Parametric Pareto Set Learning: Amortizing Multi-Objective Optimization With Parameters
提出参数化帕累托集学习框架，通过超网络学习从参数到帕累托集的映射，实现任意参数下最优解的实时推理，显著提升动态多目标优化问题的求解质量和适应性。
Parametric multiobjective optimization (PMO) addresses the challenge of solving an infinite number of multiobjective optimization problems (MOPs), where optimal solutions must adapt to varying parameters. Traditional methods, such as parameterized multiobjective evolutionary algorithms (MOEAs), generate only a finite set of solutions and are unable to capture the continuous structure of the Pareto set across the entire parameter space, thereby leaving critical trade-offs unexplored. To overcome these challenges, we propose parametric Pareto set learning (PPSL), a novel framework that leverages amortized optimization to learn a unified mapping from parameters to the Pareto set with respect to the parameter. The framework employs a hypernetwork conditioned on input parameters, enabling real-time inference of optimal solutions for any parameter setting without the need for repeated optimization. By integrating low-rank adaptation (LoRA), PPSL achieves computational efficiency and scalability for PMO problems. To verify its effectiveness, we apply PPSL to dynamic multiobjective optimization problems (DMOPs) and MOPs with shared component design, where the parameters encode time-dependent or modular constraints. The experimental results demonstrate that PPSL significantly outperforms existing methods in terms of solution quality and adaptability. Importantly, we emphasize that PPSL is not limited to the two problems tested in this work; it is broadly applicable to any real-world problem that can be modeled as a PMO problem, offering a versatile and powerful solution for a wide range of applications. Code is available at:.