Integrated integer programming and decision diagram search tree with an application to the maximum independent set problem

Jaime E. González, André Augusto Ciré, Andrea Lodi, Louis-Martin Rousseau

Abstract: We propose an optimization framework which integrates decision diagrams (DDs) and integer linear programming (ILP) to solve combinatorial optimization problems. The hybrid DD-ILP approach explores the solution space based on a recursive compilation of relaxed DDs and incorporates ILP calls to solve subproblems associated with DD nodes. The selection of DD nodes to be explored by ILP technology is a significant component of the approach. We show how supervised machine learning can be useful to detect, on-the-fly, a subproblem structure for ILP technology. We use the maximum independent set problem as a case study. Computational experiments show that, in presence of suitable problem structure, the integrated DD-ILP approach can exploit complementary strengths and improve upon the performance of both a stand-alone DD solver and an ILP solver in terms of solution time and number of solved instances.