In the context of simulation-based optimisation, time-dependent systems are notoriously time consuming. This MS seeks to gather researchers working towards reducing the computational cost. First, the forward state must be solved for the time frame of interest, which is usually done using time-stepping schemes. This solution can take a significant time for realistic problems with high spatial mesh resolution and small time steps. Thereafter, if using the adjoint method for sensitivity analysis, the backward-in-time adjoint must be solved in order to compute the gradients. This essentially doubles the computational time directly and in terms of memory usage, the full forward time history must be saved to be used during the backwards problem. Wrapping an optimisation loop around this, further increases the computational time significantly due to hundreds, if not thousands, of design iterations typically being needed. This MS focuses on efficient and fast algorithms and methods for optimisation of time-dependent systems to try to avoid or alleviate the abovementioned problems. Contributions should focus on reducing the computational cost or memory consumption for topology, shape or parameter optimisation for time-dependent systems through novel means. Not necessarily applied to optimisation but clearly suited for this context. This could be through improvements to time stepping schemes and checkpointing schemes, or through the application of parallel local-in-time adjoint methods, multiple shooting, or parallel-in-time methods. Relevant application areas include, but are not limited to, thermal diffusion, phase-change materials, fluid dynamics, solid dynamics, fluid-structure interaction, acoustics, and so on.