Abstract: Systems and methods for controlling automated systems, such as robots and other devices/resources, using integer programming and column generation techniques, are provided. The system retrieves location and movement data corresponding to at least one automated system, and processes the location and movement data using an integer linear programming algorithm. The system also optimizes the integer linear programming algorithm using a column generation algorithm, and solves a pricing problem associated with generating routes for the at least one automated system. Then, the system generates a route based on outputs of the integer linear programming algorithm, the column generation algorithm, and solving of the pricing problem, and transmits the route to the at least one automated system, the at least one automated system executing the route to control a location or a movement of the at least one automated system.

Abstract: Systems and methods for automated vehicle routing using column generation optimization are provided. The system receives capacitated vehicle routing problem (CVRP) input data and generates a minimum weight set cover problem formulation for a CVRP for performing column generation optimization over the input data. The system determines smooth-dual optimal inequalities (S-DOI) and flexible-dual optimal inequalities (F-DOI) for the CVRP for performing the column generation optimization over a valid subset of the input data. Then, the system adapts the S-DOI and the F-DOI to generate smooth and flexible dual optimal inequalities (SF-DOI) for the CVRP for performing the column generation optimization over a relaxed subset of the input data. The system utilizes the SF-DOI to accelerate column generation optimization over the relaxed subset of the input data.

Abstract: A system for generating a permutation invariant representation of a graph is provided. The system assembles a dataset including a graph having a plurality of nodes and a number of features per node and generates a first matrix and a second matrix based on the plurality of nodes and the number of features per node. The system determines a set of node embeddings by a graph convolutional network based on the first matrix and the second matrix and determines a permutation invariant representation of the graph by a permutation invariant mapping based on the set of node embeddings. The system determines a universal attribute of the graph by a fully connected network based on the permutation invariant representation of the graph.