Tutorial on Evolutionary Multiobjective Optimization

Abstract-Multi-objective optimization has been traditionally a matter of study in domains like engineering or finance, with little impact on games research. However, action-decision based on multi-objective evaluation may be beneficial in order to obtain a high quality level of play. This paper presents a Multi-objective Monte Carlo Tree Search algorithm for planning and control in real-time game domains, those where the time budget to decide the next move to make is close to 40ms. A comparison is made between the proposed algorithm, a single-objective version of Monte Carlo Tree Search and a rolling horizon implementation of Non-dominated Sorting Evolutionary Algorithm II (NSGA-II). Two different benchmarks are employed, Deep Sea Treasure and the Multi-Objective Physical Travelling Salesman Problem. Using the same heuristics on each game, the analysis is focused on how well the algorithms explore the search space. Results show that the algorithm proposed outperforms NSGA-II. Additionally, it is also shown that the algorithm is able to converge to different optimal solutions or the optimal Pareto front (if achieved during search).

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“…In the objective space, yellow dots are non-optimal objective vectors, while blue dots form a non-dominated set. From [17].…”

Section: Monte Carlo Tree Searchmentioning

confidence: 99%