MPPT aware task scheduling for nanosatellites using MIP-based ReLU proxy models

This paper investigates the use of Valid Inequalities (VIs) and Rectified Linear Unit (ReLU) neural networks in addressing the Offline Nanosatellite Task Scheduling (ONTS) problem within the context of mission planning. The ONTS problem focuses on optimizing task scheduling while adhering to energy constraints and maximizing mission objectives. We propose a methodology that incorporates VIs to enhance the solution process and embeds a ReLU proxy model within a standard Mixed Integer Linear Programming (MILP) framework to accurately predict photovoltaic (PV) power generation, aiding the scheduling process in maintaining the Maximum Power Point (MPP). In the MILP, the neural network weight vector is employed as a constant input, and an iterative technique refines the constraints. We introduce the P-split formulation to balance computational simplicity and the strength of the disjunctive constraint relaxation. The k-means algorithm identifies clusters for disjunctive constraints representing subsets of the decision space, and Bayesian hyperparameter optimization is conducted using Optuna. Our computational experiments demonstrate the effectiveness of the proposed VI methodologies in streamlining the problem-solving process, resulting in a significant speed improvement of 110 times faster on average when solving literature ONTS problem instances. Moreover, when applied to real-world nanosatellite mission planning instances, the proposed methodologies reveal the advantages of using our Maximum Power Point Tracking (MPPT) approach over a constant voltage method, capturing more energy, extending task operation duration, and increasing objective values.