even on smaller graphs if called this way. We therefore apply local optimizations to the layout computed by the maxent-stress algorithm. One optimization is based on simulated annealing, while the other is a simple local optimization algorithm.

#### Optimization of the Embedding with Simulated Annealing. {#optimization-of-the-embedding-with-simulated-annealing. .unnumbered}

Simulated annealing (SA) is a well-known metaheuristic that can escape local optima by probabilistically (based on a temperature parameter) accepting neighbor solutions that are worse than the current one, see [*e.g.*]{}Talbi [@Talbi:2009:MDI:1718024].

Our SA algorithm is sketched as Algorithm \[alg:sa\_optimizer\] in Appendix \[sub:sa-alg\]. The SA metaheuristic is often especially powerful if the initial solution is randomly chosen and can then jump between local minima. In our setting we receive an embedding from the maxent-stress algorithm as input; its global structure should be already quite good and only some of the given distances are not in their desired intervals. Therefore, our SA algorithm is only used to overcome rather narrow local minima instead of jumping to a completely different solution.

The constants in Algorithm \[alg:sa\_optimizer\] have been manually chosen in informal experiments. The outermost loop breaks after a certain number of unsuccessful improvement attempts or if the temperature is really low. The second loop 