You may consider reading the following:

http://sofia.cs.vt.edu/cs1114-ebooklet/chapter4.html

http://www.ppig.org/papers/21st-muller.pdf

http://joaoff.com/wp-content/uploads/2011/06/thesis-a4-colour.pdf

you can easily explore and innovate new algorithm as a problem solving technique by either:-

1) Studying the present algorithms for solving a certain problem, studying the drawbacks, compare between them then trying to look at how to modify for treating these drawbacks. 

or 

2) You create from Scratch an algorithm for solving the problem by looking to the problem from other sides.

Good Luck.

Prof. S. EL-Rabaie

inspire your self with mimiing the behavior of animals 

It is a very good question. Machine learning can help in exploring much further the algorithm search space, than humans.  I would consider this type of techniques.  

Evolutionary hyperheuristic has been using trees a lot but also a variety of encoding scheme. 

Patricia 

It is not very easy to develop a 'new' algorithm from scratch. I will recommend the first approach suggested by Prof. S. EL-Rabaie in his reply. You can then move on gradually to developing a completely new algorithm.

By experience you know considerably of a filed to stumble on a problem or in a new solution. You then go see if its already done and appears not to, and if possible you publish it or patent it in some cases.

In companies its more often goal driven. i.e., someone asks to address a problem and no solution is found so you try something new.

Hi George Jacob,

By experience certainly,

falling on an issue therefore a new solution will appear.