GENETIC ALGORITHMS
It is the modeling of natural selection.

Let’s consider basic terms used in this paper

• Gene;
• Chromosome;
• Fitness;
• Population;
• Crossover;
• Mutation. 

Let’s describe each of them with reference to tasks connected with trading systems.

    Gene – it is one of the system’s parameters which could be optimized. Type of moving average, averaging period or some parameter or coefficient of the digital filter, for example, etc. 

    Chromosome – it is group of genes (parameters) that have logical connection with each other, parameters of one type of input or one signal. This group participates in crossover as a whole, i.e. it is a set of parameters which can migrate between specimens as a whole. Thus successful combinations of genes have better chances to survive and reproduce. It is appropriate to combine connected parameters (of one signal for instance) into one chromosome. 

    Fitness - criterion of profit or suitability of specimen, the criterion function. It is some value that is connected with the specific trading system. By the means of fitness we report to genetic optimizer how much we are satisfied with that trading system. The greater it is – the better is the specimen. In simplest case it can be NetProfit or ProfitFactor, as in original optimization used in TradeStation for example, but we suppose that it is not correct. Results obtained with use of such simple criterions hardly can be stable. In our case user defines himself what is “vitality” of specimen (trading system). In fact one can get trading system that will show stable results in future only due to proper choice of optimization criterion. 

    Population – it is group of survived till present moment best specimens selected by best fitness. Usually trading systems are built in such way that “population” consists of most “vital”, stable systems. 

    Crossover – it is replacement of genes to analogous ones from another specimen or replacement of chromosome to analogous from another specimen of population. 

    Mutation – it is random change of some genes (parameters of system). 

Scheme of genetic algorithm work:

 Genetic algorithm for TradeStation is quite simple for users. After initialization optimizer begins to pass sets of parameters to the system being optimized. After completion of processing of historical data system reports to optimizer the result, i.e. fitness value. On the basis of obtained results optimizer forms the current population consisting of best specimens. After that optimizer applies crossover and mutation and forms new set of parameters for testing. Then system with those parameters runs again on data in question. Then fitness is compared with already existing ones of other specimens. If last fitness is better than previous then “weak” ones are replaced. On the other hand if last computed fitness is “weaker” than already existing ones then it is deleted from population (it remains for the first run) and we search for a new specimen (change parameters of the system), and so on until the search is completed. 

Building the trading systems

 There are several approaches to building the trading systems:

• General approach;
• Smart “economic” approach. 

    General Approach to building trading systems consists of the following steps: 

“Let the man think and let the machine work”…

 

Selection of following parameters: Possible set of assets. Possible set of time intervals. Possible set of concepts. Possible set of indicators that are hypothetically capable for formalization of these concepts. Possible set of indicator parameters values. Possible set of elementary rules that form the signal generation rules. Possible variants of orders (with parameters). Definition of optimization criterion of any complexity and with any limitations. For our tasks basic is monotonous growth of Equity. Definition of Genetic Algorithm parameters. Definition of out of sample time interval. Launch of TS GO – Genetic optimizer.

By the means of genetic optimization algorithm we can get the set of optimal (according to our criterion) trading systems very quickly. When using such approach our task reduces to selection of reasonable rules variants, parameters alternatives and reasonable optimization criterion.

As it often mentioned, estimation of a system or a portfolio by some criterion like “NetProfit” frequently lead to “overfitting”. Using of indirect criteria which we can create solves this problem.

We can let genetic optimizer to have possibility to select parameters and algorithms for building trading systems.

Practical realization for TradeStation.

Let’s see how Genetic Optimization is practically realized for TradeStation. Genetic optimizer consists of program with graphical interface and dynamic library (Dll), which carries out genetic selection functions. Interface of a program has the following structure:

The building of a system by the genetic selection method goes like the following:

1. First, we create the set of possible systems, which is encoded in EasyLanguage in TradeStation environment.
2. Then, parameters being optimized with the use of genetic algorithms are encoded as a “genes” and organized in “chromosomes”. Further we define possible parameters range and step of parameter value change. If step is set to 0, parameters will change continuously.
3. When “genes” are specified and combined into “chromosomes” we formulate our ideas of what is “good system” by setting the fitness – optimization criterion.
4. On final stage we apply the strategy to the graph and start the search of parameters with genetic algorithm. Then we start optimization mechanism by specifying the number of iterations in “Inputs” bookmark, in “Gen” parameter (in TradeStation format strategy window). I.e. internal TradeStation optimizer is used only as a counter of “runs” and as an initializer of genetic algorithm. For example we specify “Gen” parameter to optimize from 1 to 1000 with step equal to 1 as it shown below:

