In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, tune, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem or a machine learning problem, especially with incomplete or imperfect information or limited computation capacity. Metaheuristics sample a subset of solutions which is otherwise too large to be completely enumerated or otherwise explored. Metaheuristics may make relatively few assumptions about the optimization problem being solved and so may be usable for a variety of problems. Their use is always of interest when exact or other (approximate) methods are not available or are not expedient, either because the calculation time is too long or because, for example, the solution provided is too imprecise. Compared to optimization algorithms and iterative methods, metaheuristics do not guarantee that a globally optimal solution can be found on some class of problems. Many metaheuristics implement some form of stochastic optimization, so that the solution found is dependent on the set of random variables generated. In combinatorial optimization, there are many problems that belong to the class of NP-complete problems and thus can no longer be solved exactly in an acceptable time from a relatively low degree of complexity. Metaheuristics then often provide good solutions with less computational effort than approximation methods, iterative methods, or simple heuristics. This also applies in the field of continuous or mixed-integer optimization. As such, metaheuristics are useful approaches for optimization problems. Several books and survey papers have been published on the subject. Literature review on metaheuristic optimization, suggested that it was Fred Glover who coined the word metaheuristics. 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. Also worth mentioning are the no-free-lunch theorems, which state that there can be no metaheuristic that is better than all others for any given problem. Especially since the turn of the millennium, many metaheuristic methods have been published with claims of novelty and practical efficacy. While the field also features high-quality research, many of the more recent publications have been of poor quality; flaws include vagueness, lack of conceptual elaboration, poor experiments, and ignorance of previous literature.
Properties These are properties that characterize most metaheuristics:
Metaheuristics are strategies that guide the search process. The goal is to efficiently explore the search space in order to find optimal or near–optimal solutions. Techniques which constitute metaheuristic algorithms range from simple local search procedures to complex learning processes. Metaheuristic algorithms are approximate and usually non-deterministic. Metaheuristics are not problem-specific. However, they were often developed in relation to a problem class such as continuous or combinatorial optimization and then generalized later in some cases. They can draw on domain-specific knowledge in the form of heuristics that are controlled by a higher-level strategy of the metaheuristic. They can contain mechanisms that prevent them from getting stuck in certain areas of the search space. Modern metaheuristics often use the search history to control the search.
Classification
There are a wide variety of metaheuristics and a number of properties with respect to which to classify them. The following list is therefore to be understood as an example.
Local search vs. global search One approach is to characterize the type of search strategy. 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. 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 such as genetic algorithm or evolution strategies, particle swarm optimization, rider optimization algorithm and bacterial foraging algorithm.
Single-solution vs. population-based Another classification dimension is single solution vs population-based searches. Single solution approaches focus on modifying and improving a single candidate solution; single solution metaheuristics include simulated annealing, iterated local search, variable neighborhood search, and guided local search. Population-based approaches maintain and improve multiple candidate solutions, often using population characteristics to guide the search; population based metaheuristics include evolutionary computation and particle swarm optimization. Another category of metaheuristics is Swarm intelligence which is a collective behavior of decentralized, self-organized agents in a population or swarm. Ant colony optimization, particle swarm optimization, social cognitive optimization, bacterial foraging algorithm, and Grey Wolf Optimization are examples of this category.
Hybridization and memetic algorithms A hybrid metaheuristic is one that 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 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 or in addition to a basic mutation operator in evolutionary algorithms.
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