A global optimum is the extrema (minimum or maximum) of the objective function for the entire input search space.
Global optimization, where the algorithm searches for the global optimum by employing mechanisms to search larger parts of the search space.
— Page 37, Computational Intelligence: An Introduction, 2007.
An objective function may have one or more than one global optima, and if more than one, it is referred to as a multimodal optimization problem and each optimum will have a different input and the same objective function evaluation.
- Global Optimization: Locate the optima for an objective function that may contain local optima.
An objective function always has a global optima (otherwise we would not be interested in optimizing it), although it may also have local optima that have an objective function evaluation that is not as good as the global optima.
The global optima may be the same as the local optima, in which case it would be more appropriate to refer to the optimization problem as a local optimization, instead of global optimization.
The presence of the local optima is a major component of what defines the difficulty of a global optimization problem as it may be relatively easy to locate a local optima and relatively difficult to locate the global optima.
Global optimization or global search refers to searching for the global optima.
A global optimization algorithm, also called a global search algorithm, is intended to locate a global optima. It is suited to traversing the entire input search space and getting close to (or finding exactly) the extrema of the function.
Global optimization is used for problems with a small number of variables, where computing time is not critical, and the value of finding the true global solution is very high.
— Page 9, Convex Optimization, 2004.
Global search algorithms may involve managing a single or a population of candidate solutions from which new candidate solutions are iteratively generated and evaluated to see if they result in an improvement and taken as the new working state.
There may be debate over what exactly constitutes a global search algorithm; nevertheless, three examples of global search algorithms using our definitions include:
- Genetic Algorithm
- Simulated Annealing
- Particle Swarm Optimization