Find the optimal selection of materials to fit in a target value.
Edit By BS Editor: SizeFitter 4.0 has been uploaded. Tidier and easier to understand data management. Twice as fast as earlier versions. This was actually year 2003; no bugs have been found or reported since. SizeFitter is now a classical software tool.
Suppose that you are planning to use a range of standard elements for a construction, and the sum of the elements has to add up to a desired length. The construction can be almost anything you have in mind, e.g. a wall or a Facade. How would you select the optimal quantity of each standard unit? Take as an example the following range of units for the completion of a target length of 54 ft 6.
It is preferable that the units should add up to the desired total length of 654 inches, but working just this out is a difficult hit-and-miss task as there are millions of combinations to try out. The economically minded would like to make sure that the solution is the cheapest possible, but the cheapest solution in this case consist of 14 pieces of unit No. 6 and one piece of unit No. 3, totaling 拢789.25. But inevitably this solution leaves a surplus length of 1.25 that would need to be shaved off and this may spoil the finish.
The Multi-Objective solution is Pareto optimal for the two criteria, but this just means that you cant Improve on both criteria at the same time. The above mentioned minimum cost solution is unique for the objective. However when going for the best fit, there are multiple solutions with the same optimal fit, but with different costs, hence there is an opportunity to MOVE onto the Pareto efficient frontier, thats what has happened here.
Now you can also play with the bounds: Suppose there were only 12 of unit No. 6 in stock. Would the cheapest solution then result in an exact fit? The answer is still no. That would have resulted in a cost of ?94.10, but with 1 excess misfit. You can play with the bounds interactively. If the bound on unit No. 6 is lowered still further, the optimal quantities of the other... you can free download SizeFitter 4.0 now.