In optimization (a branch of mathematics), a candidate solution is a member of a set of possible solutions to a given problem. A candidate solution does not have to be a likely or reasonable solution to the problem. The space of all candidate solutions is called the feasible region, feasible set, search space, or solution space . In mathematics, the term optimization refers to the study of problems that have the form Given: a function f : A R from some set A to the real numbers Sought: an element x0 in A such that f(x0) ≤ f(x) for all x in A (minimization) or such that... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... In mathematics, an element (also called a member) is an object contained in a set (or more generally a class). ... In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ...
In the case of the genetic algorithm, the candidate solutions are the individuals in the population being evolved by the algorithm. A genetic algorithm (or short GA) is a search technique used in computing to find true or approximate solutions to optimization and search problems. ...
The shaded region is called the feasibleregion because it represents all the possible points that satisfy the system of inequalities.
The optimum point is located on a corner of the feasibleregion (or the intersection of two of the boundary lines), and its coordinates are usually integer values.
Each point in the feasibleregion represents a possible combination of telemark skis and cross-country skis that the manufacturer can produce and satisfy both constraints.
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