In this paper, we introduce genetic programming over context-free languages with linear constraints for combinatorial optimization, apply this method to several variants of the multidimensional knapsack problem, and discuss its performance relative to Michalewicz's genetic algorithm with penalty functions. With respect to Michalewicz's approach, we demonstrate that genetic programming over context-free languages with linear constraints improves convergence. A final result is that genetic programming over context-free languages with linear constraints is ideally suited to modeling com-plementarities between items in a knapsack problem: The more complementarities in the problem, the stronger the performance in comparison to its competitors.

Genetic algorithms, grammatical evolution, grammar-based genetic programming, combinatorial optimization, context-free grammars with linear constraints, knapsack problems
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© 2002 Massachusetts Institute of Technology
2002
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