  Evolutionary algorithms are well suited for solving the knapsack problem.
Some empirical studies claim that evolutionary algorithms can produce good
solutions to the 0-1 knapsack problem. Nonetheless, few rigorous investigations
address the quality of solutions that evolutionary algorithms may produce for
the knapsack problem. The current paper focuses on a theoretical investigation
of three types of (N+1) evolutionary algorithms that exploit bitwise mutation,
truncation selection, plus different repair methods for the 0-1 knapsack
problem. It assesses the solution quality in terms of the approximation ratio.
Our work indicates that the solution produced by pure strategy and mixed
strategy evolutionary algorithms is arbitrarily bad. Nevertheless, the
evolutionary algorithm using helper objectives may produce 1/2-approximation
solutions to the 0-1 knapsack problem.
