Optimising Monotone Chance-Constrained Submodular Functions Using Evolutionary Multi-Objective Algorithms
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Many real-world optimisation problems can be stated in terms of submodular functions. A lot of evolutionary multi-objective algorithms have recently been analyzed and applied to submodular problems with different types of constraints. We present a first runtime analysis of evolutionary multi-objective algorithms for chance-constrained submodular functions. Here, the constraint involves stochastic components and the constraint can only be violated with a small probability of alpha. We show that the GSEMO algorithm obtains the same worst case performance guarantees as recently analyzed greedy algorithms. Furthermore, we investigate the behavior of evolutionary multi-objective algorithms such as GSEMO and NSGA-II on different submodular chance constrained network problems. Our experimental results show that this leads to significant performance improvements compared to the greedy algorithm.
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