By forcing at most N out of M consecutive weights to be non-zero, the recent N:M network sparsity has received increasing attention for its two attractive advantages: 1) Promising performance at a high sparsity.

This work proposes a self-supervised training strategy designed for combinatorial problems. An obstacle in applying supervised paradigms to such problems is the need for costly target solutions often produced with exact solvers. Inspired by semi-and self-supervised learning, we show that generative models can be trained by sampling multiple solutions and using the best one according to the problem objective as a pseudo-label. In this way, we iteratively improve the model generation capability by relying only on its self-supervision, eliminating the need for optimality information. We validate this Self-Labeling Improvement Method (SLIM) on the Job Shop Scheduling (JSP), a complex combinatorial problem that is receiving much attention from the neural combinatorial community. We propose a generative model based on the well-known Pointer Network and train it with SLIM. Experiments on popular benchmarks demonstrate the potential of this approach as the resulting models outperform constructive heuristics and state-of-the-art learning proposals for the JSP. Lastly, we prove the robustness of SLIM to various parameters and its generality by applying it to the Traveling Salesman Problem.

Districting is a complex combinatorial problem that consists in partitioning a geographical area into small districts.

Leveraging this flexibility, we implement 47 novel MCBO algorithms and benchmark them against seven existing MCBO solvers and five standard black-box optimization algorithms on ten tasks, conducting over 4000 experiments.

To this end, we first establish a new class of GNNs that can solve a strictly wider variety of problems than existing GNNs. Then, we bridge the gap between GNN theory and the theory of distributed local algorithms.

There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused onobtaining high-quality solutions, scalability tobillion-sized graphs has not been adequately addressed.

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems.