I am working on an Assigning problem to expert or agent
How can I solve this problem? Can I solve it with multi objective A*? What would be an admissible heuristic function and how to calculate heuristic h(n) function ?how can i design multi objective A* algorithm for this problem please help me.
Consider KK agents A1,…AKA1,…AK and NN tasks T1,…TNT1,…TN. Each task has a certain time t(Ti)t(Ti) to be completed and each agent has a matching (or affinity) value associated with each task MAj(Ti),∀i,jMAj(Ti),∀i,j. The goal is to assign agents to tasks, such that the matching value is maximized and the overall time to complete the tasks is minimized. Moreover, an agent can be assigned to multiple tasks. However, an agent cannot start a new task before finishing the previous one.
Dear Ali Arain,
I suggest you to see link and attached files on topic.
https://docs.microsoft.com/en-us/configmgr/apps/deploy-use/link-users-and-devices-with-user-device-affinity
Best regards
If you fix the time limit, the problem reduces to a special case of the Generalized Assignment Problem (GAP). See here:
http://www.or.deis.unibo.it/kp/Chapter7.pdf
There are lots of good exact and heuristic algorithms out there for the GAP. See, e.g., these papers:
K. Jörnsten, & M. Näsberg (1986) A new Lagrangian relaxation approach to the generalized assignment problem. European Journal of Operational Research, 27, 313-323.
D.G. Cattrysse & L.N. Van Wassenhove (1992) A survey of algorithms for the generalized assignment problem. European Journal of Operational Research, 60, 260-272.
D.B. Shmoys & É. Tardos (1993) An approximation algorithm for the generalized assignment problem. Mathematical Programming, 62, 461-474.
M.W.P. Savelsbergh (1997) A branch-and-price algorithm for the generalized assignment problem. Operations Research, 45, 831-841.
Perhaps by a virtual implementation of a knowledge market.
https://www.researchgate.net/publication/221471436_The_Knowledge_Market_Agent-Mediated_Knowledge_Sharing
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