What everyone else said, but if you want a "quick and dirty" way of doing it, you can just use a simple genetic algorithm:
- Start with a couple (say 100) completely random schedules
- Measure how good they are via a fitness function (say, start at 0 and everytime a constraint is violated add 1 point. You can be fancy and add different amounts depending on the type of constraint violated)
- Sort the schedules from lowest to highest
- Pick the top 20 or so
- Generate other 80 schedules by mutating the 20 you selected before, randomly shuffling the talks, and possibly mixing up different schedules together (crossover).
- Repeat for a couple thousands of generations, the population should quickly evolve towards better schedules
- You might get stuck on local minima, but for the most part you can just run it again several times from the start and it eventually won't get stuck
- Not guaranteed to give optimum results but should give decent enough results
- Start with a couple (say 100) completely random schedules
- Measure how good they are via a fitness function (say, start at 0 and everytime a constraint is violated add 1 point. You can be fancy and add different amounts depending on the type of constraint violated)
- Sort the schedules from lowest to highest
- Pick the top 20 or so
- Generate other 80 schedules by mutating the 20 you selected before, randomly shuffling the talks, and possibly mixing up different schedules together (crossover).
- Repeat for a couple thousands of generations, the population should quickly evolve towards better schedules
- You might get stuck on local minima, but for the most part you can just run it again several times from the start and it eventually won't get stuck
- Not guaranteed to give optimum results but should give decent enough results