<p>You seem to be looking for "program synthesis", which can work in some limited instances, provided you can correctly and formally specify what your algorithm is supposed to do (without giving an implementation).
Synthesis is an effective approach to build gate-level circuits, but applying synthesis to software is so far still more of a research avenue than practical.</p>

<p>Still, here are a couple of references on the subject, </p>

<p>(Some of the most advanced work in the area in my opinion, has a tool)
program sketching by Armando Solar-Lezama</p>

<p>Check out Microsoft research page on the topic, they think it's hot topic: <a href="http://research.microsoft.com/en-us/um/people/sumitg/pubs/synthesis.html" rel="nofollow">http://research.microsoft.com/en-us/um/people/sumitg/pubs/synthesis.html</a></p>

<p>Some other similar stuff I've seen :
Model Checking-Based Genetic Programming with an Application to Mutual Exclusion. (Katz &amp; Peled @ TACAS '08), they have a more recent version on ArXiv : <a href="http://arxiv.org/abs/1402.6785" rel="nofollow">http://arxiv.org/abs/1402.6785</a></p>

<p>Essentially the search space is explored (exhaustively) using a model-checker.</p>
Exhaustive search for algorithms - existing works?
<p>You might have to read this twice so that my idea becomes clear. Please be patient.<br>
I'm looking for existing work for exhausive search for algorithms for given problems. Exhaustive search is also known as brute force search, or simply brute force.</p>

<p>Other exhaustive search algorithms search for a solution for a given problem. Usually, a solution for such a problem is some data which fulfills some requirements.</p>

<p><strong>Exhaustive search example</strong>:<br>
You want the solution for a KNAPSACK problem. That is the objects which can be packed into the bag so that there is no other combination of objects which fit into the bag and which would sum up to a bigger value than your result  combination.<br>
You can solve this by going over all possible combinations (exhaustive) and search for the one which fits into the bag and which is the most valuable one of those combinations.</p>

<p>What I'm looking for is just a special case of exhaustive search: Exhaustive search which searches for an algorithm as a solution. So in the end, <strong>I'm looking for an algorithm which searches for an algorithm which solves some given problem.</strong></p>

<p>You might say: Go google it. Well, yes I've done that. The difficulty I'm facing here is that googling for "algorithm which searches for another algorithm" results in all the same as "another search algorithm". Obviously, this has too many unwanted results, so I'm stuck here.</p>

<p>How can I find existing work related to exhaustive search for algorithms?<br>
More specifically: Has there any software been written for this? Can you point me to any links or algorithm names/better keywords in relation to this topic?</p>

<p><strong>Update</strong>:<br>
The purpose for which I'm looking for such an algorithm search is solving problems for which no good heuristics are known, e.g. prooving-algorithms or trying to finding other solution algorithms for problems which might or might not be NP-complete problems (thus proving that the problem is not NP-complete if a faster algorithm can be found; without any human interaction).</p>