Abstract
We introduce Memory with Memory Genetic Programming (MwM-GP), where we use soft assignments and soft return operations. Instead of having the new value completely overwrite the old value of registers or memory, soft assignments combine such values. Similarly, in soft return operations the value of a function node is a blend between the result of a calculation and previously returned results. In extensive empirical tests, MwM-GP almost always does as well as traditional GP, while significantly outperforming it in several cases. MwM-GP also tends to be far more consistent than traditional GP. The data suggest that MwM-GP works by successively refining an approximate solution to the target problem and that it is much less likely to have truly ineffective code. MwM-GP can continue to improve over time, but it is less likely to get the sort of exact solution that one might find with traditional GP.
Highlights
In the vast majority of programming models, dating back to the Turing machine [1] and the earliest electronic computer architectures (e.g., [2]), assignments are entirely destructive in the sense that an instruction of the form x:=y or LOAD R2 R1 completely overwrites the previous value of a memory location or register
The plot indicates that the variance for the assignment hardnesses less than 1 are significantly smaller than for traditional genetic programming (GP), meaning that using soft assignment gives us more consistent results
Those approximations are generally very close in our runs, but linear GP with soft assignment does not seem to have the “killer instinct” needed to reach the target, at least with the parameters used here. (Given that we only used 40,000 fitness evaluations per run, it is entirely possible that more generations would allow our system to further refine the solutions, but we have not explored the impact of either increasing the population size or the number of generations.) This tendency to approximate may account for the advantage of hard assignment on the degree 4 polynomial; that polynomial is sufficiently easy that traditional GP solves it exactly with a high probability, while the Memory with Memory approximations are slightly worse
Summary
In the vast majority of programming models, dating back to the Turing machine [1] and the earliest electronic computer architectures (e.g., [2]), assignments are entirely destructive in the sense that an instruction of the form x:=y or LOAD R2 R1 completely overwrites the previous value of a memory location or register. As we will illustrate, softening return operations, by making sure the value of a function node is a blend of the result of a calculation and previously returned results effectively achieves in tree-based GP what soft assignments achieve in linear register-based GP: in both cases, MwM provides significant performance improvements. Both forms of Memory with Memory require only very minor modifications to existing systems, making them easy to add.
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