# An Efficient Evolutionary Algorithm for Minimum Cost Submodular Cover

## TL;DR

This paper introduces EASC, a novel evolutionary algorithm that efficiently approximates the Minimum Cost Submodular Cover problem in expected polynomial time, outperforming greedy and other evolutionary methods.

## Contribution

The paper presents the first polynomial-time evolutionary approximation algorithm for the Minimum Cost Submodular Cover problem, incorporating submodularity principles into the evolutionary process.

## Key findings

- EASC achieves a constant, bicriteria approximation in expected polynomial time.
- EASC outperforms greedy algorithms in practical applications.
- EASC converges faster than competing evolutionary algorithms.

## Abstract

In this paper, the Minimum Cost Submodular Cover problem is studied, which is to minimize a modular cost function such that the monotone submodular benefit function is above a threshold. For this problem, an evolutionary algorithm EASC is introduced that achieves a constant, bicriteria approximation in expected polynomial time; this is the first polynomial-time evolutionary approximation algorithm for Minimum Cost Submodular Cover. To achieve this running time, ideas motivated by submodularity and monotonicity are incorporated into the evolutionary process, which likely will extend to other submodular optimization problems. In a practical application, EASC is demonstrated to outperform the greedy algorithm and converge faster than competing evolutionary algorithms for this problem.