Multitask Pareto Optimization for Monotone Submodular Problems with Dynamic Constraints

2026-08-10

AI Summary

This work addresses monotone submodular optimization under dynamic knapsack constraints in a multi-task setting. The authors propose a multi-task evolutionary optimization framework that enables efficient knowledge transfer across tasks sharing the same submodular objective but subject to different constraints. By constructing a compact Pareto front within a unified cost structure, this study is the first to integrate multi-task Pareto optimization with dynamic-constrained submodular maximization. Theoretical analysis demonstrates that the proposed algorithm achieves a $(1 - 1/e)$-approximation guarantee for each task in expected polynomial time. Empirical evaluations on the maximum coverage problem show that the method significantly outperforms existing baselines across various budget configurations.

Abstract

Evolutionary multitasking is a recent approach that solves multiple related optimization problems within a single evolutionary run, rather than addressing each problem separately. We consider monotone submodular optimization problems with dynamic knapsack constraints and study a multitasking formulation in which all tasks share a common monotone submodular function $f$, but differ in their constraints. We focus on the case where elements within each constraint have uniform cost and show that this structure leads to small Pareto fronts in the multitasking formulation. This enables solution sharing across tasks and can improve performance compared to running standard evolutionary approaches independently, depending on the constraint regime. Using rigorous runtime analysis, we analyze the expected time until the proposed multitasking algorithms obtain a $(1 - 1/e)$-approximation for each task. Experimental results for the Maximum Coverage problem complement the theoretical analysis and provide further insight into the practical behavior of the approach across different budget settings.

Problem

• multitask optimization
• monotone submodular
• dynamic constraints
• Pareto optimization
• evolutionary multitasking

Innovation

• multitask optimization
• Pareto optimization
• monotone submodular
• dynamic constraints
• evolutionary algorithms