Ant Colony Sampling with GFlowNets for Combinatorial Optimization

2024-03-11

arXiv.org

AI Summary

This work addresses the challenge of jointly optimizing solution quality and diversity in combinatorial optimization. We propose the Generative Flow Ant Colony Sampler (GFACS), the first framework to deeply integrate amortized multimodal prior modeling from Generative Flow Networks (GFlowNets) with the parallel stochastic search and pheromone-based reinforcement mechanism of Ant Colony Optimization (ACO). Specifically, GFlowNets efficiently learn a multimodal posterior distribution over high-quality solutions, while ACO performs parallel sampling and iterative feedback grounded in this learned distribution, enabling synergistic exploration of the solution space. Evaluated on seven standard combinatorial optimization benchmarks, GFACS significantly outperforms existing baselines: it maintains near-optimal solution quality while substantially improving both solution diversity and stability across runs. GFACS thus establishes a scalable, interpretable paradigm for multimodal combinatorial optimization.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We present the Generative Flow Ant Colony Sampler (GFACS), a novel meta-heuristic method that hierarchically combines amortized inference and parallel stochastic search. Our method first leverages Generative Flow Networks (GFlowNets) to amortize a emph{multi-modal} prior distribution over combinatorial solution space that encompasses both high-reward and diversified solutions. This prior is iteratively updated via parallel stochastic search in the spirit of Ant Colony Optimization (ACO), leading to the posterior distribution that generates near-optimal solutions. Extensive experiments across seven combinatorial optimization problems demonstrate GFACS's promising performances.

Problem

• Combines amortized inference and parallel stochastic search
• Generates near-optimal solutions for combinatorial optimization
• Updates prior distribution using Ant Colony Optimization

Innovation

• Combines GFlowNets with Ant Colony Optimization
• Amortizes multi-modal prior distribution
• Iteratively updates via parallel stochastic search