What is the difference between a heuristic and an algorithm?

Question

What is the difference between a heuristic and an algorithm?

Answer 1

• An algorithm is typically deterministic and proven to yield an optimal result
• A heuristic has no proof of correctness, often involves random elements, and may not yield optimal results.

Many problems for which no efficient algorithm to find an optimal solution is known have heuristic approaches that yield near-optimal results very quickly.

There are some overlaps: "genetic algorithms" is an accepted term, but strictly speaking, those are heuristics, not algorithms.

Answer 2

One of the best explanations I have read comes from the great book Code Complete, which I now quote:

A heuristic is a technique that helps you look for an answer. Its results are subject to chance because a heuristic tells you only how to look, not what to find. It doesn’t tell you how to get directly from point A to point B; it might not even know where point A and point B are. In effect, a heuristic is an algorithm in a clown suit. It’s less predict- able, it’s more fun, and it comes without a 30-day, money-back guarantee.

Here is an algorithm for driving to someone’s house: Take Highway 167 south to Puy-allup. Take the South Hill Mall exit and drive 4.5 miles up the hill. Turn right at the light by the grocery store, and then take the first left. Turn into the driveway of the large tan house on the left, at 714 North Cedar.

Here’s a heuristic for getting to someone’s house: Find the last letter we mailed you. Drive to the town in the return address. When you get to town, ask someone where our house is. Everyone knows us—someone will be glad to help you. If you can’t find anyone, call us from a public phone, and we’ll come get you.

The difference between an algorithm and a heuristic is subtle, and the two terms over-lap somewhat. For the purposes of this book, the main difference between the two is the level of indirection from the solution. An algorithm gives you the instructions directly. A heuristic tells you how to discover the instructions for yourself, or at least where to look for them.

Answer 3

Algorithm is a sequence of some operations that given an input computes something (a function) and outputs a result.

Algorithm may yield an exact or approximate values.

It also may compute a random value that is with high probability close to the exact value.

A heuristic algorithm uses some insight on input values and computes not exact value (but may be close to optimal). In some special cases, heuristic can find exact solution.

Answer 4

An algorithm is the description of an automated solution to a problem. What the algorithm does is precisely defined. The solution could or could not be the best possible one but you know from the start what kind of result you will get. You implement the algorithm using some programming language to get (a part of) a program.

Now, some problems are hard and you may not be able to get an acceptable solution in an acceptable time. In such cases you often can get a not too bad solution much faster, by applying some arbitrary choices (educated guesses): that's a heuristic.

A heuristic is still a kind of an algorithm, but one that will not explore all possible states of the problem, or will begin by exploring the most likely ones.

Typical examples are from games. When writing a chess game program you could imagine trying every possible move at some depth level and applying some evaluation function to the board. A heuristic would exclude full branches that begin with obviously bad moves.

In some cases you're not searching for the best solution, but for any solution fitting some constraint. A good heuristic would help to find a solution in a short time, but may also fail to find any if the only solutions are in the states it chose not to try.

Answer 5

An algorithm is a self-contained step-by-step set of operations to be performed 4, typically interpreted as a finite sequence of (computer or human) instructions to determine a solution to a problem such as: is there a path from A to B, or what is the smallest path between A and B. In the latter case, you could also be satisfied with a 'reasonably close' alternative solution.

There are certain categories of algorithms, of which the heuristic algorithm is one. Depending on the (proven) properties of the algorithm in this case, it falls into one of these three categories (note 1):

• Exact: the solution is proven to be an optimal (or exact solution) to the input problem
• Approximation: the deviation of the solution value is proven to be never further away from the optimal value than some pre-defined bound (for example, never more than 50% larger than the optimal value)
• Heuristic: the algorithm has not been proven to be optimal, nor within a pre-defined bound of the optimal solution

Notice that an approximation algorithm is also a heuristic, but with the stronger property that there is a proven bound to the solution (value) it outputs.

For some problems, noone has ever found an 'efficient' algorithm to compute the optimal solutions (note 2). One of those problems is the well-known Traveling Salesman Problem. Christophides' algorithm for the Traveling Salesman Problem, for example, used to be called a heuristic, as it was not proven that it was within 50% of the optimal solution. Since it has been proven, however, Christophides' algorithm is more accurately referred to as an approximation algorithm.

Due to restrictions on what computers can do, it is not always possible to efficiently find the best solution possible. If there is enough structure in a problem, there may be an efficient way to traverse the solution space, even though the solution space is huge (i.e. in the shortest path problem).

Heuristics are typically applied to improve the running time of algorithms, by adding 'expert information' or 'educated guesses' to guide the search direction. In practice, a heuristic may also be a sub-routine for an optimal algorithm, to determine where to look first.

(note 1): Additionally, algorithms are characterised by whether they include random or non-deterministic elements. An algorithm that always executes the same way and produces the same answer, is called deterministic.

(note 2): This is called the P vs NP problem, and problems that are classified as NP-complete and NP-hard are unlikely to have an 'efficient' algorithm. Note; as @Kriss mentioned in the comments, there are even 'worse' types of problems, which may need exponential time or space to compute.

There are several answers that answer part of the question. I deemed them less complete and not accurate enough, and decided not to edit the accepted answer made by @Kriss

Answer 6

Actually I don't think that there is a lot in common between them. Some algorithm use heuristics in their logic (often to make fewer calculations or get faster results). Usually heuristics are used in the so called greedy algorithms.

Heuristics is some "knowledge" that we assume is good to use in order to get the best choice in our algorithm (when a choice should be taken). For example ... a heuristics in chess could be (always take the opponents' queen if you can, since you know this is the stronger figure). Heuristics do not guarantee you that will lead you to the correct answer, but (if the assumptions is correct) often get answer which are close to the best in much shorter time.