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ATab Table of Contents Optimization
To find the optimal layouts of an anode table ATab splits this task into three steps:
1) create permutations,
2) sort the permutations according to sorting criteria,
3) select optimal layout.
The following chapters describe these procedures.
Create Permutations
Example
ATab uses the following method to find systematically all possible layouts for a given number of anodes: ATab determines all permutation of n elements (n anodes) and creates the anode change schedule according to these permutations keeping the standard anode numbering scheme constant. The next figure shows, as an example, the conversion of three permutations of eight elements (anodes) namely for 1 2 3 4 5 6 7 8 (A next figure), 5 1 6 3 2 7 4 8 (B) , and 8 7 6 5 4 3 2 1 (C) to the corresponding anode table layout.
Permutations.
This figure shows the anode change schedule corresponding to the permutations 1 2 3 4 5 6 7 8 (A), 5 1 6 3 2 7 4 8 (B), 8 7 6 5 4 3 2 1 (C) of eight elements i.e. eight anodes. ATab determines this schedule by keeping the standard anode numbering scheme constant.
New Permutations
When you click on the menu items Tools Optimization you open the Optimization Window that you see in the next figure. The window head contains a little anode table schema and several input fields, buttons and combo boxes.
Optimization Floating Window.
The head of the Optimization Window contains a little anode table schema, input fields, combo boxes and buttons. With the combo boxes you select the type of permutation and output listing to create. With the buttons you transfer the data from the ATab main view into the optimization system and you define the selection parameter for the output listing.
After you have changed the number of anodes to 8 and the number of permutation elements to 7 (7 + 1 means that ATab keeps the anode change cycle day of anode 1 constant i.e. this anode is changed always on day 1) ATab allows to create the permutations. Therefore ATab draws the anodes in blue and shows the blue Create Permutation button (next figure).
Ready to Calculate the Permutations.
ATab draws the anodes whose anode change cycle days are permutated in blue and shows the blue Create Permutation button. ATab does it after you have changed the number of anodes to 8 and the number of permutation elements to 7. 7 + 1 means that the anode 1 is changed always on cycle day 1 i.e. only permutations of 7 elements have to be created.
After you have have pressed the Calculate Permutation button ATab calculates the permutations and the evaluation values and lists all the permutation as you have selected in the Output combo box (next figure).
Result of the Permutation Calculation.
This window shows the starting parameters and the result of the permutation calculations namely the layout and evaluation values for each permutation i.e. anode table layout.
Double Anodes
When you click on an anode of the anode schema it changes its color to orange meaning it is activated to become an double anode. When you click again on an adjacent anode of the activated anode ATab converts the two anodes to an double anode i.e. these anodes are changed on the same anode cycle day. On the next figure you you see an anode table of six anodes with two single and two double anodes. Correspondingly there are only four anodes i.e. four elements to be permuted.
Double Anodes.
Double anodes are anodes to be changed on the same anode cycle day. You create a double anode by clicking on adjacent anodes with the mouse pointer. If an anode table of six anodes contains two single and two double anodes ATab must create only permutations four elements.
When you have created an anode table layout with double anodes (next figure) you may also press the Transfer Anode Table Data button to create the corresponding permutation start data.
Transfer Anode Table Data.
When you press the Transfer Anode Table Data button (symbolically shown on the right side) of the Optimization window head you transfer the data of the ATab main views into the optimization system i.e. in this example the anode table scheme changes from six single anodes to two single and two double anodes.
When you have pressed the Calculate Permutation and you have selected List All Permutations ATab creates the values shown in the next figure. On the left side of the output listing you find the permutations, the anode change sequence and the corresponding anode cycle change days.
This window shows the result of the permutation calculations. On the left side of the listing you find the permutations and the corresponding anode change sequence as well as the anode cycle change days. When you click on one of the permutation lines ATab draws the corresponding layout.
