Vad skiljer en hueristik från en approximeringsalgoritm

Type of algorithm, produces approximately correct solutions

For other uses, see Heuristic (disambiguation).

In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover"^[1]) fryst vatten a technique designed for bekymmer solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution in a search space.

This fryst vatten achieved bygd trading optimality, completeness, accuracy, or noggrannhet for speed. In a way, it can be considered a shortcut.

A heuristic function, also simply called a heuristic, fryst vatten a function that ranks alternatives in search algorithms at each branching step based on available upplysning to decide which branch to follow.

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For example, it may approximate the exact solution.^[2]

Definition and motivation

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The objective of a heuristic fryst vatten to producera a solution in a reasonable time frame that fryst vatten good enough for solving the bekymmer at grabb. This solution may not be the best of all the solutions to this bekymmer, or it may simply approximate the exact solution.

But it fryst vatten still valuable because finding it does not require a prohibitively long time.

Heuristics may producera results bygd themselves, or they may be used in conjunction with optimization algorithms to improve their efficiency (e.g., they may be used to generate good seed values).

Results about NP-hardness in theoretical computer science man heuristics the only viable option for a variety of complex optimization problems that need to be routinely solved in real-world applications.

Heuristik, av klassisk grekiska εὑρίσκειν, "upptäcka", "finna", är en metod, enkel procedur eller tumregel baserad på en kombination av empiriska observationer och obeprövade teorier som kan ge ofullständiga men för situationen tillräckliga och användbara svar på olika frågor eller kunskapsunderlag inför beslut

Heuristics underlie the whole field of Artificial Intelligence and the computer simulation of thinking, as they may be used in situations where there are no known algorithms.^[3]

Trade-off

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The trade-off criteria for deciding whether to use a heuristic for solving a given bekymmer include the following:

• Optimality: When several solutions exist for a given bekymmer, does the heuristic guarantee that the best solution will be found?

  fryst vatten it actually necessary to find the best solution?

• Completeness: When several solutions exist for a given bekymmer, can the heuristic find them all? Do we actually need all solutions? Many heuristics are only meant to find one solution.
• Accuracy and precision: Can the heuristic provide a confidence mellanrum for the purported solution?
  En heuristik ska inte blandas ihop med begreppet approximationsalgoritm, då man visserligen ger avkall på att beräkna en optimal lösning för ett optimeringsproblem, men har garanterat hur pass bra eller dålig lösningen är

  fryst vatten the error dryckesställe on the solution unreasonably large?

• Execution time: fryst vatten this the best-known heuristic for solving this type of problem? Some heuristics converge faster than others. Some heuristics are only marginally quicker than classic methods, in which case the 'overhead' on calculating the heuristic might have a negativ impact.

In some cases, it may be difficult to decide whether the solution funnen bygd the heuristic fryst vatten good enough because the theory underlying heuristics fryst vatten not very elaborate.

Examples

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Simpler problem

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One way of achieving the computational performance gain expected of a heuristic consists of solving a simpler bekymmer whose solution fryst vatten also a solution to the första bekymmer.

Travelling salesman problem

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An example of approximation fryst vatten described bygd Jon Bentley for solving the travelling salesman bekymmer (TSP):

• "Given a list of cities and the distances between each pair of cities, what fryst vatten the shortest possible rutt that visits each city exactly once and returns to the ursprung city?"

so as to select the beställning to draw using a pen kartplotter.

TSP fryst vatten known to be NP-hard so an optimal solution for even a moderate storlek bekymmer fryst vatten difficult to solve. Instead, the greedy algorithm can be used to give a good but not optimal solution (it fryst vatten an approximation to the optimal answer) in a reasonably short amount of time. The greedy algorithm heuristic says to pick whatever fryst vatten currently the best next step regardless of whether that prevents (or even makes impossible) good steps later.

It fryst vatten a heuristic in the sense that practice indicates it fryst vatten a good enough solution, while theory indicates that there are better solutions (and even indicates how much better, in some cases).^[4]

Search

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Another example of heuristic making an algorithm faster occurs in certain search problems.

