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EventPresent Cint *es. int m, int cb) ( // Used by the Rules function to simplify coding int i ; forti=cb-m+l; ic=cb; i++)
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) /I process next bar 1 The Cf + code implements the rule templates and system trading strategy. The function Rules implements the rule templates. Arguments vl, ~2, ~3, and v4 (which correspond to the four numbers that comprise any one of the three genes) provide all the information required to instantiate a rule template. Argument vl is used to select, via a switch statement, the required rule template from the 10 that are available; arguments ~2, ~3, and ~4, are used to till in the blanks (required parameters, desired directions of comparison, etc.) to yield a fully defined rule. The rule is then immediately evaluated for all bars, and the evaluations (1 for TRUE, 0 for FALSE) are placed in ans, a floating-point vector used to return the results to the caller. The macro, BiasedPosScaZe(x,n), is used to map numbers ranging from 0 to 1,000 to a range of 0 to a, with more numbers mapping to smaller values than larger ones. The macro is used to compute such things as lookbacks and movingaverage periods from ~2, ~3, or ~4, the values of which are ultimately derived from the genetic algorithm and scaled to range from 0 to 1,000. The macro is nonlinear (Biased) so that a finer-grained exploration occurs for smaller periods or lookbacks than for larger ones. For example, suppose there is a moving average, with a period that ranges from 2 to 100 bars. The intention is to search as much between periods 2, 3, and 4 as between 30, 50, and 90; i.e., the scale should be spread for small numbers. This is desired because, in terms of trading results, the change from a moving average to a 5-bar moving average is likely to be much greater than the change from a 50-bar to a moving average. The macro, LinearScnle(x,a,b), performs a linear mapping of the range 0 1,000 to the range a b. The macro is usually used when calculating thresholds or deviations. In the rule template code, all parameters are scaled inside Rules, rather than inside the GA as is the usual practice. The GA has been instructed to produce numbers between 0 and 1,000, except for chromosome elements 1, 5, and 9, which are the first numbers in each gene, and which serve as rule template selectors. The reason for local scaling is that templates for different kinds of rules require parameter and control values having different ranges to be properly instantiated. The process of evolving trading systems involves asking the genetic optimizer to provide a guess as to a chromosome. The genetic optimizer then ran domly picks two members of the population and mates them (as specified by the crossover, mutation rate, and chunk-size properties). The resultant offspring is then returned as a potential solution. When the GA component is told the fitness
of the solution it has just provided, it compares that fitness with that of the leastfit member of the population it maintains. If the fitness of the offspring is greater than the fitness of the least-fit member, the GA replaces the least-fit member with the offspring solution. This process is repeated generation after generation, and is handled by the shell code (not shown), which, in turn, makes repeated calls to function Model to simulate the trading and evaluate the system s fitness. The code for function Model is almost identical to that used in earlier chapters. Prior to the bar indexing loop in which trading orders are generated, the function R&s is invoked three times (once for each gene), with the results being placed in time series rulel, ruZe2, and n&3. A average true range is also calculated, as it is necessary for the standard exit and for rule evaluation. Inside the loop, the rule evaluations are checked for the current bar (ndel[cb], rule2[cb], ruZe3[cb]), and if all evaluations are TRUE, a buy (or a sell, if the short side is being examined) is generated. Entries are programmed in the standard manner for each of the three orders tested. Only the in-sample data is used to in the evolutionary process. The output produced by the shell program permits the selection of desirable solutions that may be traded on their own or as a group. The solutions may be easily translated into understandable rules to see if they make sense and to use as elements in other systems. TEST RESULTS Six tests were performed. The evolutionary process was used to evolve optimal entry rules for the long and short sides with each of the three entry orders: at open, on stop, and on limit. In all cases, a maximum of 2,500 generations of genetic processing was specified. The task of computing all the solutions and saving them to tiles took only a few hours on a fast Pentium, which demonstrates the practicality of this technique. For each test, the genetic process produced a tabular file (GFiles 1 through 6) consisting of lines corresponding to each of the generations; i.e., each line represents a specific solution. Most of the early solutions were close to random and not very good, but the quality of the solutions improved as generations progressed; this is normal for a GA. Each line contains information regarding the performance of the particular solution that corresponds to the line, as well as to the complete chromosome, i.e., the set of parameters that represents the gene, which, in turn, corresponds to the solution expressed in the line. The best solutions for the long entry at open and for the short entry at open were selected. These solutions were used to generate the six tests conducted below. More specifically, the solution that provided the best long entry at open was tested and its performance was evaluated in the usual way on both samples. The same solution was also tested and evaluated with entry on stop and on limit. The same procedure was followed for the short side: The best evolved solution for a
short entry at open was determined. It was then tested on both samples with each of the other two order types, The optimal solution for each order type was not selected separately from our genetic runs because doing so would not allow comparability across orders. For example, the optimal entry at open might involve a breakout, while the optimal entry for a stop might involve countertrend momentum-totally different models. By assuming that the entry-at-open model (in which all trades generated by the model are taken) represents a good, overall model, the normal course of evaluating that model with the other orders was followed. Since the model is kept constant, this approach permits meaningful comparisons to be made across orders.
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