Timetable Scheduling

Assign \( N \) tasks \( \{T_1, T_2, \dots, T_N\} \) to a set of \( K \) ordered slots \( \{s_1, s_2, \dots, s_K\} \). Slots can be a structured grid (days × periods) or a flat list. Tasks may also need a resource picked from \( \{r_1, r_2, \dots, r_R\} \) (rooms, vehicles, examiners) when resources are enabled.

Each task carries free-form attributes, e.g. \( \text{instructor} \), \( \text{cohort} \), \( \text{type} \). You pick which of those attributes count as conflict-causing. A pair of tasks clashes when they share a slot and share at least one conflict-causing attribute value:

\[ \mathrm{clash}(T_i, T_j) = \mathbb{1}\bigl[\, s(T_i) = s(T_j) \;\land\; \exists\, a \in A_c : T_i.a = T_j.a \,\bigr] \]

When resources are enabled, two tasks sharing the same \( (slot, resource) \) pair also count as a clash.

The chromosome has one gene per task. Without resources, the gene is the slot index. With resources, the gene encodes both: \( \text{gene}_i = s_i \cdot R + r_i \). The fitness rewards conflict-free assignments:

\[ f(x) = \frac{1}{1 + w_h \cdot \sum_{i \lt j} \mathrm{clash}(T_i, T_j)} \]

where \( w_h \) is the hard-violation weight you tune below. Fitness is 1 when no pair clashes and shrinks as violations accumulate.

Example: four lessons taught by Alice (2) and Bob (2) in 4 time slots, with instructor marked conflict-causing. A clash-free schedule puts Alice's two lessons in different slots and Bob's two in different slots. The Random fill button in the form will seed a small example you can run as-is.