For optimization, from Wikipedia:In computer science, metaheuristic designates a computational method  that optimizes a problem by iteratively trying to improve a candidate  solution with regard to a given measure of quality. Metaheuristics  make few or no assumptions about the problem being optimized and can  search very large spaces of candidate solutions. However,  metaheuristics do not guarantee an optimal solution is ever found.  Many metaheuristics implement some form of stochastic optimization.Other terms having a similar meaning as metaheuristic, are:  derivative-free, direct search, black-box, or indeed just heuristic  optimizer. Several books and survey papers have been published on the  subject.I wonder how to tell whether an optimization method is metaheuristic or not? For example, (1) Is the simplex method for linearprogramming metaheuristic?  (2) Are the majority of nonlinearprogramming methods such as gradient descent, Lagrangian multipliermethod, penalty methods, Interior point methods (barrier methods),metaheuristic? (3) Are all gradient-free methods, such as NelderMead method or downhill simplex method, metaheuristic?What are some optimization methods that are not metaheuristic?More generally (going beyond optimization) for problem solvingtechniques, from Wikipedia:Heuristic refers to experience-based techniques for problem solving,  learning, and discovery. Where an exhaustive search is impractical,  heuristic methods are used to speed up the process of finding a  satisfactory solution. Examples of this method include using a rule of  thumb, an educated guess, an intuitive judgment, or common sense.In more precise terms, heuristics are strategies using readily  accessible, though loosely applicable, information to control problem  solving in human beings and machines.I wonder how to understand the meaning of heuristic?how can I tell whether a problem solving,learning, and discovery technique is heuristic or not? What are some problem solving,learning, and discovery techniques that are not heuristic?Thanks and regards!
Meaning of (meta)heuristic methods
optimization;heuristics
Heuristic is something that works in many cases in practice, though there is no detailed argument for why it should work well. Metaheuristics is not an algorithm but a general heuristic scheme or idea that can be used inside specific algorithms. For example, the simplex algorithm for linear programming is neither heuristics nor metaheuristics, as it has a well-established convergence theory. The sqame holds for sequential quadtatic programming or interior point methods. (Interior point methods are a general scheme, but not heuristic and hence not a metaheuristics, as there is a quite strong theory associated with it.)The Nelder-Mead = downhill simplex algorithm for minimizing a function is heuristics (it actually may fail on quite simple problems in higher dimensions), and tabu search is metaheuristics (as quite a lot of diverse algorithms can be written that employ tabu search, but are otherwise of quite different quality.