Generalized profitable tour problems for online activity routing system

A next-generation system for online route guidance and activity recommendations was studied to support decisions that considered multiple activity itineraries whose utilities account for their spatial proximities for a user. For the solution of the underlying problem, the problem of the profitable tour and the problem of the prize-collecting traveling salesman were extended to generalized cases with the expansion of single nodes to clusters to handle various activity types. The generalized formulations addressed several uses, including routing with refueling, the pub crawl problem, and the romantic date problem. Test cases compared an insertion heuristic and a multisolution genetic algorithm with exact solutions. Both algorithms worked well even with the constraints of time windows and with the fast computational times that are necessary for online decision support. The multisolution genetic algorithm tended to be slower than the insertion heuristic was, but the multisolution algorithm could handle a wider variety of problems and could provide a set of solutions from which a user could browse to account for unobserved preferences.