Effectiveness of approximation strategy in surrogate-assisted fireworks algorithm

We investigate the effectiveness of approximation strategy in a surrogate-assisted fireworks algorithm, which obtains the elite from approximate fitness landscape to enhance its optimization performance. We study the effectiveness of approximation strategy from the aspects of approximation method, sampling data selection method and sampling size. We discuss and analyse the optimization performance of each method. For the approximation method, we use least square approximation, spline interpolation, Newton interpolation, and support vector regression to approximate fitness landscape of fireworks algorithm in projected lower dimensional, original and higher dimensional search space. With regard to the sampling data selection method, we define three approaches, i.e., best sampling method, distance near the best fitness individual sampling method, and random sampling method to investigate each sampling method’s performance. With regard to sample size, this is set as 3, 5, and 10 sampling data in both the approximation method and sampling method. We discuss and compare the optimization performance of each method using statistical tests. The advantages of the fireworks algorithm, a number of open topics, and new discoveries arising from evaluation results, such as multi-production mechanism of the fireworks algorithm, optimization performance of each method, elite rank, interpolation times and extrapolation times of elites are analysed and discussed.