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

Learning Primal Heuristics for Mixed Integer Programs