  An important challenge in reinforcement learning, including evolutionary
robotics, is to solve multimodal problems, where agents have to act in
qualitatively different ways depending on the circumstances. Because multimodal
problems are often too difficult to solve directly, it is helpful to take
advantage of staging, where a difficult task is divided into simpler subtasks
that can serve as stepping stones for solving the overall problem.
Unfortunately, choosing an effective ordering for these subtasks is difficult,
and a poor ordering can reduce the speed and performance of the learning
process. Here, we provide a thorough introduction and investigation of the
Combinatorial Multi-Objective Evolutionary Algorithm (CMOEA), which avoids
ordering subtasks by allowing all combinations of subtasks to be explored
simultaneously. We compare CMOEA against two algorithms that can similarly
optimize on multiple subtasks simultaneously: NSGA-II and Lexicase Selection.
The algorithms are tested on a multimodal robotics problem with six subtasks as
well as a maze navigation problem with a hundred subtasks. On these problems,
CMOEA either outperforms or is competitive with the controls. Separately, we
show that adding a linear combination over all objectives can improve the
ability of NSGA-II to solve these multimodal problems. Lastly, we show that, in
contrast to NSGA-II and Lexicase Selection, CMOEA can effectively leverage
secondary objectives to achieve state-of-the-art results on the robotics task.
In general, our experiments suggest that CMOEA is a promising, state-of-the-art
algorithm for solving multimodal problems.
