Combining solutions of the optimum satisfiability problem using evolutionary tunneling

The optimum satisfiability problem involves determining values for Boolean variables to satisfy a Boolean expression, while maximizing the sum of coefficients associated with the variables chosen to be true. Existing literature has identified a tabu search heuristic as the best method to deal with h...

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Published in:Mendel (Brno (Czech Republic)) Vol. 26; no. 1; pp. 23 - 29
Main Authors: da Silva, Rodrigo Ferreira, Hvattum, Lars Magnus, Glover, Fred
Format: Journal Article
Language:English
Published: Brno University of Technology 01.08.2020
Subjects:
adaptive memory programming
boolean optimization
metaheuristic
recombination operator
tabu search
zero-one integer programming
ISSN:1803-3814, 2571-3701
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Abstract The optimum satisfiability problem involves determining values for Boolean variables to satisfy a Boolean expression, while maximizing the sum of coefficients associated with the variables chosen to be true. Existing literature has identified a tabu search heuristic as the best method to deal with hard instances of the problem. This paper combines the tabu search with a simple evolutionary heuristic based on the idea of tunneling between local optima. When combining a set of solutions, variables with common values in all solutions are identified and fixed. The remaining free variables in the problem may be decomposed into several independent subproblems, so that parts of the solutions combined can be extracted and combined in an improved solution. This solution can be further improved by applying the tabu search in an improvement stage. The value of the new heuristic is demonstrated in extensive computational experiments on both existing and new test instances.
AbstractList The optimum satisfiability problem involves determining values for Boolean variables to satisfy a Boolean expression, while maximizing the sum of coefficients associated with the variables chosen to be true. Existing literature has identified a tabu search heuristic as the best method to deal with hard instances of the problem. This paper combines the tabu search with a simple evolutionary heuristic based on the idea of tunneling between local optima. When combining a set of solutions, variables with common values in all solutions are identified and fixed. The remaining free variables in the problem may be decomposed into several independent subproblems, so that parts of the solutions combined can be extracted and combined in an improved solution. This solution can be further improved by applying the tabu search in an improvement stage. The value of the new heuristic is demonstrated in extensive computational experiments on both existing and new test instances.
Author Glover, Fred
Hvattum, Lars Magnus
da Silva, Rodrigo Ferreira
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SubjectTerms adaptive memory programming
boolean optimization
metaheuristic
recombination operator
tabu search
zero-one integer programming
Title Combining solutions of the optimum satisfiability problem using evolutionary tunneling
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