All displays give a graph of the best current performance. The scales for the graph are taken from the design’s performance parameters. Where appropriate, the values of the targets are indicated on the graphs.
Above the graph there is a data window that presents details of the refinement progress and it is here that the various displays differ.
Once the refinement or synthesis is under way it will terminate without supervision when criteria set in the parameters editor are satisfied. These depend on the particular technique but they involve a target figure of merit, or a certain number of iterations or cycles, or a certain range of the figures of merit. However, some control can be exerted on it as it proceeds and this may be of benefit to the process. The control involves selecting the pause button that is at the top right of the display. This presents the user with a number of options that depend to some extent on the technique. All include the option to terminate the process either accepting the best design so far or returning to the starting design. It is also possible to recycle the process. This means simply resetting a number of the parameters so that the refinement is effectively restarted from the beginning but adopting as starting design the best current one. This works very well in Simplex where a periodic disturbance of this type helps to improve the convergence and is recommended. In some of the processes it is possible to change a number of the
parameters of the refinement. Finally it is possible to resume the process with no changes at all.
Simplex Progress
The display below shows the current range of figures of merit together with the results of the current assessment of a replacement design. The first choice is the design reflected in the center of gravity and this is indicated by the letter A. Should A be acceptable then a further assessment of a design that goes even further (twice as far) in the same direction is shown as B. The better of A or B is accepted. Should A be unsatisfactory then a design that is half way from the existing design to the center of gravity is assessed as design C.
If this is better it will be accepted. Should neither A nor C be acceptable it is a sign that the extent of the simplex is greater than a simple merit function minimum and so the simplex should be reduced in size. All designs are then moved towards the best design and the process then continued.
The plot of the performance of the current design uses the parameters that have already been set up for performance calculations.
The pause button at the upper left brings up a pause box with a number of options.
The refinement may be terminated with either the preservation of the best design or a return to the starting design. The refinement parameters may be changed without
terminating the process. The recycle command starts up a completely fresh simplex based on the current best design and helps to revitalize the convergence if it has become sluggish. In fact it is recommended that recycle should be activated at least once towards the end of the process.
Optimac Progress
Optimac shows a number of entries in a window displaying the performance curve.
The particular entries depend on the stage of the process. A typical display might be as shown.
The upper line shows the cycle and iteration numbers. On the next line are the current number of layers and the search number. A cycle number indicates that this is synthesis.
Optimac refinement is indicated by the term Optimac Progress instead of Optimac Cycle.
Refinement rather than synthesis is selected by entering zero for the number of synthesis cycles in the parameters dialog box. The iteration number gives the number of iterations so far completed in the current synthesis cycle, that is in the refinement that follows a change in the number of layers.
At each iteration, a number of directions in parameter space equal to the number of layers is searched. These directions are set up in different ways and the search number indicates which direction is currently being searched. The progress of the search is indicated in the small display box at the top right of the progress window. This shows the various evaluations of the merit function as vertical lines that are either green or red
plotted against the magnitude of the current displacement vector. Green indicates a negative vector and red a positive. Note that this does not mean that the layers are necessarily thinner or thicker. The vector positive direction in parameter space is quite arbitrary. The dark line across the lower part of the progress box indicates the current best figure of merit and gives an idea of scale. The vector scale is simply arranged so that the width corresponds to the searched region. Sometimes it will be clear that the region actually searched is smaller and this indicates that over the missing part at least one of the thicknesses involved became negative.
Starting, current, and best figure of merit are self-explanatory. The vector shown corresponds to the best value for the particular search direction. The improvement displayed is unity if the current reduction in the figure of merit represents 1% of the limiting range for the merit function scaled to take account of the current merit function.
For example, if the limiting range is 0.1 then RI of 1.0 indicates an improvement of 0.001, or 0.1%, in the current figure of merit. If the relative improvement falls below 1.0 then the current direction set is considered to be failing and, after an evaluation
procedure, a different technique is substituted unless the procedure indicates that it is worth continuing with the current one. The particular procedure is indicated in parentheses after the improvement figure. G (standing for gradient) is the simplest and represents changes in just one single layer at a time. If the changes in the layers are small then G reproduces roughly the same alterations as does one of the gradient methods. C indicates that the directions within the set are being changed. The way in which they are changed ensures the generation of a conjugate set. A indicates no change in the set. B and BMod represent a number of alternative sets, BMod being not just one but several different sets and Rand represents a completely random but mutually orthogonal set. All of these are either changed, based on the current results when the letter C is displayed, or retained unchanged, when the letter A is displayed. The details of the sets are
unimportant from the user's point of view but the technique can be thought of as constantly probing and searching in new directions to reach deeper and deeper levels of the merit function.
