Abstract
A new construction is introduced for creating random MAX-3SAT instances with low nonlinearity. Instead of generating random clauses, we generate random SAT expressions over 3 variables and then convert these into CNF SAT clauses. We prove that this yields structured problems with much lower nonlinearity. We also introduce a new method for weighting MAX-SAT clauses that preserves low nonlinearity and also breaks up plateaus. We evaluate these new problems by enumeration of instances with \(n = 30\) variables. One unexpected result is that Partition Crossover creates more tunnels on these semi-structured MAX-SAT problems compared to results on random NK landscapes. We show that Partition Crossover induces hypercube lattices over subsets of local optima; all of the local optima which appear in a lattice can be evaluated with a single linear equation.
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Notes
- 1.
In general, each Walsh coefficient except \(w_0\) is zero in \(\left( {\begin{array}{c}2^{k-1}\\ c/2\end{array}}\right) ^2\) out of \(\left( {\begin{array}{c}2^k\\ c\end{array}}\right) \) functions.
- 2.
- 3.
However, any neighborhood local search operator will suffice.
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Acknowledgements
This work was supported by an National Science Foundation (NSF) grant to D. Whitley, Award Number:1908866. This work was also partially funded by Universidad de Málaga, Ministerio de Ciencia, Innovación y Universidades del Gobierno de España under grant PID 2020-116727RB-I00, and by EU Horizon 2020 research and innovative program (grant 952215, TAILOR ICT-48 network).
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Whitley, D., Ochoa, G., Floyd, N., Chicano, F. (2024). Reduction-Based MAX-3SAT with Low Nonlinearity and Lattices Under Recombination. In: Stützle, T., Wagner, M. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2024. Lecture Notes in Computer Science, vol 14632. Springer, Cham. https://doi.org/10.1007/978-3-031-57712-3_8
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