  Evolutionary algorithms are particularly effective for optimisation problems
with dynamic and stochastic components. We propose multi-objective evolutionary
approaches for the knapsack problem with stochastic profits under static and
dynamic weight constraints. The chance-constrained problem model allows us to
effectively capture the stochastic profits and associate a confidence level to
the solutions' profits. We consider a bi-objective formulation that maximises
expected profit and minimises variance, which allows optimising the problem
independent of a specific confidence level on the profit. We derive a
three-objective formulation by relaxing the weight constraint into an
additional objective. We consider the GSEMO algorithm with standard and a
sliding window-based parent selection to evaluate the objective formulations.
Moreover, we modify fitness formulations and algorithms for the dynamic problem
variant to store some infeasible solutions to cater to future changes. We
conduct experimental investigations on both problems using the proposed problem
formulations and algorithms. Our results show that three-objective approaches
outperform approaches that use bi-objective formulations, and they further
improve when GSEMO uses sliding window selection.
