Book ; Online: Calculating lexicase selection probabilities is NP-Hard
2023
Abstract: Calculating the probability of an individual solution being selected under lexicase selection is an important problem in attempts to develop a deeper theoretical understanding of lexicase selection, a state-of-the art parent selection algorithm in ... ...
Abstract | Calculating the probability of an individual solution being selected under lexicase selection is an important problem in attempts to develop a deeper theoretical understanding of lexicase selection, a state-of-the art parent selection algorithm in evolutionary computation. Discovering a fast solution to this problem would also have implications for efforts to develop practical improvements to lexicase selection. Here, I prove that this problem, which I name lex-prob, is NP-Hard. I achieve this proof by reducing SAT, a well-known NP-Complete problem, to lex-prob in polynomial time. This reduction involves an intermediate step in which a popular variant of lexicase selection, epsilon-lexicase selection, is reduced to standard lexicase selection. This proof has important practical implications for anyone needing a fast way of calculating the probabilities of individual solutions being selected under lexicase selection. Doing so in polynomial time would be incredibly challenging, if not all-together impossible. Thus, finding approximation algorithms or practical optimizations for speeding up the brute-force solution is likely more worthwhile. This result also has deeper theoretical implications about the relationship between epsilon-lexicase selection and lexicase selection and the relationship between lex-prob and other NP-Hard problems. |
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Keywords | Computer Science - Neural and Evolutionary Computing ; Computer Science - Computational Complexity ; F.2 |
Subject code | 519 |
Publishing date | 2023-01-17 |
Publishing country | us |
Document type | Book ; Online |
Database | BASE - Bielefeld Academic Search Engine (life sciences selection) |
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