Archive-based Single-Objective Evolutionary Algorithms for Submodular Optimization
This work addresses a key bottleneck in combinatorial optimization for researchers and practitioners, offering a novel approach to handle constrained submodular problems more effectively.
The paper tackles constrained submodular optimization problems, which are NP-hard and challenging for single-objective evolutionary algorithms due to local optima, by introducing new single-objective algorithms that are provably successful for different classes of these problems.
Constrained submodular optimization problems play a key role in the area of combinatorial optimization as they capture many NP-hard optimization problems. So far, Pareto optimization approaches using multi-objective formulations have been shown to be successful to tackle these problems while single-objective formulations lead to difficulties for algorithms such as the $(1+1)$-EA due to the presence of local optima. We introduce for the first time single-objective algorithms that are provably successful for different classes of constrained submodular maximization problems. Our algorithms are variants of the $(1+λ)$-EA and $(1+1)$-EA and increase the feasible region of the search space incrementally in order to deal with the considered submodular problems.