The optimization task in COPASI allows you to minimize an objective function by adjusting one or more parameters within specified ranges. This concept may sound abstract at first, so let’s clarify it with a simple example.
Suppose you have a model with several reactions, and the fluxes of two of these reactions (let’s call them R1 and R2) are influenced by a particular parameter, k (either directly or indirectly). Your goal is to determine the optimal value of k that maximizes the ratio R1/R2. Next, we’ll see how to set this up in COPASI.
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| Optimization Task Dialog |
To access the Optimization dialog in COPASI, navigate to the tree view and select Task → Optimization. This will open a screen similar to the one shown above.
At the top of the Optimization dialog is an Expression field, where you
enter your objective function, the expression that COPASI will try to
minimize during optimization. For example, suppose you want to optimize the
value of a parameter k so that the ratio of the fluxes through two
reactions, R1 and R2, is minimized.
For this example, we’ll use the second approach (assuming both fluxes are always positive).
You cannot simply type R1/R2 as the objective function, because COPASI
does not directly recognize the names R1 and R2. Instead, follow these
steps:
( in the Expression field.R1 and click OK. COPASI inserts the correct object reference into
your expression./, then repeat the object selection process for R2.).Note: You may edit only the parts of the expression not formed by object references from the Object Browser. Object reference strings inserted via selection should not be modified directly, but you may delete an entire identifier if needed.
COPASI offers several optimization methods, selectable from the dropdown menu below the objective function field. Each method has its own parameters, which are detailed in the Methods section.
The optimization task can be run on many different subtasks. You choose which
one to use by selecting the corresponding check boxes. For the R1/R2 example,
you would usually select the Time Course option.
Next, you must specify which parameter(s) COPASI will optimize. In the middle section of the dialog, after the Object label, is another field allowing you to choose the parameter to scan. Click the adjacent button to open the Object Browser and select the correct parameter. You can specify multiple parameters if needed.
Below the Object field, supply upper and lower bounds for each
parameter. The bounds can be numerical values or expressions involving other
parameters. By default, the bounds are set to -Infinity and +Infinity,
but since computers cannot truly handle infinite values, the optimization
searches over the range of representable double precision numbers.
To use custom bounds, uncheck the +Inf or -Inf boxes and enter your
desired limits. You can also specify limits relative to the start value
(e.g., entering +20% sets the upper bound to 20% above the initial value).
The start value is the initial estimate COPASI uses for optimization; by
default, it uses the parameter’s current value, but you may override it
manually, randomize it, reset to model values, or set it to the most recent
optimized result. If your start value is outside the specified bounds, COPASI
will adjust it to the nearest allowed boundary.
To remove a parameter from the scan list, select it and click the delete button. Add more parameters with the new button; you may select and edit multiple parameters together. The order in which parameters appear matters only if the bounds of one parameter depend on another, COPASI does not track such dependencies automatically, so arrange as needed.
In addition to optimizing parameters, COPASI allows you to specify constraints. Constraints restrict the solution after each simulation step (whether a time course or steady-state calculation). For example, you could constrain the steady-state concentration of a species to lie within a given range. The Constraints tab lets you define each constraint as an object with upper and lower limits, using the same selection and entry process as for optimization parameters. Multiple constraints can be specified.
If the Randomize Start Values checkbox is enabled, COPASI will generate random starting values (within the specified bounds) for each optimization parameter.
The Create Parameter Sets checkbox, when enabled will cause COPASI to create Parameter Sets with the initial and the final state of the model.
Once you’ve configured parameters, constraints, and the objective function, click Run to begin optimization. While running, COPASI displays a progress dialog that shows the current best (smallest) objective function value found so far. Since this dialog closes automatically at the end, you may also want to define a report to log optimization results during the calculation.
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| Optimization Progress Dialog |
In most cases, the default report name Optimization is sufficient. The default report includes a summary of all settings you provided for the optimization run. It also outputs intermediate results whenever the target value improves and concludes with a summary of the final result.
The easiest way to create a custom report is to use the output assistant. Alternatively, you can create a report manually, as described in the output section.
Once you have defined a report for the Optimization task, click the Report button at the bottom of the dialog. In the dialog that opens, select your desired report from the Report Definitions dropdown list, then choose or type a filename in the Target field for where the report should be saved. You can type the filename directly or click the Browse button to select a location. When finished, click the Confirm button.
The next time you run the optimization, COPASI will save the report to the location you specified.