Optimizing Neural Network for Efficient Solution of Mathematical Optimization Problems

In this paper, we explore integrating neural networks (NN) into optimization problems, presenting a Python-centric methodology that seamlessly incorporates an internally developed NN tool with the CPLEX optimization engine and the docplex library. The NN model is trained for each optimization task using datasets generated within the variable domain, aligning with specific problem constraints. The study begins with evaluating the system's performance on a fundamental linear optimization problem, utilizing a multilayer perceptron to approximate the linear function and incorporating activation functions in hidden and output layers. A numerical illustration involves a mixed-integer linear programming (MILP) problem, where the NN's predictive power is compared against the optimal values achieved through Python implementations.