Analysis of Multitasking Pareto Optimization for Monotone Submodular Problems

TL;DR

This paper introduces multitasking Pareto optimization for monotone submodular problems, enabling simultaneous solutions to related problems with shared functions and constraints, leading to efficiency gains.

Contribution

It presents a novel multitasking formulation for monotone submodular problems with shared functions, demonstrating theoretical and experimental benefits over separate runs.

Findings

Multitasking approaches produce small Pareto fronts.

Shared solutions improve efficiency compared to independent runs.

Experimental results highlight effectiveness for uniform costs, limitations for varied costs.

Abstract

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately. We introduce multitasking formulations of these problems that are an effective way to solve multiple related problems with a single run. In our setting the given problems share a monotone submodular function $f$ but have different knapsack constraints. We examine the case where elements within a constraint have the same cost and show that our multitasking formulations result in small Pareto fronts. This allows the population to share solutions between all problems leading to significant improvements compared to running several classical approaches independently. Using rigorous runtime analysis, we analyze the expected time until the introduced multitasking approaches obtain a $(1-1/e)$-approximation for each of the given problems. Our experimental investigations for the maximum coverage problem give further insight into the dynamics behind how the approach works and doesn't work in practice for problems where elements within a constraint also have varied costs.