Papers › Improved Evolutionary Algorithms for Submodular Maximization with Cost Constraints
Improved Evolutionary Algorithms for Submodular Maximization with Cost Constraints
Yanhui Zhu, Samik Basu, A Pavan
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We present an evolutionary algorithm evo-SMC for the problem of Submodular Maximization under Cost constraints (SMC). Our algorithm achieves 1/2-approximation with a high probability 1-1/n within 𝒪(n²Kᵦ) iterations, where Kᵦ denotes the maximum size of a feasible solution set with cost constraint β. To the best of our knowledge, this is the best approximation guarantee offered by evolutionary algorithms for this problem. We further refine evo-SMC, and develop st-evo-SMC. This stochastic version yields a significantly faster algorithm while maintaining the approximation ratio of 1/2, with probability 1-ϵ. The required number of iterations reduces to 𝒪(nKᵦlog(1/ϵ)/p), where the user defined parameters p ∈(0,1] represents the stochasticity probability, and ϵ∈(0,1] denotes the error threshold. Finally, the empirical evaluations carried out through extensive experimentation substantiate the efficiency and effectiveness of our proposed algorithms. Our algorithms consistently outperform existing methods, producing higher-quality solutions.
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