The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic. To address these issues, we propose a machine learning (ML) framework for variable branching in MIP.Our method observes the decisions made by Strong Branching (SB), a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Based on the collected data, we learn an easy-to-evaluate surrogate function that mimics the SB strategy, by means of solving a learning-to-rank problem, common in ML. The learned ranking function is then used for branching. The learning is instance-specific, and is performed on-the-fly while executing a branch-and-bound search to solve the MIP instance. Experiments on benchmark instances indicate that our method produces significantly smaller search trees than existing heuristics, and is competitive with a state-of-the-art commercial solver.

There are currently two broad strategies for optimal Multi-agent Pathfinding (MAPF): (1) search-based methods, which model and solve MAPF directly, and (2) compilation-based solvers, which reduce MAPF to instances of well-known combinatorial problems, and thus, can benefit from advances in solver techniques. In this work, we present an optimal algorithm, BCP, that hybridizes both approaches using Branch-and-Cut-and-Price, a decomposition framework developed for mathematical optimization. We formalize BCP and compare it empirically against CBSH and CBSH-RM, two leading search-based solvers. Conclusive results on standard benchmarks indicate that its performance exceeds the state-of-the-art: solving more instances on smaller grids and scaling reliably to 100 or more agents on larger game maps.

This paper tackles the problem of substitution-tolerant subgraph isomorphism which is a specific class of error-tolerant isomorphism. This problem aims at finding a subgraph isomorphism of a pattern graph S in a target graph G. This isomorphism only considers label substitutions and forbids vertex and edge insertion in G. This kind of subgraph isomorphism is often needed in pattern recognition problems when graphs are attributed with real values and no exact matching can be found between attributes due to noise.Our proposal to solve the problem of substitution-tolerant subgraph isomorphism relies on its formulation in the Integer Linear Program (ILP) formalism. Using a general ILP solver, the approach is able to find, if one exists, a mapping of a pattern graph into a target graph such that the topology of the searched graph is kept and the editing operations between the labels have a minimal cost.This technique is evaluated on both a set of synthetic graphs and a problem of symbol detection in technical drawings. In the second case, document and symbol images are represented by vector-attributed Region Adjacency Graphs built from a segmentation process. Obtained results demonstrate the relevance of considering subgraph isomorphism as an optimization process.