Metaheuristic

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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. [1] [2] 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. [3] [4] [5] [6] 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.

Contents

Compared to optimization algorithms and iterative methods, metaheuristics do not guarantee that a globally optimal solution can be found on some class of problems. [3] Many metaheuristics implement some form of stochastic optimization, so that the solution found is dependent on the set of random variables generated. [2] 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. [7] [8] Metaheuristics then often provide good solutions with less computational effort than approximation methods, iterative methods, or simple heuristics. [3] [4] This also applies in the field of continuous or mixed-integer optimization. [4] [9] [10] As such, metaheuristics are useful approaches for optimization problems. [2] Several books and survey papers have been published on the subject. [2] [3] [4] [11] [12] Literature review on metaheuristic optimization, [13] suggested that it was Fred Glover who coined the word metaheuristics. [14]

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. [3] [15] 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. [16] [17]

Properties

These are properties that characterize most metaheuristics: [3]

Classification

Euler diagram of the different classifications of metaheuristics. Metaheuristics classification.svg
Euler diagram of the different classifications of metaheuristics.

There are a wide variety of metaheuristics [2] [4] and a number of properties with respect to which to classify them. [3] [24] [25] [26] The following list is therefore to be understood as an example.

One approach is to characterize the type of search strategy. [3] 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. [3] 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 [27] and bacterial foraging algorithm. [28]

Single-solution vs. population-based

Another classification dimension is single solution vs population-based searches. [3] [12] 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. [12] 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. [12] 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, [29] particle swarm optimization, [12] social cognitive optimization and bacterial foraging algorithm [28] 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 [30] 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.

Parallel metaheuristics

A parallel metaheuristic is one that 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.

With population-based metaheuristics, the population itself can be parallelized by either processing each individual or group with a separate thread or the metaheuristic itself runs on one computer and the offspring are evaluated in a distributed manner per iteration. [31] The latter is particularly useful if the computational effort for the evaluation is considerably greater than that for the generation of descendants. This is the case in many practical applications, especially in simulation-based calculations of solution quality. [32] [33]

Nature-inspired and metaphor-based metaheuristics

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. Nature acts as a source of concepts, mechanisms and principles for designing of artificial computing systems to deal with complex computational problems. Such metaheuristics include simulated annealing, evolutionary algorithms, ant colony optimization and particle swarm optimization.

A large number of more recent metaphor-inspired metaheuristics have started to attract criticism in the research community for hiding their lack of novelty behind an elaborate metaphor. [16] [17] [25] As a result, a number of renowned scientists of the field have proposed a research agenda for the standardization of metaheuristics in order to make them more comparable, among other things. [34] Another consequence is that the publication guidelines of a number of scientific journals have been adapted accordingly. [35] [36] [37]

Applications

Most metaheuristics are search methods and when using them, the evaluation function should be subject to greater demands than a mathematical optimization. Not only does the desired target state have to be formulated, but the evaluation should also reward improvements to a solution on the way to the target in order to support and accelerate the search process. The fitness functions of evolutionary or memetic algorithms can serve as an example.

Metaheuristics are used for all types of optimization problems, ranging from continuous through mixed integer problems to combinatorial optimization or combinations thereof. [9] [38] [39] In combinatorial optimization, 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. [40] [41] Additionally, multidimensional combinatorial problems, including most design problems in engineering [6] [42] [43] [44] such as form-finding and behavior-finding, suffer from the curse of dimensionality, which also makes them infeasible for exhaustive search or analytical methods.

Metaheuristics are also frequently applied to scheduling problems. A typical representative of this combinatorial task class is job shop scheduling, which involves assigning the work steps of jobs to processing stations in such a way that all jobs are completed on time and altogether in the shortest possible time. [5] [45] In practice, restrictions often have to be observed, e.g. by limiting the permissible sequence of work steps of a job through predefined workflows [46] and/or with regard to resource utilisation, e.g. in the form of smoothing the energy demand. [47] [48] Popular metaheuristics for combinatorial problems include genetic algorithms by Holland et al., [49] scatter search [50] and tabu search [51] by Glover.

Another large field of application are optimization tasks in continuous or mixed-integer search spaces. This includes, e.g., design optimization [6] [52] [53] or various engineering tasks. [54] [55] [56] An example of the mixture of combinatorial and continuous optimization is the planning of favourable motion paths for industrial robots. [57] [58]

Metaheuristic Optimization Frameworks

A MOF can be defined as ‘‘a set of software tools that provide a correct and reusable implementation of a set of metaheuristics, and the basic mechanisms to accelerate the implementation of its partner subordinate heuristics (possibly including solution encodings and technique-specific operators), which are necessary to solve a particular problem instance using techniques provided’’. [59]

There are many candidate optimization tools which can be considered as a MOF of varying feature. The following list of 33 MOFs is compared and evaluated in detail in: [59] Comet, EvA2, evolvica, Evolutionary::Algorithm, GAPlayground, jaga, JCLEC, JGAP, jMetal, n-genes, Open Beagle, Opt4j, ParadisEO/EO, Pisa, Watchmaker, FOM, Hypercube, HotFrame, Templar, EasyLocal, iOpt, OptQuest, JDEAL, Optimization Algorithm Toolkit, HeuristicLab, MAFRA, Localizer, GALIB, DREAM, Discropt, MALLBA, MAGMA, and UOF. There have been a number of publications on the support of parallel implementations, which was missing in this comparative study, particularly from the late 10s onwards. [32] [33] [60] [61] [62]

Contributions

Many different metaheuristics are in existence and new variants are continually being proposed. Some of the most significant contributions to the field are:

See also

Related Research Articles

<span class="mw-page-title-main">Genetic algorithm</span> Competitive algorithm for searching a problem space

In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems via biologically inspired operators such as selection, crossover, and mutation. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, and causal inference.

