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In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity.^{[1]} Metaheuristics sample a set of solutions which is too large to be completely sampled. Metaheuristics may make few assumptions about the optimization problem being solved, and so they may be usable for a variety of problems.^{[2]}
Compared to optimization algorithms and iterative methods, metaheuristics do not guarantee that a globally optimal solution can be found on some class of problems.^{[2]} Many metaheuristics implement some form of stochastic optimization, so that the solution found is dependent on the set of random variables generated.^{[1]} By searching over a large set of feasible solutions, metaheuristics can often find good solutions with less computational effort than optimization algorithms, iterative methods, or simple heuristics.^{[2]} As such, they are useful approaches for optimization problems.^{[1]} Several books and survey papers have been published on the subject.^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}
Most literature on metaheuristics is experimental in nature, describing empirical results based on computer experiments with the algorithms. But some formal theoretical results are also available, often on convergence and the possibility of finding the global optimum.^{[2]} Many metaheuristic methods have been published with claims of novelty and practical efficacy. Unfortunately, many of the publications have been of poor quality; flaws include vagueness, lack of conceptual elaboration, poor experiments, and ignorance of previous literature. The field also features high-quality research.^{[6]}
These are properties that characterize most metaheuristics:^{[2]}
There are a wide variety of metaheuristics^{[1]} and a number of properties along which to classify them.^{[2]}
One approach is to characterize the type of search strategy.^{[2]} One type of search strategy is an improvement on simple local search algorithms. A well known local search algorithm is the hill climbing method which is used to find local optimums. However, hill climbing does not guarantee finding global optimum solutions.
Many metaheuristic ideas were proposed to improve local search heuristic in order to find better solutions. Such metaheuristics include simulated annealing, tabu search, iterated local search, variable neighborhood search, and GRASP.^{[2]} These metaheuristics can both be classified as local search-based or global search metaheuristics.
Other global search metaheuristic that are not local search-based are usually population-based metaheuristics. Such metaheuristics include ant colony optimization, evolutionary computation, particle swarm optimization, and genetic algorithms.^{[2]}
Another classification dimension is single solution vs population-based searches.^{[2]}^{[5]} Single solution approaches focus on modifying and improving a single candidate solution; single solution metaheuristics include Ant colony optimization,^{[7]} particle swarm optimization,^{[5]} social cognitive optimization, and artificial bee colony ^{[8]} algorithms are examples of this category.
A hybrid metaheuristic is one which combines a metaheuristic with other optimization approaches, such as algorithms from mathematical programming, constraint programming, and machine learning. Both components of a hybrid metaheuristic may run concurrently and exchange information to guide the search.
On the other hand, Memetic algorithms^{[9]} represent the synergy of evolutionary or any population-based approach with separate individual learning or local improvement procedures for problem search. An example of memetic algorithm is the use of a local search algorithm instead of a basic mutation operator in evolutionary algorithms.
A parallel metaheuristic is one which uses the techniques of parallel programming to run multiple metaheuristic searches in parallel; these may range from simple distributed schemes to concurrent search runs that interact to improve the overall solution.
A very active area of research is the design of nature-inspired metaheuristics. Many recent metaheuristics, especially evolutionary computation-based algorithms, are inspired by natural systems. Such metaheuristics include Ant colony optimization, particle swarm optimization, cuckoo search, and artificial bee colony to cite a few.
Metaheuristics are used for combinatorial optimization in which an optimal solution is sought over a discrete search-space. An example problem is the travelling salesman problem where the search-space of candidate solutions grows faster than exponentially as the size of the problem increases, which makes an exhaustive search for the optimal solution infeasible. Additionally, multidimensional combinatorial problems, including most design problems in engineering^{[10]} such as form-finding and behavior-finding, suffer from the curse of dimensionality, which also makes them infeasible for exhaustive search or analytical methods. Popular metaheuristics for combinatorial problems include simulated annealing by Kirkpatrick et al.,^{[11]} genetic algorithms by Holland et al.,^{[12]} scatter search^{[13]} and tabu search^{[14]} by Glover. Literature review on metaheuristic optimization,^{[15]} suggested that it was Fred Glover who coined the word metaheuristics ^{[16]}
Many different metaheuristics are in existence and new variants are continually being proposed. Some of the most significant contributions to the field are:
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