The synthesis is made up of a number of phases. These are indicated by Phase, just below Improvement. Refinement indicates a period of refinement with the number of layers remaining constant. At the end of each set of iterations that make up a synthesis cycle the Inserting Layers phase is entered. Here, layers that are not useful in maintaining the figure of merit are removed and others are added. The added layers at this stage have thicknesses corresponding to the synthesis step. A number of different techniques based on experience are used for adding the layers and several may be involved. Sometimes the design is also deliberately perturbed. Immediately after the additions the merit figure, and the number of layers, will usually show increases. The effect of the changes is then assessed in an operation known as Initialization that
measures the rate of merit improvement and accepts the changed design only if the rate is considered satisfactory. Then the refinement portion of the cycle will recommence.
Otherwise an alternative systematic phase known as a Screening Search will be initiated. This screening search begins by discarding useless layers and then explores a large number of alternatives but is triggered only when the normal processes of addition and perturbation fail.
The process may terminate in several ways. If the merit figure falls below the set range or if the number of cycles exceeds the number entered then the termination will be
automatic. Often, however, the process may be terminated manually. This can be done by selecting the pause button which brings up a pause box similar to that for simplex.
When the process terminates it may be, if the synthesis parameter is large or if the termination occurs during an initialization, that an earlier cycle had a better figure of merit. If so this will be pointed out and the opportunity given to accept the better earlier design rather than the poorer later one.
Annealing Progress
Simulated Annealing has a similar display, shown below, although the various entries are different in detail.
The current figure of merit is that calculated for the latest perturbation of the design. If this figure of merit is an improvement on the existing one then it will be accepted and the improvement item will show briefly a positive figure. If the figure of merit is worse than the current one then it may be accepted with a probability determined by the Boltzmann function. Then the improvement will show briefly a negative value. The best figure of merit indicates the lowest merit figure so far which is being held until a still better figure is achieved
Conjugate Gradient Progress
The Conjugate Gradient display is relatively simple. The figure of merit at the start of refinement is displayed together with the current figure of merit.
Clicking on the Pause button displays the following options:
Selecting Save Best Design stops the refinement and stores the best design in the design editor. Continue closes the window and continues refinement. Plot Now causes the progress display plot to be updated with the performance of the current design. Abort Refinement stops refinement but does not change the contents of the design window.
Quasi-Newton Progress
The Quasi-Newton display is relatively simple. The figure of merit at the start of refinement is displayed together with the current figure of merit.
Clicking on the Pause button displays the following options:
Selecting Save Best Design stops the refinement and stores the best design in the design editor. Continue closes the window and continues refinement. Plot Now causes the progress display plot to be updated with the performance of the current design. Abort Refinement stops refinement but does not change the contents of the design window.
Needle Synthesis Progress
The Needle Synthesis display is shown below. The figure of merit at the start of refinement is displayed together with the current figure of merit. The current synthesis cycle number is also displayed together with the current phase of synthesis. The
displayed phases are Adding Layers shown when Needle Synthesis is determining where to add layers, Refining when Needle Synthesis is performing Conjugate Gradient refinement and Compacting when Needle Synthesis is removing thin layers.
Clicking on the Pause button displays the following options:
Selecting Save Best Design stops the synthesis and stores the best design in the design editor. Continue closes the window and continues synthesis. Next Cycle causes synthesis to begin the next synthesis cycle by adding new layers. Add Material forces Needle Synthesis to add extra material to one end of the design. Plot Now causes the progress display plot to be updated with the performance of the current design. Abort Synthesis stops synthesis but does not change the contents of the design window.
Differential Evolution Progress
The Differential Evolution display is shown below. The current generation is displayed together with the current population member being evaluated. Finally the current best and worst merit figures in the current generation are also shown.
Clicking on the Pause button displays the following options:
Selecting Save Best Design stops the refinement and stores the best design in the design editor. Continue closes the window and continues refinement. Abort Refinement stops refinement but does not change the contents of the design window.