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In this exercise, a population of three-rule entry models are evolved using OptEvolve, a C+ + genetic optimizer (Scientific Consultant Services, 516-696. 3333). Each gene corresponds to a block of four numbers and to a rule, via the one-to-one mapping of sets of numbers to sets of rules. Each chromosome contains three genes. A chromosome, as generated by the GA, therefore consists of 12 numbers: The first four numbers correspond to the first gene (or rule), the next four correspond to the second gene (or rule), and the last four correspond to the third gene (or rule). The GA itself has to be informed of the gene size so it does not break up intrinsic genes when performing crossover. Crossover should only occur at the boundaries of genes, i.e., four number blocks. In the current example,
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this will be achieved by setting the chunk size, a property of the genetic optimizer component, to four. As mentioned, each gene is composed of four numbers. The first number is nothing more than an index into a table of possible rule templates. For example, if that number is 1, a price-comparison template in which the difference between two closing prices is compared with a threshold (see code) is selected. The remaining three numbers in the gene then control the two lookback periods for the prices being compared and the threshold. If the first number of the four-number block is 2, a price-to-moving-average comparison template would be selected. In that case, two of the remaining three numbers would control the period of the moving average and the direction of the comparison (whether the price should be above or below the moving average). In general, if the first number in the block of four numbers that represents a gene is n, then the n&rule template is used, and any required parameters are determined by reference to the remaining three numbers in the four-number block. This decoding scheme makes it easy to maintain an expandable database of rule templates. Each of the three blocks of four numbers is mapped to a corresponding rule. For any 12-number chromosome, a 3-rule entry model is produced. The Rule Templates
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The first rule template (case I in function Rules) defines a comparison between two prices and a threshold: The rule takes on a value of TRUE if the closing price lb1 bars ago is greater than some threshold factor (thr) plus the closing price lb2 bars ago. Otherwise, the rule takes on the value of FALSE. The unknowns (Ibl, lb2, and thr) are left as the blanks to be tilled in during instantiation. This template has been included because the kind of rule it represents was useful in previous investigations. The second rule template (case 2) involves simple moving averages, which are often used to determine trend. Usually the market is thought to be trending up if the price is above its moving average and trending down if the price is below its moving average. There are only two unknowns in this template: The first (per) controls the number of bars in the moving average, and the second (~4) controls the direction of comparison (above or below). The third rule template (case 3) is identical to the second (cuse 2), except that an exponential moving average is used rather than a simple moving average. Much discussion has occurred regarding the importance of open interest. Larry Williams (1979) mentioned that a decline in total open interest, during a period when the market has been moving sideways, indicates potential for a strong rally. A shrinking of open interest may be interpreted as a decline in available contracts, producing a condition where demand may outweigh supply. The fourth rule template (case 4) simply computes the percentage decline in open interest from 161 bars ago to 1 bar ago (open interest is generally not available for the current
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