Discrete Optimization with Decision Diagrams
提出一种通用分支定界算法，用二元决策图替代传统线性规划松弛，提供分支定界和启发式解，在最大稳定集、最大割和最大2-可满足性问题中优于商业整数规划求解器。
We propose a general branch-and-bound algorithm for discrete optimization in which binary decision diagrams (BDDs) play the role of the traditional linear programming relaxation. In particular, relaxed BDD representations of the problem provide bounds and guidance for branching, and restricted BDDs supply a primal heuristic. Each problem is given a dynamic programming model that allows one to exploit recursive structure, even though the problem is not solved by dynamic programming. A novel search scheme branches within relaxed BDDs rather than on values of variables. Preliminary testing shows that a rudimentary BDD-based solver is competitive with or superior to a leading commercial integer programming solver for the maximum stable set problem, the maximum cut problem on a graph, and the maximum 2-satisfiability problem. Specific to the maximum cut problem, we tested the BDD-based solver on a classical benchmark set and identified tighter relaxation bounds than have ever been found by any technique, nearly closing the entire optimality gap on four large-scale instances.