Why Response Matters: Simultaneous Bi-Level Optimization for Network Design Problems

Network design problems such as the optimization of road capacities, public transport lines and
frequencies, mobility hub locations, shared mobility services and traffic signal settings have been
extensively studied in literature using sequential bi-level optimization. However, due to the
computational burden, the design and response spaces that have been considered so far are rather
limited, resulting in suboptimal designs. In this paper we introduce a new framework for simultaneous
bi-level optimization that contributes to the existing literature by optimizing designs and responses
simultaneously rather than sequentially, and by using machine learning for the design and response
optimization instead of only for the design optimization, thus allowing for a much larger design and
response space. Based on experiments for the city of Amsterdam in which parking lot locations and
tariffs are optimized, this paper demonstrates that simultaneous design and response optimization is
possible and that designs created with a small fixed response space, which is common practice, may be
worse than expected, due to the fact that a population can respond in a different way than anticipated
during design optimization. The proposed design and response optimization framework is able to
automatically learn responses, leading to designs that are 21% to 53% better than designs created with
a fixed response space depending on the indicator chosen. In future work, the framework can be
extended to a multi-level optimization framework to include multiple stakeholder groups that all
respond to each other by simultaneously running machine learning algorithms for each stakeholder
group.