I have a set consisting of
$$\Omega = \{a_1, a_2, \cdots, a_n\}$$
and I have to obtain another set, formed by the sum of the elements of the first set, such that the new elements do not exceed a certain constant $c$. However, that set must be the set that has the least number of elements possible. An example,
$$\Omega = \{5, 10, 10, 14, 20\}$$ If $c = 20$, let $s_1 = \{\{5, 10\}, \{10\}, \{14\}, \{20\}\}$ and $s_2 = \{ \{10, 10\}, \{5, 14\}, \{20\}\}$.
If $s_1$ and $s_2$ were the only two sets that meet the constraint (sum of elements less than or equal to 20), $s_2$ would be selected, because $\#(s_2) < \#(s_1)$.
A possible solution to my problem would be to generate all possible sets, check which ones meet the criteria and get the smallest one. However, this solution became unfeasible for a set ($ \Omega $) of 16 elements. Would anyone have a better approach, or any suggestions on how to solve the problem?
Thank you in advance and sorry for the informality.