  Symmetry in mathematical optimisation is of broad and current interest. In
problem classes such as mixed-integer linear programming (MILP), equivalent
solutions created by symmetric variables and constraints may combinatorially
increase the search space. Identifying problem symmetries is an important step
towards expediting tree-based algorithms such as branch-and-cut because
computationally classifying equivalence allows state-of-the-art solver software
to omit symmetric solutions. But symmetry has not been characterised in several
critically important process systems engineering applications such as heat
exchanger network synthesis; neither do current MILP solvers detect or use
symmetries for these energy efficiency problems. This paper uses group theory
to study the MILP transshipment model of heat exchanger network synthesis and
identifies several types of symmetry arising in the problem.
