Multi-objective Evolutionary Algorithms are Generally Good: Maximizing Monotone Submodular Functions over Sequences

TL;DR

This paper extends the theoretical understanding of evolutionary algorithms by analyzing their effectiveness in maximizing monotone submodular functions over sequences, demonstrating both theoretical guarantees and empirical success.

Contribution

It introduces the analysis of EAs for sequence-based submodular maximization, providing theoretical approximation guarantees and empirical validation across multiple applications.

Findings

GSEMO achieves or improves known approximation guarantees in polynomial time.

Empirical results show GSEMO performs well in various real-world applications.

Theoretical analysis covers multiple classes of sequence-based submodular functions.

Abstract

Evolutionary algorithms (EAs) are general-purpose optimization algorithms, inspired by natural evolution. Recent theoretical studies have shown that EAs can achieve good approximation guarantees for solving the problem classes of submodular optimization, which have a wide range of applications, such as maximum coverage, sparse regression, influence maximization, document summarization and sensor placement, just to name a few. Though they have provided some theoretical explanation for the general-purpose nature of EAs, the considered submodular objective functions are defined only over sets or multisets. To complement this line of research, this paper studies the problem class of maximizing monotone submodular functions over sequences, where the objective function depends on the order of items. We prove that for each kind of previously studied monotone submodular objective functions over sequences, i.e., prefix monotone submodular functions, weakly monotone and strongly submodular functions, and DAG monotone submodular functions, a simple multi-objective EA, i.e., GSEMO, can always reach or improve the best known approximation guarantee after running polynomial time in expectation. Note that these best-known approximation guarantees can be obtained only by different greedy-style algorithms before. Empirical studies on various applications, e.g., accomplishing tasks, maximizing information gain, search-and-tracking and recommender systems, show the excellent performance of the GSEMO.