Column generation (CG) is a powerful technique for solving optimization problems that involve a large number of variables or columns. This technique begins by solving a smaller problem with a subset of columns and gradually generates additional columns as needed. However, the generation of columns often requires solving difficult subproblems repeatedly, which can be a bottleneck for CG. To address this challenge, we propose a novel method called machine learning enhanced ant colony optimization (MLACO), to efficiently generate multiple high-quality columns from a sub-problem. Specifically, we train a ML model to predict the optimal solution of a subproblem, and then integrate this ML prediction into the probabilistic model of ACO to sample multiple high-quality columns. Our experimental results on the bin packing problem with conflicts show that the MLACO method significantly improves the performance of CG compared to several state-of-the-art methods. Furthermore, when our method is incorporated into a Branch-and-Price method, it leads to a significant reduction in solution time.

Column generation (CG) is a well-established method for solving large-scale linear programs. It involves iteratively optimizing a subproblem containing a subset of columns and using its dual solution to generate new columns with negative reduced costs. This process continues until the dual values converge to the optimal dual solution to the original problem. A natural phenomenon in CG is the heavy oscillation of the dual values during iterations, which can lead to a substantial slowdown in the convergence rate. *Stabilization* techniques are devised to accelerate the convergence of dual values by using information beyond the state of the current subproblem. However, there remains a significant gap in obtaining more accurate dual values at an earlier stage. To further narrow this gap, this paper introduces a novel approach consisting of 1) a *machine learning* approach for accurate prediction of optimal dual solutions and 2) an *adaptive stabilization* technique that effectively capitalizes on accurate predictions. On the graph coloring problem, we show that our method achieves a significantly improved convergence rate compared to traditional methods.

Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a subproblem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of the current subproblem. The new columns are generated as needed by repeatedly solving a pricing problem, which is often NP-hard and is a bottleneck of the CG approach. To tackle this, we propose a Machine-Learning-based Pricing Heuristic (MLPH) that can generate many high-quality columns efficiently. In each iteration of CG, our MLPH leverages an ML model to predict the optimal solution of the pricing problem, which is then used to guide a sampling method to efficiently generate multiple high-quality columns. Using the graph coloring problem, we empirically show that MLPH significantly enhances CG as compared to six state-of-the-art methods, and the improvement in CG can lead to substantially better performance of the branch-and-price exact method.

This paper proposes a novel primal heuristic for Mixed Integer Programs, by employing machine learning techniques. Mixed Integer Programming is a general technique for formulating combinatorial optimization problems. Inside a solver, primal heuristics play a critical role in finding good feasible solutions that enable one to tighten the duality gap from the outset of the Branch-and-Bound algorithm (B&B), greatly improving its performance by pruning the B&B tree aggressively. In this paper, we investigate whether effective primal heuristics can be automatically learned via machine learning. We propose a new method to represent an optimization problem as a graph, and train a Graph Convolutional Network on solved problem instances with known optimal solutions. This in turn can predict the values of decision variables in the optimal solution for an unseen problem instance of a similar type. The prediction of variable solutions is then leveraged by a novel configuration of the B&B method, Probabilistic Branching with guided Depth-first Search (PB-DFS) approach, aiming to find (near-)optimal solutions quickly. The experimental results show that this new heuristic can find better primal solutions at a much earlier stage of the solving process, compared to other state-of-the-art primal heuristics.

In this paper, we would like to demonstrate an intelligent traffic analytics system called T4, which enables intelligent analytics over real-time and historical trajectories from vehicles. At the front end, we visualize the current traffic flow and result trajectories of different types of queries, as well as the histograms of traffic flow and traffic lights. At the back end, T4 is able to support multiple types of common queries over trajectories, with compact storage, efficient index and fast pruning algorithms. The output of those queries can be used for further monitoring and analytics purposes. Moreover, we train the deep models for traffic flow prediction and traffic light control to reduce traffic congestion. A preliminary version of T4 is available at https://sites.google.com/site/shengwangcs/torch.