We will be considering two types of optimisation problems: sequential optimisation and global optimisation. These approaches can be applied to the same problem but will generally yield distinctly different results. Depending on your objective one or the other might be the best fit for your problem.
Consider a problem that involves optimising the parameters of a system across a number of time steps. This problem can be approached as either:
- sequential optimisation — the system is optimised for each time step independently; or
- global optimisation — the system is optimised for all time steps simultaneously.
Sequential Optimisation
Sequential optimisation solves a problem step-by-step, where the solution at each step depends on the outcome of the previous step. Decisions are made incrementally, taking into account only the past and present state, thereby ensuring causality.
The problem to be solved for each step has fewer variables and constraints, making it more computationally efficient. However, this approach is greedy (optimising for the present without regard for the future) and will likely sacrifice global optimality.
Global Optimisation
Global optimisation solves the problem over the full time horizon in one go, aiming for a globally optimal solution. All decisions are considered simultaneously.
Because decisions can depend on future states, the results may not be realistic because they do not account for causality (the future can influence the present!). Since all steps are solved at the same time the dimensionality of the problem can be high, requiring more computational power and time (the “curse of dimensionality”).
Conclusion
Sequential Optimisation is ideal for real-time or dynamic systems where causality is critical and decisions must adapt to new information. Global Optimisation excels in static, long-term planning problems where computational resources and perfect foresight are available.
Both approaches can complementary. For example, global optimisation can provide a baseline solution for planning purposes, and sequential optimisation can refine it in real time.