Many search methodsThe method by which new consistent decision set can be identified in such a manner that eventually the 'best' decision set will be found. have been developed but most are only suitable for a rather restricted range of types of model, constraints, and decision variables. Use of these specialised techniques takes a substantial investment but may be justified for key decisions. The techniques that can be used for a reasonably wide range of optimisation situations are:
| Method | Description |
|---|---|
| Calculus and Gradient Search | Basically high school maths (first derivatives are zero at maxima) carried out in a systematic manner. Suitable when there are few and continuous decision variables together with smooth models and simple constraints. Can also use numerical methods to find maxima and minima. |
| 'What-if' | An expert runs a valid decision set through the model, evaluates the outcome and identifies a new decision set. Not really an optimisation method but can be used to find 'acceptable' decisions. Suitable when there is a good but slow model and not too many decision variables. |
| Stochastic | Values for decision variables are selected randomly but within the constraints. The model is run for each decision set and cost determined. The decision set with the least cost is selected. Again this is not a true optimisation, but if many decisions sets are tried the best that is found should at least be good. Well suited for discrete decision variables. |
| Branch & Bound | The search space is considered as a tree with branches starting at each choice for a variable. As each choice is made the cost function is run on the decisions that have been made so far. If the cost is more than the cost for a full decision set that has already been found then the complete branch can ignored. Can only be used when the cost function is increasing for each new decision made. Only suited for discrete decision variables. |
| Genetic Algorithms | Genetic algorithms are designed to work in same way as evolution. The individual decisions are considered to be genes and the model and cost function represent success in reproducing. After running a number of decision sets, the best sets are retained and combined to form the next generation. If the decision variables have been represented as genes in a suitable way after a number of generations the method should find a good solution. |
| Linear Programming | The most powerful general purpose optimisation method when there are large numbers of continuous decision variables. The main restriction is that the model, constraints and cost function can only be linear expressions of the decision variables. However it provides a true optimisation and can deal with very large numbers of decision variables. |
| Integer Programming | An extension of linear programming which enables some discrete decision variables to be included. Uses linear programming for the continuous variables and branch and bound for the discrete variables. |
Please browse use the menu on the left to see more information on some of these search methods.
Optimal Solutions 4U can provide advice on the selection of optimisation methods for particular types of decisions. 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.