Optimisation Definition and Difficulty

 Introduction 

The computational time needed to simulate a realistic RAM problem for which all the input parameters are given is normally between minutes and days. Some of the input parameters in such problems cannot be readily controlled to yield desirable results. For example, it is not possible to reduce the lightning rate which may cause delays on vessels on their way to support a failed wind turbine in an offshore wind farm. Some other input parameters can be readily changed; for example, the number of spare parts of each replaceable type of component, the number of repair teams, the number and frequency of preventive maintenance tasks and any other controllable parameters representing supportive Resources for the system performance. In such circumstances we try to find the set of input values which will maximise performance. For example, for ageing systems, preventive maintenance may be vital once in a while; but how much? "Not at all", will result in a strongly increasing failure rate, but on the other extreme, too much will cause the system to be always under maintenance and hence unavailable and therefore not performing. So, there will be an optimal maintenance plan for which the performance will maximise. Another example would be spare parts allocation. This is slightly different since the performance is a monotonic function of the spare parts allocation. The more spares the better the performance; so the optimum would be the maximum. But, spare parts cost money, where the latter can be regarded as a constraint on the former. Then, we may define spare parts optimisation as one of the following:

For a given budget, provide the best performance and find the spare parts allocation which will yield it.

For a minimal required performance, find the cheapest spares mixture which will maintain it.

Since preventive maintenance costs money we can include it in these constraints; and since failure cost money as well, and also there is a cost rate for system down-time, such that everything can be transformed into cost units, we can add another definition to spare parts and maintenance optimisation that is:

Minimise the entire cost (or maximise profit) and find the corresponding spare parts mixture with the maintenance plan to provide it.

The Resources space also has a great many degrees of freedom. In order to build up the topology of the performance as function of all the Resources, one must execute an unrealistic number of MCS, and each might last minutes, hours or days. Therefore, running a search algorithm testing each and every possible combination of Resources, and for each, obtaining the objective function, in order to find the optimum point, would be unrealistic. So, we must compromise. In such circumstances a hybrid approach can be used. Here the hybrid approach uses a fast analytic search algorithm which learns from MCS. This will be introduced shortly, but it requires acquaintance with the idea of Sufficiency, which will be used in the GA process as well, and is therefore defined next.

 Sufficiency 

 References 

Download the document
 ACROBAT PDF (257 Ko) 

 General  Mail 

 Mirce 16  Prior Meetings and Documents 

 Mirce 16 Follow-up  ...RAM... ...Using Genetic Algorithms 

 Abstract  Introduction  Optimisation Definition and Difficulty  Sufficiency  RAM Model  Proposed Solution  Resources Density  Genetic  Summary  References 

last update:  December 12, 2006