On Complexity of Optimal Recombination for Binary Representations of Solutions

We consider an optimization problem of finding the best possible offspring as a result of a recombination operator in an evolutionary algorithm, given two parent solutions. The optimal recombination is studied in the case, where a vector of binary variables is used as a solution encoding. By means of efficient reductions of the optimal recombination problems (ORPs) we show the polynomial solvability of the ORPs for the maximum weight set packing problem, the minimum weight set partition problem and the linear Boolean programming problems with at most two variables per inequality and some other problems. Also we identify several NP-hard cases of optimal recombination: the Boolean linear programming problems with three variables per inequality, the knapsack, the set covering, the p-median and some other problems. Keywords Complexity, Evolutionary Algorithm, Optimal Recombination, Optimized Crossover

• Type: Journal
• Year: 2008
• Where: EC
• Authors: Anton V. Eremeev
• Keywords: EC 2008, ECommerce, Evolutionary Algorithm, Optimal Recombination, Optimal Recombination Problems