    For the convenience one can use implemented EasyLanguage functions:

• TS.GO.Start(FileName) - Launch of optimizer and definition of file name for the storing of current population. This function always must be executed on the first bar.
• TS.GO.Mode(ModeGO) - Setting of optimizer functioning mode.
• TS.GO.Popul(NPop) - Definition of population size, from 10 to 1000.
• TS.GO.Chrom(Name) - Definition of new chromosome or search by name of already existing one.
• TS.GO.Gen(Name,Chrom,Min,Max,Incr) – Definition of new gene of search by name of already existing one.
• TS.GO.Next(Generation) - Addition new candidate to population or selection of best specimen of population after optimization is complete.
• TS.GO.Finish – Returns the indication of last run of a system when optimization is complete and TradeStation is forming the report.
• TS.GO.Error - Returns error code of last function.
• TS.GO.Var(Name) - Definition of user variable. Variable is associated with current specimen of population and gives possibility of saving user-defined data.
• TS.GO.Get(Name,Individ) - Gets the value of gene or user-defined variable Name from specimen of population number Individ.
• TS.GO.Set(Name,Val) - Sets new value of user-defined variable Name for current specimen of population.
• TS.GO.Fitness(Fitness) - Inform the optimizer that run of the system is complete.
• TS.GO.FreshBlood(FB_factor) – Setting of the “fresh blood” factor of the system. This function increases the effective size of population and does not allow leaders to dominate, which gives a chance to other candidates. This speeds up optimization due to richer variety of gene pool and decreases system’s tendencies to overfitting.
• TS.GO.Stat – Computation of standard characteristics of trading system. 
• TS.GO.ShowViewer - Show Viewer immediately.

More detailed information with the description of functions and principles of building of trading systems can be found on the support forum: http://support.tsresearchgroup.com/ 

Let’s point on advances of genetic optimization once more:

• Arbitrary optimization criteria;
• Computiation of criterion on the part of the history (In Sample/Out Of Sample);
• Great extent of parameter space;
• Quick results;
• If system has variable number of parameters it is possible to optimize that number.

Fighting with the “OVERFITTING” of the systems (Curve Fitting)

There are different ways of fighting the so-called “overfitting” of the systems or “overoptmimization” as it frequently called. Let’s consider those variants which we apply in the field of genetic optimization:

• “Strict” optimization conditions;
• Usage of “Fresh Blood” function from TSGO arsenal;
• Building of non-trivial optimization criterion.

“Strict” optimization conditions.

We interpret strict optimization conditions as the following settings of systems testing:

• Setting of significant slippage, one percent per deal for example;
• Limitations of drawdowns;
• Big number of iterations;
• Big “leverage”.

In practice it was noticed that such testing sets hard conditions for the systems and only really “tough” systems survive. It forces genetic optimizer to select only those systems that are most stable to adverse conditions and impacts. “Survived” systems showed most stable results when were tested on out of sample data.

“FreshBlood” function

“FreshBlood” function causes purposeful perturbance to fitness. As a result the effective size of population increases and convergence improves. It can be considered as a launch of optimizer on variety of price histories that are resulted from initial by perturbance.

Building of non-trivial optimization criterion (Fitness)

In our opinion, building of non-trivial optimization criterion is one of the most essential moments of trading systems building. As it we mentioned above in order to lower the risk of overfitting it is necessary to use another characteristics than NetProfit etc., but those which are associated with desirable behavior of Equity as a whole, not only with its absolute value at the end of the testing period. We can maximize the average of the following value for example:

[log W(T)/W(0) + 2/T * sum { log (W(t)/Wmax(t) }], t = 0,..., T,
where Wmax(t) = max{Wmax(t),W(t)}
i.e. we tend to condition the monotonous growth of Equity W(t)).

Optimization in case of large amount of parameters.

