TRIZ (Теория решения изобретательских задач) is "a problem-solving, analysis and forecasting tool derived from the study of patterns of invention in the global patent literature". It was developed by Soviet engineer and researcher Genrich Altshuller and his colleagues, beginning in 1946. In English the name is typically rendered as "the theory of inventive problem solving", and occasionally goes by the English acronym "TIPS". The approach involves identifying generalisable problems and borrowing solutions from other fields. TRIZ practitioners aim to create an algorithmic approach to the invention of new systems, and the refinement of old systems.
TRIZ enables the generation of new ideas and solutions for problem solving. It is intended for application in problem formulation, system analysis, failure analysis, and patterns of system evolution. Splits have occurred within TRIZ advocacy, and interpretation of its findings and applications are disputed. 
The TRIZ Matrix is a database of known solutions (principles) able to overcome contradictions. I.e, You need a static object to be longer without becoming heavier. This is a contradiction. The improving feature is ' #4, length of stationary object ' and the worsening factor is ' #2, weight of stationary object '. Use the matrix to discover possible ways of solutions, the principles. 
- Video: TRIZ & Systematic Innovation
- http://trizindia.org/ (reportedly involved with open source)
- Paper: Why Reinvent The Wheel? The Efficacy Of Systematic Problem Solving Method Triz And Its Value For Innovation In Engineering And Its Implications For Engineering Management
- Trends of evolution
- wikipedia: Laws of Technical Systems Evolution
- appropedia: Critical thinking - mentions The Three Questions, Six Thinking Hats, Lateral Thinking and the PO (Provocative Operation).