On Scalability of Multi-Objective Evolutionary Algorithms on Combinatorial Optimisation Problems

2026-04-20

AI Summary

This study investigates the scalability of multi-objective evolutionary algorithms (MOEAs) on combinatorial optimization problems as problem dimensionality increases from 50 to 5,000. Through a comparative analysis of SEMO, NSGA-II, SMS-EMOA, and MOEA/D, the authors observe that SEMO exhibits significantly slower convergence in high-dimensional settings due to its lack of crossover operators. By innovatively incorporating crossover into SEMO, they achieve a substantial improvement in convergence efficiency, albeit with a slight reduction in the uniformity of the Pareto front. The findings underscore the critical role of crossover mechanisms in enabling effective search in large-scale multi-objective combinatorial optimization and provide empirical evidence to guide the design of scalable MOEAs.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Scalability of evolutionary algorithms refers to assessing how their performance changes as problem size increases. In the area of multi-objective optimisation, research on the scalability of multi-objective evolutionary algorithms (MOEAs) has predominantly focussed on continuous problems. However, multi-objective combinatorial optimisation problems (MOCOPs) differ from continuous ones. Their discrete and rigid structure often brings rugged landscape, numerous local optimal solutions and disjoint global optimal regions. This leads to different behaviour of MOEAs. For example, SEMO, a simple MOEA without mating selection and diversity maintenance mechanisms, has been shown to be highly competitive, and in many cases to outperform more sophisticated MOEAs on MOCOPs. Yet, it remains unclear whether such findings hold for large-scale cases. In this paper, we conduct an empirical investigation into the scalability of MOEAs on combinatorial problems, with problem size from 50 to 5,000. Our results show that SEMO experiences a decline in convergence speed as dimensionality increases, compared to other MOEAs such as NSGA-II, SMS-EMOA and MOEA/D. We further demonstrate that the absence of crossover is a major contributor to SEMO's underperformance in large-scale problems, and that incorporating crossover into SEMO can substantially accelerate convergence in general, despite being detrimental in spreading solutions over the Pareto front.

Problem

• scalability
• multi-objective evolutionary algorithms
• combinatorial optimisation problems
• large-scale optimization
• Pareto front

Innovation

• scalability
• multi-objective evolutionary algorithms
• combinatorial optimisation
• crossover operator
• SEMO