PBS Core Algorithms
This algorithm is used in conjunction with greedy algorithm to improve overall satisfaction.
"Back Tracking" means the core remembers and tracks back the awarded pairings of senior crewmembers when awarding junior crewmembers. The purpose of back tracking is to do swapping. When awarding a junior crewmember, if his/her preferred pairing has been awarded to a senior already, the core tracks back to find which senior crewmember has been awarded this pairing, then tries to swap the pairing with the currently available pairings at this junior level if and only if the swapping does not degrade the senior's preferences and does not violate the legality of the line. A successful swapping the honors junior's preferences without affecting the satisfaction of the senior crewmember.
However, unless the swapping happens between the seniorities next to each other, it has a great chance to violate seniority and needs a secondary or third swap to honor the seniority. For example, a number 10 crewmember swapped a pairing with number 2. The core needs to make sure the pairing that is going to be awarded to number 10 will not improve the satisfaction of number 3 to number 9. If it can, this pairing should be awarded to the crewmember senior to number 10. In short, the swapping will trigger another swapping and so on. So the swapping becomes shuffling, which is a group of swapping.
Both swapping and shuffling are inefficient. How deep the "back tracking" can go is questionable. The result is unpredictable. It is another feature of many PBS on the market today.
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