Ant Colony Sampling with GFlowNets for Combinatorial Optimization

This paper introduces the Generative Flow Ant Colony Sampler (GFACS), a novel neural-guided meta-heuristic algorithm for combinatorial optimization. GFACS integrates generative flow networks (GFlowNets) with the ant colony optimization (ACO) methodology. GFlowNets, a generative model that learns a constructive policy in combinatorial spaces, enhance ACO by providing an informed prior distribution of decision variables conditioned on input graph instances. Furthermore, we introduce a novel combination of training tricks, including search-guided local exploration, energy normalization, and energy shaping to improve GFACS. Our experimental results demonstrate that GFACS outperforms baseline ACO algorithms in seven CO tasks and is competitive with problem-specific heuristics for vehicle routing problems. The source code is available at \url{https://github.com/ai4co/gfacs}.

Genetic-guided GFlowNets: Advancing in Practical Molecular Optimization Benchmark

This paper proposes a novel variant of GFlowNet, genetic-guided GFlowNet (Genetic GFN), which integrates an iterative genetic search into GFlowNet. Genetic search effectively guides the GFlowNet to high-rewarded regions, addressing global over-exploration that results in training inefficiency and exploring limited regions. In addition, training strategies, such as rank-based replay training and unsupervised maximum likelihood pre-training, are further introduced to improve the sample efficiency of Genetic GFN. The proposed method shows a state-of-the-art score of 16.213, significantly outperforming the reported best score in the benchmark of 15.185, in practical molecular optimization (PMO), which is an official benchmark for sample-efficient molecular optimization. Remarkably, ours exceeds all baselines, including reinforcement learning, Bayesian optimization, generative models, GFlowNets, and genetic algorithms, in 14 out of 23 tasks.

Solving NP-hard Min-max Routing Problems as Sequential Generation with Equity Context

Min-max routing problems aim to minimize the maximum tour length among agents as they collaboratively visit all cities, i.e., the completion time. These problems include impactful real-world applications but are known as NP-hard. Existing methods are facing challenges, particularly in large-scale problems that require the coordination of numerous agents to cover thousands of cities. This paper proposes a new deep-learning framework to solve large-scale min-max routing problems. We model the simultaneous decision-making of multiple agents as a sequential generation process, allowing the utilization of scalable deep-learning models for sequential decision-making. In the sequentially approximated problem, we propose a scalable contextual Transformer model, Equity-Transformer, which generates sequential actions considering an equitable workload among other agents. The effectiveness of Equity-Transformer is demonstrated through its superior performance in two representative min-max routing tasks: the min-max multiple traveling salesman problem (min-max mTSP) and the min-max multiple pick-up and delivery problem (min-max mPDP). Notably, our method achieves significant reductions of runtime, approximately 335 times, and cost values of about 53% compared to a competitive heuristic (LKH3) in the case of 100 vehicles with 1,000 cities of mTSP. We provide reproducible source code: https://github.com/kaist-silab/equity-transformer