# On the usefulness of linkage processing for solving MAX-SAT

@inproceedings{Sadowski2013OnTU, title={On the usefulness of linkage processing for solving MAX-SAT}, author={Krzysztof L. Sadowski and Peter A. N. Bosman and Dirk Thierens}, booktitle={Annual Conference on Genetic and Evolutionary Computation}, year={2013} }

Mixing of partial solutions is a key mechanism used for creating new solutions in many Genetic Algorithms (GAs). However, this mixing can be disruptive and generate improved solutions inefficiently. Exploring a problem's structure can help in establishing less disruptive operators, leading to more efficient mixing. One way of using a problem's structure is to consider variable linkage information. Once a proper linkage model for a problem is obtained, mixing becomes more efficient.
This paper…

## 18 Citations

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## References

SHOWING 1-10 OF 13 REFERENCES

### Linkage neighbors, optimal mixing and forced improvements in genetic algorithms

- Computer ScienceGECCO '12
- 2012

This paper considers a technique called Forced Improvements (FI), that allows LTGA to converge to a single solution without requiring an explicit, diversity-reducing, selection step, and considers a different linkage model, called Linkage Neighbors (LN), that is more flexible, yet can be learned equally efficiently from data.

### BOA: the Bayesian optimization algorithm

- Computer Science
- 1999

Preliminary experiments show that the BOA outperforms the simple genetic algorithm even on decomposable functions with tight building blocks as a problem size grows.

### A New Method for Solving Hard Satisfiability Problems

- Computer ScienceAAAI
- 1992

A greedy local search procedure called GSAT is introduced for solving propositional satisfiability problems and its good performance suggests that it may be advantageous to reformulate reasoning tasks that have traditionally been viewed as theorem-proving problems as model-finding tasks.

### Maximum Satisfiability: Anatomy of the Fitness Landscape for a Hard Combinatorial Optimization Problem

- Computer ScienceIEEE Transactions on Evolutionary Computation
- 2012

These analyses show why the problem becomes hard for local search algorithms as the system size increases and how a recently proposed algorithm can exploit long-range correlations in the fitness landscape to improve on the state-of-the-art heuristic algorithms.

### Genetic Algorithm Behavior in the MAXSAT Domain

- Computer SciencePPSN
- 1998

This work has shown that all nonzero Walsh coefficients can be computed exactly for MAXSAT problems in polynomial time using only the clause information, and unless P=NP, this low order information cannot reliably lead to the global optimum, thus nontrivial MAXSat problems must be deceptive.

### Local search strategies for satisfiability testing

- Computer ScienceCliques, Coloring, and Satisfiability
- 1993

The power of local search for satissability testing can be further enhanced by employing a new strategy, called mixed random walk, for escaping from local minima, which allows us to handle formulas that are substantially larger than those that can be solved with basic local search.

### SATLIB: An Online Resource for Research on SAT

- Computer Science
- 2000

An overview of SATLIB is given and its current set of benchmark problems are described, to encourage all members of the community to utilise it for their SAT-related research and to improve it by submitting new benchmark problems, SAT solvers, and bibliography entries.

### Hierarchical BOA Solves Ising Spin Glasses and MAXSAT

- Computer ScienceGECCO
- 2003

The results indicate that hBOA is capable of solving enormously difficult problems that cannot be solved by other optimizers and still provide competitive or better performance than problem-specific approaches on other problems.

### Optimal implementations of UPGMA and other common clustering algorithms

- Computer ScienceInf. Process. Lett.
- 2007

### Predetermined versus learned linkage models

- Computer ScienceGECCO '12
- 2012

Experimental results show that - for problems with intricate interaction structure - the a priori fixed models are actually less efficient than LTGA that dynamically learns a hierarchical tree model.