There is a special
class of problems, examples of which are particularly common in the
fields of operations research and engineering design, in which the
task is to find the optimum * permutation* of some control variables.
These are known as * combinatorial* optimization problems. The most
famous example is the * traveling salesman problem* (TSP) in which the
shortest cyclical itinerary visiting **N** cities is sought. The
solutions to such problems are usually represented as * ordered* lists
of integers (indicating, for example in the TSP, the cities in the
order they are to be visited), and they are, of course, constrained,
since not all integer lists represent valid solutions. These and
other classifications are summarized in Table 1.
Table 2 lists application examples
from the wide range of fields where optimization is employed and
gives their classifications under this taxonomy.

Section 2 details
methods appropriate to * unconstrained continuous
univariate/multivariate problems*, and Section 3
mentions methods appropriate to * constrained continuous
multivariate problems*. Section considers methods
appropriate to * (mixed) integer multivariate
problems*, and Section 4 discusses what to do if none of these
methods succeed. In general, the optimization of the complex
functions that occur in many practical applications is difficult.
However, with persistence and resourcefulness solutions can often be
obtained.