Improved Evolutionary Algorithms for Submodular Maximization with Cost Constraints
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913470677516288 |
|---|---|
| author | Zhu, Yanhui Basu, Samik Pavan, A |
| author_facet | Zhu, Yanhui Basu, Samik Pavan, A |
| contents | 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 $\mathcal{O}(n^2K_β)$ iterations, where $K_β$ 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 $\mathcal{O}(nK_β\log{(1/ε)}/p)$, where the user defined parameters $p \in (0,1]$ represents the stochasticity probability, and $ε\in (0,1]$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved Evolutionary Algorithms for Submodular Maximization with Cost Constraints Zhu, Yanhui Basu, Samik Pavan, A Data Structures and Algorithms 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 $\mathcal{O}(n^2K_β)$ iterations, where $K_β$ 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 $\mathcal{O}(nK_β\log{(1/ε)}/p)$, where the user defined parameters $p \in (0,1]$ represents the stochasticity probability, and $ε\in (0,1]$ 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. |
| title | Improved Evolutionary Algorithms for Submodular Maximization with Cost Constraints |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2405.05942 |