Generalizing Space Logistics Network Optimization with Integrated Machine Learning and Mathematical Programming

TL;DR

This paper introduces a novel framework that integrates machine learning models into mixed-integer linear programming to effectively handle nonlinear constraints in space logistics network optimization.

Contribution

It develops a systematic approach to incorporate trained ML models into MILP formulations, enabling nonlinear constraints to be addressed in space logistics optimization.

Findings

First demonstration of ML models used directly in MILP for space logistics.

Enhanced modeling of nonlinear relationships in space mission planning.

Potential for more accurate and flexible space logistics optimization.

Abstract

Recent growing complexity in space missions has led to an active research field of space logistics and mission design. This research field leverages the key ideas and methods used to handle complex terrestrial logistics to tackle space logistics design problems. A typical goal in space logistics is to optimize the commodity flow to satisfy some mission objectives with the lowest cost. One of the successful space logistics approaches is network flow modeling and optimization using mixed-integer linear programming (MILP). A caveat of the conventional MILP-based network approach for space logistics is its incapability of handling nonlinearity. For example, in the MILP formulation, the spacecraft structure mass and fuel/payload capacity are approximated by a linear relationship. However, this oversimplified relationship cannot characterize a realistic spacecraft design. Other types of nonlinearity can appear when a nonlinear time-dependent trajectory model is considered in an event-driven network, where the time step of each event itself is a variable. In response to this challenge, this Note develops a new systematic general framework to handle nonlinearity in the MILP-based space logistics formulation using machine learning (ML). Specifically, we replace the nonlinear constraints in the space logistics formulation with trained ML models that are compatible with MILP. The MILP-compatible ML model includes linear regression, PWL approximations, neural networks (NN) with Rectified Linear Unit (ReLU) activations, decision tree regression, and random forest regression, among others; these models can be translated into MILP formulations with a definition of additional variables and constraints while maintaining the linearity. This Note provides the first demonstration of using such trained ML models directly in a MILP-based space logistics optimization formulation.