Published on Thu Apr 23 2020

Tip the Balance: Improving Exploration of Balanced Crossover Operators by Adaptive Bias

Luca Manzoni, Luca Mariot, Eva Tuba

The use of balanced crossover operators in Genetic Algorithms (GA) ensures the binary strings generated as offsprings have the same Hamming weight of their parents. Although this method reduces the size of the search space, the resulting fitness landscape often becomes more difficult for the GA to explore.

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Abstract

The use of balanced crossover operators in Genetic Algorithms (GA) ensures that the binary strings generated as offsprings have the same Hamming weight of the parents, a constraint which is sought in certain discrete optimization problems. Although this method reduces the size of the search space, the resulting fitness landscape often becomes more difficult for the GA to explore and to discover optimal solutions. This issue has been studied in this paper by applying an adaptive bias strategy to a counter-based crossover operator that introduces unbalancedness in the offspring with a certain probability, which is decreased throughout the evolutionary process. Experiments show that improving the exploration of the search space with this adaptive bias strategy is beneficial for the GA performances in terms of the number of optimal solutions found for the balanced nonlinear Boolean functions problem.

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In several combinatorial optimization problems arising in cryptography and design theory, the admissible solutions must often satisfy a balancedness constraint. For this reason, several works in the literature tackling theseoptimization problems with Genetic Algorithms introduced new balanced crossover operators.
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