The Ultimate Solution Approach to Intractable Problems

There is now strong belief that P ? NP. This means that some very common problems cannot be solved efficiently under current and so called Von Neumann type computer architectures including parallel configurations. And, this will remain the case even in relatively low dimensions. What one may hope to achieve is the best possible solution given the available facilities within the allowed time. This makes the current definition of the optimum redundant for practical purposes. Therefore, a new definition of the optimum is required as well as appropriate approaches to find it. This paper will put forward a definition for the practical or sensible optimum, the s-optimum, consider its consequences and suggest what can be the ultimate approach to finding it. Although this approach is generic and can be applied in any context, optimisation and search are the specific contexts we will be concerned with here.