Expanding Permutations
The basic idea of expanding permutations is to add anodes to an existing optimal anode table layout and create permutations of these new anodes to find a new optimal layout. ATab lets you choose between three types of expansions:
expand left: the new (blue) anodes are added left to the (grey) constant anodes.
expand left and right: the new (blue) anodes are added left and right to the (grey) constant anodes.
expand right: the new (blue) anodes are added right to the (grey) constant anodes. minus bottom right.
You must also decide how anode change sequence will take place: the new anodes before, after or mixed with the constant anodes. The next figure shows the corresponding head of the Optimization window where you choose the parameters for the expansion calculation.
Parameters for the Expansion Calculation.
Before you start the expansion permutations calculations you define beside the number of anodes and number of permutations the type of expansion (expand right in the figure) as well as anode change mode (mixed start with new elements). Then you press the Create Permutations button to start the calculation.
The next figure shows one of the new layouts. Since the mixed anode change mode is set the following anode change sequence is executed: first the two new anodes 5 and 9, then the constant anodes 1-2 (double anode) and 3, then again the new anodes 10 and 4 and finally the constant anodes 6 and 7-8 are changed.
Expanding Permutations Result.
This figure shows one of the calculations result with the following anode change sequence: 5, 9 (new anodes), 1-2, 3 (constant anodes with one double anode), 10, 4 (new an odes) and 6 7-8 (constant anodes).
The next figure represents a little bit more complex example: a first step determined new permutations for 5 + 1 elements i.e. four double and two normal anodes and the second step calculated expansion permutations for 7 + 1 elements (eight double anodes), expand left and right with, mixed anode change mode start with the new anodes.
For this example ATab determined at first new permutations for 5 + 1 elements (four double and two normal anodes) and then expansion permutations for 7 + 1 elements (eight double anodes). At the top you see the corresponding permutation anode table schema.
Sorting Permutations
Sorting by Absolute Values
In the examples discussed up to now ATab has sorted the permutations by the permutation number. The next figure shows the first ten permutations of six (actually 5+1) elements sorted by their numbers. In the last magenta line ATab represents the values of the reference layout.
Sorting by Permutation Number.
Normally ATab sorts the permutations by their numbers. This figure shows the first ten of the 120 permutations for six (5+1) elements. The last magenta line represents the values of the corresponding Reference layout.
You may also sort the permutations by the evaluations values, for instance, by the average anode distance (d) or by the average anode surface differences between adjacent anodes (ΔA(b)) as you see in the next figure. You do this by selecting "absolute values" of the Sorting combo box. The clicking on the corresponding button in the listing head tells ATab the values to sort. Clicking again on the button will switch between ascending and descending order.
Sorting the Evaluation Values.
Selecting "absolute values" and clicking on the corresponding button in the listing head tells ATab to sort the permutations by the corresponding evaluation values. In the upper listing the permutation are sorted by the average anode distance (d) and in the lower listing by average surface difference between anodes (ΔA(b)). Clicking again on the buttons toggles between ascending and descending sorting order.
Sorting by Relative Values
ATab determines the weighted relative difference of the actual permutation layout value minus a Reference layout value and adds them up to a key value. (Equ. 1). The ATab sorts then the permutation by these key values considering in this way the influence of several layout parameter on the permutation sorting.
(1)
The next figure shows the Sorting Parameter window and the Optimization window with the results of corresponding relative sorting. You open the Sorting Parameter window by clicking on the Sorting Parameter button in the head of the Optimization window. In the Sorting Parameter window you enter or modify the weighting factors. ATab sorts the permutation by descending key values therefore you set a minus sign for a value when you want that a negative difference permutation value minus reference value should be added to the key value. You find the weighting factors in the head of listing of the results. The darker columns indicate a weighting factor wi = 0.
Sorting Parameter Window and Results of Sorting Relative Values.
In the Sorting Parameter window you enter the weighting factors. A negative sign means that a negative relative difference layout permutation value minus reference value is added to the key value. The Optimization window shows the corresponding sorting results. ATab is sorting the permutation values by a descending order of the key values. The weighting factors you find in the head of the listing.
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