Continuous Search Space
A Continuous Search Space is a search space that is a continuous space.
- AKA: Feasible Region.
- Context:
- It can be a Task Input to a Continuous Space Search Task.
- …
- Example(s):
- …
- Counter-Example(s):
- See: Constraint Satisfaction, Mathematical Optimization, Candidate Solution, Objective Function, Integer Programming, Linear Programming, Convex Set, Polytope.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/feasible_region Retrieved:2015-12-13.
- In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.
For example, consider the problem
:Minimize [math]\displaystyle{ x^2+y^4 }[/math] with respect to the variables [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y, }[/math] subject to : [math]\displaystyle{ 1 \le x \le 10 }[/math] and : [math]\displaystyle{ 5 \le y \le 12. \, }[/math] Here the feasible set is the set of pairs (x, y) in which the value of x is at least 1 and at most 10 and the value of y is at least 5 and at most 12. Note that the feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is [math]\displaystyle{ x^2+y^4. }[/math] In many problems, the feasible set reflects a constraint that one or more variables must be non-negative. In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible set is a convex polytope: a region in multidimensional space whose boundaries are formed by hyperplanes and whose corners are vertices.
Constraint satisfaction is the process of finding a point in the feasible region.
- In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.