An experimental study of prediction methods in robust optimization over time

Abstract

Robust Optimization Over Time (ROOT) is a new method of solving Dynamic Optimization Problems in respect to choosing a robust solution, that would last over a number of environment changes, rather than the approach that chooses the optimal solution at every change. ROOT methods currently show that ROOT can be solved by predicting an individual fitness for a number of future environment changes. In this work, a benchmark problem based on the Modified Moving Peaks Benchmark (MMPB) is proposed that includes an attractor heuristic, that guides optima to a determined location in the environment, resulting in a more predictable optimum. We study a number of time series forecasting methods to test different prediction methods of future fitness values in a ROOT method. Four time series regression techniques are considered as the prediction method: Linear and Quadratic Regression, an Autoregressive model, and Support Vector Regression. We find that there is not much difference in choosing a simple Linear Regression to more advanced prediction methods. We also suggest that current benchmark problems that cannot be predicted will deceive the optimizer and ROOT framework as the peaks may move using a random walk. Results show an improvement in comparison with MMPB used in most ROOT studies.