  Evolutionary algorithms have been widely used for a range of stochastic
optimization problems in order to address complex real-world optimization
problems. We consider the knapsack problem where the profits involve
uncertainties. Such a stochastic setting reflects important real-world
scenarios where the profit that can be realized is uncertain. We introduce
different ways of dealing with stochastic profits based on tail inequalities
such as Chebyshev's inequality and Hoeffding bounds that allow to limit the
impact of uncertainties. We examine simple evolutionary algorithms and the use
of heavy tail mutation and a problem-specific crossover operator for optimizing
uncertain profits. Our experimental investigations on different benchmarks
instances show the results of different approaches based on tail inequalities
as well as improvements achievable through heavy tail mutation and the problem
specific crossover operator.
