Multi-Objective-Optimization-with-WealthLab

You’d need to create a new ScoreCard using our API, or use our Concierge development service and we could build it for you.

https://www.wealth-lab.com/Support/ExtensionApi/ScoreCard

QUOTE:
is there an extension pack which allows multiple parameters in the definition of ‘best’?

Yes. This extension is called finantic.ScoreCard.
(see https://www.wealth-lab.com/extension/detail/finantic.ScoreCard)

Among many other useful features it contains the "FormulaSoreCard".

This ScoreCard allows you to create new performance metrics that are combinations of existing metrics. (with arbitrary complexity if you wish so).

This allows for multi-objective optimization or multi-criteria optimization.

Your case is rather simple to implement:


With finantic.Scorecard installed:
* Go to Extensions->Formula Screcard
* This Opens the "FormulaScoreCardControl" window
* Click "New..."
* This opens the "Create New Formula Metric" window
* Enter meaningful values for Name, Label, Category and so on (see screenshot above)
* Enter the Formula that calculates your new metric.

I entered:

CODE:
AvgTradesPerMonth > 0.1666 ? ProfitPerBar : -10

This is a standard C# expression. It means:
If AvgTradesPerMonth is larger than 0.1666 then the metric is ProfitPerBar
If AvgTradesPerMonth is smaller, than it returns -10.

You might adapt by clicking the "Variables..." Button and choosing any other available component.

By clicking the "Evaluate" button it shows the result of your formula (based on the last backtest) (see screenshot above)

Any of the metrics defined that way can be used as a target metric for the "Shrinking Window" optimizer.

Or the SMAC optimizer, which is highly recommended.
(Part of finantic.Optimizer extension)

Please don't get confused by the calculation time shown above. The time above includes one time initialization of the expression engine. This is done once for the complete scorecard.

A second click on "Evaluate" shows:

Calc.Time: 47.876 ms

QUOTE:
This allows for multi-objective optimization or multi-criteria optimization.

Can you provide some examples of how to implement this in the extension?

As a start:

Say we want a SharpeRatio of 2.0 have the same *weight* as an APR of 20.

Then I'd define a combined metric like so:

Here I use the formula

CODE:
SharpeRatio / 2.0 + APR / 20.0

This weights an improvement in Sharpe Ratio from 1.0 to 2.0 as much as an improvement in APR form 10% to 20%.

It is possible to extend this to more metrics of course.

There are also functions like

CODE:
Clamp(value, min, max)

to limit the input range of an individual metric.

Or things like Sqrt(), Log(), Exp() to modify the relative influence of a single metric.

Or more general:

Multi objective optimization is implemented by a target metric that combines individual metrics for each objective.

The first step is to define desireable ranges and weights for an individaul metric, examples:

Sharpe Ratio: min: 0.0, best 2.0 weight 3.0
WinRate: min 50% best 55%, weight 0.75
... and so on ...

Then the final target metric will consist of a sum (or product) of individual terms.

Each term should be scaled to the same range and multiplied by the weight:
Sharpe Term: Sharpe Ratio / 2.0 * 3.0
WinRate Term: (WinRate - 50.0) / (55 -50) * 0.75

The final "Multi Objective Metric" is the sum of these terms:

MOM := Sharpe Ratio / 2.0 * 3.0 + (WinRate - 50.0) / (55 -50) * 0.75

Enter the formula:

CODE:
Sharpe Ratio / 2.0 * 3.0 + (WinRate - 50.0) / (55 -50) * 0.75

into the Formula field of a new formula metric of the FormulaScorecard and you are ready to conduct a multi-objective optimization with Wealth-Lab.

An existing example of this idea is the WL Score. See Help->Performance Visualizers->Metrics Report->WL Score:

QUOTE:
It is calculated by first finding the Annualized Risk Adjusted Return, which is simply the Annual Percentage Return, or APR, divided by percent Exposure. For profitable systems, the RAR is adjusted by multiplying the sum of 1 plus the Max Drawdown Percent (a negative number). Consequently, profitable but risky systems, which typically have periods with large drawdowns, will have a lower score than an equally profitable system that assumes less risk.

With a little arithmetic you could see that this is the same type of formula as above. The multi objective metric is a product of individual terms in this case.

Thanks, I'll give these a try.

@Eugene: Could you please change the title of this topic to:
"Multi-Objective Optimization with Wealth-Lab"
and add the #KnowHow tag?

Done. Good title.

Great, thanks. Please also add the #KnowHow tag.

QUOTE:
is there an extension ... which allows multiple parameters in the definition of ‘best’?

The guidance in Post #1, or Post #2 and Post #3 are the right answers.

In "theory," what you are trying to do makes good sense. But in practice (from a numerical analysis perspective), you have to recognize the parameter optimizer has serious limitations. As you make the multidimensional solution vector space rougher, the optimizer is more likely to get trapped in a local minimum (or maximum) when optimizing your parameter values.

The optimizer can handle pursing multiple minima or maxima to a limit (some optimizers have a setting for that limit), but if there are too many of them, then it could be trapped in several local minima or maxima. My recommendation would be to smooth out the solution vector space by:

1) minimizing the criteria you're trying to optimize against,
2) minimizing the number of parameters you are trying to optimize at once,
3) using a divide and conquer approach by grouping related parameters together and optimizing those groupings independently,
4) trying different optimizers.

Your numerical analysis professor probably told you to never do 3), and he's right in theory. But in practice, real world optimizers have limitations. And they can easily get stuck in a local min/maxima when you create a really rough solution vector space by design. The best approach is to avoid such a design. Good luck and happy computing.

QUOTE:
it could be trapped in several local minima or maxima.

The SMAC optimizer does a rather good job in these cases. In fact the SMAC algorithm makes no assumptions about the "roughness" or even differentiability of the solution space.