning methods are employed to select the optimal algorithm for a given problem. Therefore, the accuracy of the algorithm selection framework heavily relies on the choice of FLA metrics. Although researchers have paid great attention to designing FLA metrics to quantify the problem characteristics, there is still no agreement on which combination of FLA metrics should be employed. In this paper, we present some well-performed FLA metrics, discuss their contributions and limitations in detail, and map each FLA metric to the captured problem characteristics. Moreover, computational complexity of each FLA metric is carefully analysed. We propose two criteria to follow when selecting FLA metrics. We hope our work can help researchers identify the best combination of FLA metrics.