This chapter gives a brief introduction to the formulation of optimisation problems and solving algorithms. After mentioning the different classes of problems, such as continuous/discrete, local/global and single-/multi-objective, and introducing some of the useful terminology, the chapter is split in two main parts: (1) formulations and algorithms for continuous problems, including optimal control, and (2) formulations and algorithms for integer and mixed-integer problems. Both sections first consider standard deterministic methods that have been derived starting by optimality criteria, then more recent heuristics derived by experience and sometimes inspired by nature. This gives the basis to better read and understand some of the following chapters on more advanced topics.


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