An Optimisation Solution, also known as an Optimisation Scheme, is made up of the following parts:
The level of difficulty of an optimisation problem primarily lies in the number of variables in the decision set and the smoothness of the model. Constraints actually tend to aid the search methodThe method by which new consistent decision set can be identified in such a manner that eventually the 'best' decision set will be found. by reducing the space that has to be searched. Of course there may be so many constraints (over-constrained) that there is no valid set of decisions.
It must be stressed that any aspect of the optimisation problem that does not form part of the model, constraints or cost functionA function that returns a value from a well ordered set for each of the outcomes from a set of decisions. The well ordered set is usually the set of all real number and the cost can often be interpreted in monetary terms.. will have no influence on the result of the optimisation. In particular anything that effects the 'quality' of the decision must be part of the cost function.
The modelA simplified description providing a basis for an empirical understanding and representation of a system that can be used to forecast its behaviour according to a set of decisions. is usually a set of equations but may be a simulation. The ways of representing decisions may be restricted by the choice of search method.
The term Cost Function should not be taken too literally, profits are obviously negative costs but in addition the 'cost' can apply to any quantity which can be ordered (for which the relationships < and > have meaning). However it must be possible to convert all aspects of a 'good' decision into the cost units so that monetary value is still the most common cost units.
Optimal Solutions 4U can provide advice on how optimal decision problems can be stated and on what search method should be used. We would be pleased to offer consultancy on this, or any other aspect of Optimisation. You can get in touch by sending a message from our Contact Us page, or by calling us on the number below.