Disputes between “adherents” and “opponents” of the systems with large amount of parameters don’t fade to this day. It practice we noticed the following moments that can significantly influence the results:

• The volume of data and “strictness” of the system.
• If the system has a lot of internal non-controllable degrees of freedom then “overfitting” is possible when there is a little number of parameters.
• Optimization of digital filer with 100 coefficients and taking into account this number in fitness is not without reason (in our humble opinion).

Building the system consisting of blocks.

New approach in trading systems building which was described above was realized in development of genetic optimizer for TradeStation. It uses TradeStation built-in approach to building of strategies from already made signals in StrategyBuilder.

Principle of work is showed below:

• All signals including Manager are included in strategy in TradeStation Strategy Builder.
• Manager is the standard block, which is included in every strategy. Its purpose is to control the optimization process. It can be the same for the many strategies. All strategy control parameters are defined in it as input parameters or Inputs.
• Manager organizes the generation of the new specimen, the In Sample/OOS calculation, calculates the fitness, etc.
• Each signal as usually realizes one variant of entry or exit or the set of entries/exits of the same type.
• Each signal has standard structure and contains the description of the optimization parameters in the beginning of the code.
• In the beginning of the work each signal registers its optimization parameters. During optimization process it selects values of it’s parameters from the current specimen of population and carries out its work with those parameters.

As a result of such approach we can get absolutely new system or method of trade, which possibly would never be invented by us.

When we had converted basic signals based on technical analysis indicators (moving averages, stochastics, momentums, etc.) according to this method and made a block from each signal, then it turned out that even among signals built on analogous basic principles there are exact “leaders”. It points that perspectives of creation and investigation of behavior of systems based on traditional methods of technical analysis are far from exhausted.

I want to finish my presentation by the following thesis:

• In wild nature usually the most adaptive to environment organisms do survive, but not those ones who had learned best skills and abilities some time before.
• The quickest adaptation to environment is provided by the intellect, since it makes possible even the changing of the environment.

Does it take place in the exchange trade?...

Questions please.

Question:
Which parameter it is better to optimize and is it possible to optimize such parameter of the system as “leverage”?

Answer:
It is hard to answer unambiguously. What one SHOULD NOT DO: One should not choose NetProfit criterion since if we have such parameter as leverage then it is clear that the best specimen will be the one with the maximal lever because it will have the maximal profit.

Question:
Then what criterion is better to avoid overfitting and improve the stability of the system?

Answer:
First, it is necessary to choose another optimization criterion than that one which characterizes only the profitability of the system. In another words it is necessary to include in fitness indirect parameters, i.e. those parameters that characterize the quality of the system indirectly. It can be the number of deals or trading time for example. Second: it is possible to apply “FreshBlood” function, which causes perturbances and system that had maximal fitness and replaced other specimens from population could be not the best as a result of usage of this function. As a result we would keep in population other more viable specimens which could show better results on “out of sample” data for example. This problem as a whole is known as getting in the local extremum. In TSGO search goes rather uniformly on the whole plane. As a result we get population that is the section of the whole plane that we have. Though if there is a local peak it can be the first specimen in our population. In such case we might choose not the best specimen in future. On the whole the stability of the system can be conditioned by some limitations. One can set bigger transaction costs for example. If the system generates too many number of deals then such system will not survive. In reality such strict conditions may not occur but I think one will feel more comfortable with such system than with system that was tested under more soft conditions.

Question:
What number of iterations it is necessary to choose when using genetic optimization? Will it be better if we choose as big number as possible?

Answer:
Several hundreds of iterations are enough for proper result. In order to estimate the situation quickly one hundred is enough.

Question:
When it is necessary to stop the optimization?

Answer:
It depends on number of iterations we specified and what result was obtained. If the number of signals, coefficients and filers is big and we set strict limitations on population size but there are no specimens with good fitness then we should continue the optimization.

Question:
What is the reason of testing on “sample” data in your program for genetic optimization in TradeStation and then representing the results obtained on “out of sample data” at the same time in your example of signal?

Answer:
There is no specific reason. It is just technical possibility to make useful search on “sample” data and then without even pressing a key get the same result on “out of sample” data. Actually it is the variant of technical solution for those who need it.

Question:
How much time does it take to find a proper result in your example of system?

Answer:
The search of proper solution from several thousands of variants takes for several minutes.

Moscow, 2004..
Trade Smart Research
www.tsresearch.com