Combinatorial Acyclicity Models for Potential-based Flows
- Potential-based flows constitute a basic model to represent physical behavior in networks.
Under natural assumptions, the flow in such networks must be acyclic. The goal of this
paper is to exploit this property for the solution of corresponding optimization problems.
To this end, we introduce several combinatorial models for acyclic flows, based on binary
variables for flow directions. We compare these models and introduce a particular model
that tries to capture acyclicity together with the supply/demand behavior. We analyze
properties of this model, including variable fixing rules. Our computational results show
that the usage of the corresponding constraints speeds up solution times by about a factor
of 3 on average and a speed-up of a factor of almost 5 for the time to prove optimality.