2018/09/10 by Quentin Cappart, Cappart, Quentin, Emmanuel Goutierre +5 · 2 citations
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Formal Methods in Verification
paper · pdf · doi:10.48550/arxiv.1809.03359
openalex publication_date 2018/09/10 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
Finding tight bounds on the optimal solution is a critical element of\npractical solution methods for discrete optimization problems. In the last\ndecade, decision diagrams (DDs) have brought a new perspective on obtaining\nupper and lower bounds that can be significantly better than classical bounding\nmechanisms, such as linear relaxations. It is well known that the quality of\nthe bounds achieved through this flexible bounding method is highly reliant on\nthe ordering of variables chosen for building the diagram, and finding an\nordering that optimizes standard metrics is an NP-hard problem. In this paper,\nwe propose an innovative and generic approach based on deep reinforcement\nlearning for obtaining an ordering for tightening the bounds obtained with\nrelaxed and restricted DDs. We apply the approach to both the Maximum\nIndependent Set Problem and the Maximum Cut Problem. Experimental results on\nsynthetic instances show that the deep reinforcement learning approach, by\nachieving tighter objective function bounds, generally outperforms ordering\nmethods commonly used in the literature when the distribution of instances is\nknown. To the best knowledge of the authors, this is the first paper to apply\nmachine learning to directly improve relaxation bounds obtained by\ngeneral-purpose bounding mechanisms for combinatorial optimization problems.\n