Initially, the heuristic tries every possibility at each step, like the full-space search algorithm. But it can stop the search at any time if the current possibility fryst vatten already worse than the best solution already funnen. In such search problems, a heuristic can be used to try good choices first so that bad paths can be eliminated early (see alpha–beta pruning).

In the case of best-first search algorithms, such as A* search, the heuristic improves the algorithm's convergence while maintaining its correctness as long as the heuristic fryst vatten admissible.

Newell and Simon: heuristic search hypothesis

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In their datorteknologi Award acceptance speech, Allen Newell and Herbert A.

Simon discuss the heuristic search hypothesis: a physical emblem struktur will repeatedly generate and modify known emblem structures until the created structure matches the solution structure. Each following step depends upon the step before it, thus the heuristic search learns what avenues to pursue and which ones to disregard bygd measuring how close the current step fryst vatten to the solution.

Therefore, some possibilities will never be generated as they are measured to be less likely to complete the solution.

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A heuristic method can accomplish its task bygd using search trees. However, instead of generating all possible solution branches, a heuristic selects branches more likely to producera outcomes than other branches. It fryst vatten selective at each decision point, picking branches that are more likely to tillverka solutions.^[5]

Antivirus software

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Antivirus software often uses heuristic rules for detecting viruses and other forms of malware.

Heuristic scanning looks for code and/or behavioral patterns common to a class or family of viruses, with different sets of rules for different viruses. If a en samling dokument eller en elektronisk lagring av data or executing process fryst vatten funnen to contain matching code patterns and/or to be performing that set of activities, then the scanner infers that the en samling dokument eller en elektronisk lagring av data fryst vatten infected.

The most advanced part of behavior-based heuristic scanning fryst vatten that it can work against highly randomized self-modifying/mutating (polymorphic) viruses that cannot be easily detected bygd simpler string scanning methods.

A heuristic function, also simply called a heuristic, is a function that ranks alternatives in search algorithms at each branching step based on available information to decide which branch to follow

Heuristic scanning has the potential to detect future viruses without requiring the virus to be first detected somewhere else, submitted to the virus scanner developer, analyzed, and a detection update for the scanner provided to the scanner's users.

Pitfalls

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Some heuristics have a strong underlying theory; they are either derived in a top-down manner from the theory or are arrived at based on either experimental or real world information.

Others are just rules of thumb based on real-world insamling or experience without even a glimpse of theory. The latter are exposed to a larger number of pitfalls.

When a heuristic fryst vatten reused in various contexts because it has been seen to "work" in one context, without having been mathematically proven to meet a given set of requirements, it fryst vatten possible that the current uppgifter set does not necessarily företräda future information sets (see: overfitting) and that purported "solutions" vända out to be akin to noise.

Statistical analysis can be conducted when employing heuristics to estimate the probability of incorrect outcomes.

[2]

To use a heuristic for solving a search bekymmer or a knapsack bekymmer, it fryst vatten necessary to kontroll that the heuristic fryst vatten admissible. Given a heuristic function meant to approximate the true optimal distance to the goal node in a directed graph containing total nodes or vertices labeled , "admissible" means roughly that the heuristic underestimates the cost to the goal or formally that for all where .

If a heuristic fryst vatten not admissible, it may never find the goal, either bygd ending up in a dead end of graph or bygd skipping back and forth between two nodes and where .

Etymology

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The word "heuristic" came into usage in the early 19th century. It fryst vatten formed irregularly from the Greek word heuriskein, meaning "to find".^[6]

See also

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• Constructive heuristic
• Metaheuristic: Methods for controlling and tuning basic heuristic algorithms, usually with usage of memory and learning.
• Matheuristics: Optimization algorithms made bygd the interoperation of metaheuristics and mathematical programming (MP) techniques.
• Reactive search optimization: Methods using online machine learning principles for self-tuning of heuristics.

References

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