Stochastic Population Update Can Provably Be Helpful in Multi-Objective Evolutionary Algorithms

2023-06-05

International Joint Conference on Artificial Intelligence

AI Summary

This paper investigates whether deterministic population update mechanisms in multi-objective evolutionary algorithms (MOEAs) can be replaced by stochastic ones to improve search efficiency. Method: We conduct theoretical runtime analysis and empirical evaluation of stochastic population updates on the SMS-EMOA and NSGA-II frameworks, applied to the bi-objective OneJumpZeroJump and RealRoyalRoad benchmark problems. Our approach integrates rigorous runtime analysis, modeling of nondominated sorting, and probabilistic selection mechanisms. Contribution/Results: We provide the first strict runtime proof showing that stochastic updates reduce the expected optimization time of SMS-EMOA on OneJumpZeroJump from exponential to polynomial—achieving exponential speedup. This challenges the long-standing paradigm of relying exclusively on deterministic updates in MOEAs. Empirical results further demonstrate that multiple MOEA variants adopting stochastic updates exhibit significantly improved convergence and diversity across benchmarks.

Abstract

Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update is a key component in multi-objective EAs (MOEAs), and it is performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the first population-size ranked solutions (based on some selection criteria, e.g., non-dominated sorting, crowdedness and indicators) from the collections of the current population and newly-generated solutions. In this paper, we question this practice. We analytically present that introducing randomness into the population update procedure in MOEAs can be beneficial for the search. More specifically, we prove that the expected running time of a well-established MOEA (SMS-EMOA) for solving a commonly studied bi-objective problem, OneJumpZeroJump, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed stochastic population update method. This work is an attempt to challenge a common practice for the population update in MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.

Problem

• Stochastic population update in MOEAs
• Reduces expected running time exponentially
• Improves search efficiency in multi-objective optimization

Innovation

• Stochastic population update mechanism
• Exponentially decreased running time
• Improved multi-objective evolutionary algorithms