  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.
