Title: Learning-Based Directed Graph Abstraction of Combinatorial Spaces for Order-Preserving Search in Mixed-Combinatorial Nonlinear Optimization

Abstract:

Mixed-combinatorial nonlinear programming (MCNLP) challenges are prevalent in various engineering design and planning contexts, stemming from categorical selections, component arrangements, geometric configurations, and integrated task-motion planning. Conventional methods for representing combinatorial spaces, such as binary or integer encodings, frequently suffer from increased dimensionality, the introduction of spurious relationships, and the necessity for extra compatibility constraints. Addressing these limitations, this study leverages recent advancements in vehicle/network routing and robot planning, which focus on utilizing Graph Neural Networks (GNNs) to learn search heuristics within combinatorial domains.

Specifically, this work introduces a novel structured abstraction of the combinatorial space. It employs an Edge Field Graph Network (EFGN) to learn a mapping that transforms an undirected, fully connected graph of combinations into a directed graph that highlights improvement trajectories. To validate the efficacy of this abstraction approach for solving MCNLPs, we integrate it into a contemporary optimization framework. This framework exclusively searches through non-combinatorial (continuous) variables, utilizing the abstraction model to identify the most appropriate combination for each candidate design, functioning similarly to a recommender system.

This direction-aware abstraction offers a potentially more interpretable and scalable method for retrieving combinations than the original recommendation system within that framework. We evaluated the proposed method by integrating it with established Particle Swarm Optimization and genetic algorithm solvers across three benchmark nonlinear problems featuring varying counts of variables and combinations. The results indicate that the GNN-based recommender consistently outperforms baseline solvers utilizing indexified combinations, demonstrating superior robustness and achieving better mean optimum values across multiple experimental runs.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC