A search acceleration method for optimization problems with transport simulation constraints

- New method to accelerate the approximate solution of optimization problems with transport simulation constraints.
- Applicable to real-valued, discrete, binary decision variables.
- Compatible with broad class of optimization algorithms and search heuristics.
- Compatible with broad range of iterated transport simulators (e.g. stochastic/deterministic, macroscopic/microscopic).
- Minimal parametrization, self-tuning capabilities.
- Efficiency demonstration with a non-trivial road pricing problem.

This work contributes to the rapid approximation of solutions to optimization problems that are constrained by iteratively solved transport simulations. Given an objective function, a set of candidate decision variables and a black-box transport simulation that is solved by iteratively attaining a (deterministic or stochastic) equilibrium, the proposed method approximates the best decision variable out of the candidate set without having to run the transport simulation to convergence for every single candidate decision variable. This method can be inserted into a broad class of optimization algorithms or search heuristics that implement the following logic: (i) Create variations of a given, currently best decision variable, (ii) identify one out of these variations as the new currently best decision variable, and (iii) iterate steps (i) and (ii) until no further improvement can be attained. A probabilistic and an asymptotic performance bound are established and exploited in the formulation of an efficient heuristic that is tailored towards tight computational budgets. The efficiency of the method is substantiated through a comprehensive simulation study with a non-trivial road pricing problem. The method is compatible with a broad range of simulators and requires minimal parametrization.