How to Solve It: Modern Heuristics by Michalewicz Zbigniew & David B. Fogel

How to Solve It: Modern Heuristics by Michalewicz Zbigniew & David B. Fogel

Author:Michalewicz, Zbigniew & David B. Fogel [Michalewicz, Zbigniew]
Language: eng
Format: mobi
Publisher: Springer - A
Published: 2004-12-07T16:00:00+00:00


10.4.4 Crossover operators and their probabilities

When working with binary representations, in contrast to a mutation rate pm that’s applied to each bit, the crossover rate pe acts on a pair of solutions, giving the probability that the selected pair undergoes recombination. The efforts of De Jong [93], Grefenstette [201], and Schaffer [412] suggested values for pe that range from 0.6 to 0.95. Given that the mutation rates in these efforts were always very low, it’s not surprising that high rates of recombination were required. For alternative coding schemes that don’t rely on binary strings, however, you have to be cautious about applying the same settings because the effect of recombination within various representations can be entirely different.

In what follows here, we’ll treat mechanisms for controlling recombination probabilities and mechanisms for controlling the recombination mechanism itself separately. Let’s begin with efforts to control the probability of the operator.

Davis [91] adapted the rate of variation operators (e.g., crossover) by rewarding those that show success in creating better offspring. This is a form of reinforcement learning where the reward is propagated back to operators that acted a few generations in the past, in the hope that these operators helped set up the current rewards. Rewards are diminished as they are propagated back in time to operators used previously. In a similar vein, Julstrom [249] adapted the rates of crossover and mutation by comparing the respective improvements that were obtained using these operators in the past generation (or longer). The probability of crossover was set to the ratio of the credit assigned for the improvements made by crossover divided by the number of instances of crossover, taken as a ratio to that same quotient summed with the analogous quotient for mutation



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