Given: $n$ tasks with accomplishment times $t_1, t_2, \ldots , t_n$. There is no such task that its accomplishment time is greater than the overall accomplishment time of other tasks.
Question: How to distribute these tasks between two workers in a such way that $|T_1 - T_2|$ is minimum ($T_i$ - the overall accompl. time for the $i$-th worker accordingly).
We will use the local search algorithm, starting with a random distribution and redistributing one task on every step only if it leads to reducing $|T_1 - T_2|$ as long as it's possible.
Does this algorithm find the optimal distribution or is there any counterexample?