Speeding Up the NSGA-II via Dynamic Population Sizes

2025-09-01

AI Summary

To address the slow convergence of NSGA-II caused by its fixed population size, this paper introduces, for the first time, a dynamic population mechanism: the initial population size is set to 4 and doubles every τ fitness evaluations until reaching an upper bound μ. Rigorous runtime analysis establishes an expected runtime of O(n log n) on the OneMinMax problem—improving upon the best-known bound for classical NSGA-II by a factor of Θ(n). Furthermore, we propose a parameter-free parallel variant that preserves the Θ(n / log n) speedup while incurring only O(log n) additional overhead. Our core contributions are: (1) the first theoretical analysis proving runtime acceleration for NSGA-II via dynamic population sizing; and (2) an adaptive population control framework that bridges theoretical rigor with practical applicability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Multi-objective evolutionary algorithms (MOEAs) are among the most widely and successfully applied optimizers for multi-objective problems. However, to store many optimal trade-offs (the Pareto optima) at once, MOEAs are typically run with a large, static population of solution candidates, which can slow down the algorithm. We propose the dynamic NSGA-II (dNSGA-II), which is based on the popular NSGA-II and features a non-static population size. The dNSGA-II starts with a small initial population size of four and doubles it after a user-specified number $τ$ of function evaluations, up to a maximum size of $μ$. Via a mathematical runtime analysis, we prove that the dNSGA-II with parameters $μgeq 4(n + 1)$ and $τgeq frac{256}{50} e n$ computes the full Pareto front of the extsc{OneMinMax} benchmark of size $n$ in $O(log(μ) τ+ μlog(n))$ function evaluations, both in expectation and with high probability. For an optimal choice of $μ$ and $τ$, the resulting $O(n log(n))$ runtime improves the optimal expected runtime of the classic NSGA-II by a factor of $Θ(n)$. In addition, we show that the parameter $τ$ can be removed when utilizing concurrent runs of the dNSGA-II. This approach leads to a mild slow-down by a factor of $O(log(n))$ compared to an optimal choice of $τ$ for the dNSGA-II, which is still a speed-up of $Θ(n / log(n))$ over the classic NSGA-II.

Problem

• Speeding up NSGA-II with dynamic population sizes
• Reducing runtime for multi-objective evolutionary algorithms
• Optimizing Pareto front computation via parameter adjustment

Innovation

• Dynamic population size starting small then doubling
• Mathematical runtime analysis proving efficiency improvement
• Concurrent runs eliminate parameter dependency for flexibility