Recently, there has been much work on the design of general heuristics for graph-based, combinatorial optimization problems via the incorporation of Graph Neural Networks (GNNs) to learn distribution-specific solution structures.However, there is a lack of consistency in the evaluation of these heuristics, in terms of the baselines and instances chosen, which makes it difficult to assess the relative performance of the algorithms. In this paper, we propose an open-source benchmark suite MaxCut-Bench dedicated to the NP-hard Maximum Cut problem in both its weighted and unweighted variants, based on a careful selection of instances curated from diverse graph datasets. The suite offers a unified interface to various heuristics, both traditional and machine learning-based. Next, we use the benchmark in an attempt to systematically corroborate or reproduce the results of several, popular learning-based approaches, including S2V-DQN [31], ECO-DQN [4], among others, in terms of three dimensions: objective value, generalization, and scalability. Our empirical results show that several of the learned heuristics fail to outperform a naive greedy algorithm, and that only one of them consistently outperforms Tabu Search, a simple, general heuristic based upon local search. Furthermore, we find that the performance of ECO-DQN remains the same or is improved if the GNN is replaced by a simple linear regression on a subset of the features that are related to Tabu Search. Code, data, and pretrained models are available at: \url{https://github.com/ankurnath/MaxCut-Bench}.

Many complex problems encountered in both production and daily life can be conceptualized as combinatorial optimization problems (COPs) over graphs. Recent years, reinforcement learning (RL) based models have emerged as a promising direction, which treat the COPs solving as a heuristic learning problem. However, current finite-horizon-MDP based RL models have inherent limitations. They are not allowed to explore adquately for improving solutions at test time, which may be necessary given the complexity of NP-hard optimization tasks. Some recent attempts solve this issue by focusing on reward design and state feature engineering, which are tedious and ad-hoc. In this work, we instead propose a much simpler but more effective technique, named gauge transformation (GT). The technique is originated from physics, but is very effective in enabling RL agents to explore to continuously improve the solutions during test. Morever, GT is very simple, which can be implemented with less than 10 lines of Python codes, and can be applied to a vast majority of RL models. Experimentally, we show that traditional RL models with GT technique produce the state-of-the-art performances on the MaxCut problem. Furthermore, since GT is independent of any RL models, it can be seamlessly integrated into various RL frameworks, paving the way of these models for more effective explorations in the solving of general COPs.

In recent years, combining neural networks with local search heuristics has become popular in the field of combinatorial optimization. Despite its considerable computational demands, this approach has exhibited promising outcomes with minimal manual engineering. However, we have identified three critical limitations in the empirical evaluation of these integration attempts. Firstly, instances with moderate complexity and weak baselines pose a challenge in accurately evaluating the effectiveness of learning-based approaches. Secondly, the absence of an ablation study makes it difficult to quantify and attribute improvements accurately to the deep learning architecture. Lastly, the generalization of learned heuristics across diverse distributions remains underexplored. In this study, we conduct a comprehensive investigation into these identified limitations. Surprisingly, we demonstrate that a simple learned heuristic based on Tabu Search surpasses state-of-the-art (SOTA) learned heuristics in terms of performance and generalizability. Our findings challenge prevailing assumptions and open up exciting avenues for future research and innovation in combinatorial optimization.

These issues can be more intense in unsupervised tasks Combinatorial optimization is a broad and challenging due to lacking supervision information [27]. In addition, field with real-world applications ranging from traffic routing the large message vectors restrict the scalability because of to recommendation engines. As these problems are often memory overhead. In light of the local search algorithms' NP-hard [1]-[5], an efficient algorithm to find the best performance and the limitation of GNNs, we study how is solution in all instances with feasible resources is unlikely to the performance of a lightweight model directly using node exist. Therefore, researchers have turned to design heuristics features in the cardinality-constrained maximization problems, [5]-[9] in addition to approximation algorithms [10]-[16] then a natural question would be: In light of the local and enumeration [17], [18]. Among many well-known algorithms, search algorithms' performance and the limitation of GNNs, the standard greedy algorithm (Greedy) [19] provides we study how is the performance of a lightweight model the optimal (1 1/e)-approximation ratio for monotone directly using node features in the cardinality-constrained submodular instances, but this theoretical guarantee does maximization problems. Is it possible to design a lightweight not hold for non-submodular functions [20]. The limitation DQN model that can explore solution space like local search of Greedy has led to the development of greedy local (LS) does and serve as a general-purpose algorithm for search techniques that provide a feasible solution for various the combinatorial problem yet remain efficient in terms of applications. These techniques usually allow deletion and exchange runtime and memory consumption?

Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable, reinforcement learning (RL) has shown promise as a framework with which efficient heuristic methods to tackle these problems can be learned. Previous works construct the solution subset incrementally, adding one element at a time, however, the irreversible nature of this approach prevents the agent from revising its earlier decisions, which may be necessary given the complexity of the optimization task. We instead propose that the agent should seek to continuously improve the solution by learning to explore at test time. Our approach of exploratory combinatorial optimization (ECO-DQN) is, in principle, applicable to any combinatorial problem that can be defined on a graph. Experimentally, we show our method to produce state-of-the-art RL performance on the Maximum Cut problem. Moreover, because ECO-DQN can start from any arbitrary configuration, it can be combined with other search methods to further improve performance, which we demonstrate using a simple random search.