An Improved Multi-Objective Genetic Model for Stock Selection with Domain Knowledge - Technologies and Applications of Artificial Intelligence - page 70

where and are defined as the scores of portfolios and ; and
are defined as the non-dominated (front) rankings of portfolios and ; and
and are defined as the crowding distances of portfolios and .
We also use the following two rules inspired from financial knowledge to improve the
scoring model:

(1) Removing the portfolio with negative returns, i.e.,

if 0 , then 0 .

(2) Adjusting the return by risk (similar to the idea of the Sharpe ratio), i.e.,

;

(8)

if ,

where is the cumulative total return by Eq. (5); is defined as the score of
portfolio ; is defined as the modified score; is the standard deviation of
all the average yearly returns; and is the number of years.

6. According to step 5, define the fitness of a chromosome as the function of the an-
nualized return and the risk of a portfolio, as follows:

fitness ,

(9)

where is the final score of portfolio defined by step 5; is the mod-
ified score of portfolio defined by step 5, as well.

7. Repeat the following until a sufficient number of offspring are generated.

─ Select one pair of chromosomes as parents;
─ Apply crossover;
─ Apply mutation.

In this study, we use the tournament selection scheme, and one-point crossover
scheme with rate of 0.7, and the mutation rate of 0.005 are used.

8. Replace the parents with the offspring to generate a new generation of chromo-
somes.
9. Return to step 2 until the termination conditions are met (we use 50 generations as
the termination condition for this study).

4 Experimental Results

To further obtain the performance discrepancy of our method and the others, we use
the 14 fundamental variables and the half-yearly returns of stocks from textile sector
in Taiwan's stock market for years ranging from 1992 to 2012.