In combinatorial optimization, A is some subset of a discrete space, like binary strings, permutations, or sets of integers.
In continuous optimization, A is some subset of the Euclidean space R n, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. Given: a function f : A → R from some set A to the real numbers Search for: an element x 0 in A such that f( x 0) ≤ f( x) for all x in A. For example, the inputs can be design parameters of a motor, the output can be the power consumption, or the inputs can be business choices and the output can be the obtained profit.Īn optimization problem, in this case a minimization problem, can be represented in the following way Many real-world problems can be modeled in this way. Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process.
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