Robust Optimization Over Time: Problem Difficulties and Benchmark Problems

Abstract

The focus of most research in evolutionary dynamic optimization has been tracking moving optimum (TMO). Yet, TMO does not capture all the characteristics of real-world dynamic optimization problems (DOPs), especially in situations where a solution's future fitness has to be considered. To account for a solution's future fitness explicitly, we propose to find robust solutions to DOPs, which are formulated as the robust optimization over time (ROOT) problem. In this paper we analyze two robustness definitions in ROOT and then develop two types of benchmark problems for the two robustness definitions in ROOT, respectively. The two types of benchmark problems are motivated by the inappropriateness of existing DOP benchmarks for the study of ROOT. Additionally, we evaluate four representative methods from the literature on our proposed ROOT benchmarks, in order to gain a better understanding of ROOT problems and their relationship to more popular TMO problems. The experimental results are analyzed, which show the strengths and weaknesses of different methods in solving ROOT problems with different dynamics. In particular, the real challenges of ROOT problems have been revealed for the first time by the experimental results on our proposed ROOT benchmarks.

New Sampling Strategies When Searching for Robust Solutions

“…We observe that strategies PMS- [4,8] and PMS- [8,8] perform similarly at the end of EA search process, but PMS- [4,8] converges faster than PMS- [8,8], indicating that our sampling budget adjustment can save evaluations without sacrificing the performance of the final solution. PMS- [4,10] provides the best final solution in all test problems, but converges more slowly.…”

“…We consider the setting where the sampling budget per generation is allowed to change between 4 and 8 as default, which is abbreviated as the PMS- [4,8] strategy. We firstly test the effect of rising the lower limit of PMS- [4,8]. As such, we consistently use 8 evaluations throughout the search process and denote this strategy as PMS- [8,8].…”

“…Secondly, we study the impact of increasing the upper limit on the convergence behaviour. Therefore, we include PMS- [4,10] in this experiment, whose upper limit is set to 10. The approximation region is fixed at 120% of each direction of an individual's perturbed region.…”

“…7, PMS- [4,8] and PMS- [8,8] archive has a sufficient number of samples, indicating that PMS- [4,8] saves evaluations when the average Wasserstein distance is monotonously decreasing anyway. Moreover, we observe that the convergence of PMS- [4,10] is slow at early iterations. This is because PMS-[4, 10] is allowed to spend more evaluations exploring the correct search directions at early iterations.…”

“…There are also different concepts related to robustness, including optimising the worst-case performance [3], robust optimisation over time [4], and active robustness [5]. The most widely researched robustness concept however, Xin Fei, Jürgen Branke and Nalân Gülpınar are with Warwick Business School, The University of Warwick, Coventry CV4 7AL, UK.…”