  In practise, it is often desirable to provide the decision-maker with a rich
set of diverse solutions of decent quality instead of just a single solution.
In this paper we study evolutionary diversity optimization for the knapsack
problem (KP). Our goal is to evolve a population of solutions that all have a
profit of at least $(1-\varepsilon)\cdot OPT$, where OPT is the value of an
optimal solution. Furthermore, they should differ in structure with respect to
an entropy-based diversity measure. To this end we propose a simple
$(\mu+1)$-EA with initial approximate solutions calculated by a well-known
FPTAS for the KP. We investigate the effect of different standard mutation
operators and introduce biased mutation and crossover which puts strong
probability on flipping bits of low and/or high frequency within the
population. An experimental study on different instances and settings shows
that the proposed mutation operators in most cases perform slightly inferior in
the long term, but show strong benefits if the number of function evaluations
is severely limited.