<span class="mw-page-title-main">Simulated annealing</span> Probabilistic optimization technique and metaheuristic

Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optimum. It is often used when the search space is discrete. For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms such as gradient descent or branch and bound.

In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions. Evolution of the population then takes place after the repeated application of the above operators.

<span class="mw-page-title-main">Evolutionary computation</span> Trial and error problem solvers with a metaheuristic or stochastic optimization character

In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, they are a family of population-based trial and error problem solvers with a metaheuristic or stochastic optimization character.

<span class="mw-page-title-main">Particle swarm optimization</span> Iterative simulation method

In computational science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. It solves a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle's position and velocity. Each particle's movement is influenced by its local best known position, but is also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions.

Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of the function .

<span class="mw-page-title-main">Ant colony optimization algorithms</span> Optimization algorithm

In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems that can be reduced to finding good paths through graphs. Artificial ants represent multi-agent methods inspired by the behavior of real ants. The pheromone-based communication of biological ants is often the predominant paradigm used. Combinations of artificial ants and local search algorithms have become a preferred method for numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing.

The greedy randomized adaptive search procedure is a metaheuristic algorithm commonly applied to combinatorial optimization problems. GRASP typically consists of iterations made up from successive constructions of a greedy randomized solution and subsequent iterative improvements of it through a local search. The greedy randomized solutions are generated by adding elements to the problem's solution set from a list of elements ranked by a greedy function according to the quality of the solution they will achieve. To obtain variability in the candidate set of greedy solutions, well-ranked candidate elements are often placed in a restricted candidate list (RCL), and chosen at random when building up the solution. This kind of greedy randomized construction method is also known as a semi-greedy heuristic, first described in Hart and Shogan (1987).

A memetic algorithm (MA) in computer science and operations research, is an extension of the traditional genetic algorithm (GA) or more general evolutionary algorithm (EA). It may provide a sufficiently good solution to an optimization problem. It uses a suitable heuristic or local search technique to improve the quality of solutions generated by the EA and to reduce the likelihood of premature convergence.

Extremal optimization (EO) is an optimization heuristic inspired by the Bak–Sneppen model of self-organized criticality from the field of statistical physics. This heuristic was designed initially to address combinatorial optimization problems such as the travelling salesman problem and spin glasses, although the technique has been demonstrated to function in optimization domains.

Search-based software engineering (SBSE) applies metaheuristic search techniques such as genetic algorithms, simulated annealing and tabu search to software engineering problems. Many activities in software engineering can be stated as optimization problems. Optimization techniques of operations research such as linear programming or dynamic programming are often impractical for large scale software engineering problems because of their computational complexity or their assumptions on the problem structure. Researchers and practitioners use metaheuristic search techniques, which impose little assumptions on the problem structure, to find near-optimal or "good-enough" solutions.

Parallel metaheuristic is a class of techniques that are capable of reducing both the numerical effort and the run time of a metaheuristic. To this end, concepts and technologies from the field of parallelism in computer science are used to enhance and even completely modify the behavior of existing metaheuristics. Just as it exists a long list of metaheuristics like evolutionary algorithms, particle swarm, ant colony optimization, simulated annealing, etc. it also exists a large set of different techniques strongly or loosely based in these ones, whose behavior encompasses the multiple parallel execution of algorithm components that cooperate in some way to solve a problem on a given parallel hardware platform.

A hyper-heuristic is a heuristic search method that seeks to automate, often by the incorporation of machine learning techniques, the process of selecting, combining, generating or adapting several simpler heuristics to efficiently solve computational search problems. One of the motivations for studying hyper-heuristics is to build systems which can handle classes of problems rather than solving just one problem.

<span class="mw-page-title-main">Meta-optimization</span>

In numerical optimization, meta-optimization is the use of one optimization method to tune another optimization method. Meta-optimization is reported to have been used as early as in the late 1970s by Mercer and Sampson for finding optimal parameter settings of a genetic algorithm.

<span class="mw-page-title-main">HeuristicLab</span> Software environment

HeuristicLab is a software environment for heuristic and evolutionary algorithms, developed by members of the Heuristic and Evolutionary Algorithm Laboratory (HEAL) at the University of Applied Sciences Upper Austria, in Hagenberg im Mühlkreis. HeuristicLab has a strong focus on providing a graphical user interface so that users are not required to have comprehensive programming skills to adjust and extend the algorithms for a particular problem. In HeuristicLab algorithms are represented as operator graphs and changing or rearranging operators can be done by drag-and-drop without actually writing code. The software thereby tries to shift algorithm development capability from the software engineer to the user and practitioner. Developers can still extend the functionality on code level and can use HeuristicLab's plug-in mechanism that allows them to integrate custom algorithms, solution representations or optimization problems.

The Genetic and Evolutionary Computation Conference (GECCO) is the premier conference in the area of genetic and evolutionary computation. GECCO has been held every year since 1999, when it was first established as a recombination of the International Conference on Genetic Algorithms (ICGA) and the Annual Genetic Programming Conference (GP).

This is a chronological table of metaheuristic algorithms that only contains fundamental computational intelligence algorithms. Hybrid algorithms and multi-objective algorithms are not listed in the table below.

<span class="mw-page-title-main">Gabriela Ochoa</span> Venezuelan British computer scientist

Gabriela Ochoa is a Venezuelan British computer scientist and Professor at the University of Stirling. Her research considers evolutionary algorithms and heuristic search methods.

A large-scale capacitated arc routing problem (LSCARP) is a variant of the capacitated arc routing problem that covers 300 or more edges to model complex arc routing problems at large scales.

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