Archive-based Single-Objective Evolutionary Algorithms for Submodular Optimization

• URL: http://arxiv.org/abs/2406.13414v1
• Date: Wed, 19 Jun 2024 10:08:12 GMT
• Title: Archive-based Single-Objective Evolutionary Algorithms for Submodular Optimization
• Authors: Frank Neumann, Günter Rudolph,
• Abstract summary: We introduce for the first time single-objective algorithms that are provably successful for different classes of constrained submodular problems. Our algorithms are variants of the $(lambda)$-EA and $(+1)$-EA.
• Score: 9.852567834643288
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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