Two Stage Quantum Optimization for the School Timetabling Problem

Timetabling is an NP-Hard problem that searches for periodic scheduling of events that must meet a set of hard and soft constraints. Because of the difficulty in finding an exact solution, the use of heuristics to address the problem is a common practice. When only the hard constraints are considered, the timetabling problem can be reduced to graph vertex coloring. This similarity between both problems has motivated the use of graph coloring heuristics as a means to solve the timetabling problem. We propose the use of the Quantum Approximate Optimization Algorithm as a heuristic to solve the school timetabling problem. The QAOA is a hybrid quantum-classical algorithm that can be used to address combinatorial optimization problems. We simulated QAOA in a minimal example with 42 qubits using the Ket Quantum Programming Language and our results showed that it is possible to apply QAOA to the school timetabling problem.