Self-stabilization qualifies the ability of a distributed system to recover after transient failures. sasa is a simulator of self-stabilizing algorithms written in the atomic-state model, the most commonly used model in the self-stabilizing area. A simulator is, in particular, useful to study the time complexity of algorithms. For example, one can experimentally check whether existing theoretical bounds are correct or tight. Simulations are also useful to get insights when no bound is known. In this paper, we use sasa to investigate the worst cases of various well-known self-stabilization algorithms. We apply classical optimization methods (such as local search, branch and bound, Tabu list) on the two sources of non-determinism: the choice of initial configuration and the scheduling of process activations (daemon). We propose a methodology based on heuristics and an open-source tool to find tighter worst-case lower bounds.