Solving Combinatorial Optimization Problems using Statistical Learning




Naguib, Andrew

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This thesis examines the use of geometric deep neural networks to provide competent solutions (in terms of runtime versus duality gap), not necessarily incumbent, to the capacitated vehicle routing problem and the bin packing problem—which have non-deterministic polynomial computational complexity. The core idea is based on learning to approximate the decisions made by the branch and bound algorithm using the computationally expensive strong branching strategy. The classifiers - graph convolutional neural network, Graph- SAGE, and graph attention network - are trained on six topologically different (to investigate the geographical dispersion effect on optimality) instances and evaluated on eight additional instances. The experiments we conducted show that the proposed approach is able to match the performance of the branch and bound algorithm and improve upon it on two different branching strategies, while requiring significantly less computation time and explored branching nodes.



combinatorial optimization, vehicle routing problem, bin packing problem, geometric deep learning