Archive-Based Single-Objective Evolutionary Algorithms for Submodular Optimization

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 \((1+\lambda )\) -EA and \((1+1)\) -EA and increase the feasible region of the search space incrementally in order to deal with the considered submodular problems.