A stationary object is hidden in location i, i ¼ 1; 2; Á Á Á ; K, with probability p i . There are M sensors available and each location can be searched by at most one sensor at each instant of time. Each search of a location takes one unit of time and is conducted independently of previous searches, so that a search of location i finds the object, if it is in that location, with probability a i . After each search of a location a sensor may either continue to search the same location or switch without any delay to another location. We determine optimal search strategies that maximize the total probability of successful search in N units of time, discuss an implementation of an optimal search strategy, and specify conditions under which the solution can be obtained by a forward induction argument. Finally, we discuss the relationship to multi-armed bandits with multiple plays.
Abstract:We propose an optimal electric energy management of a cooperative multi-microgrid community with sequentially coordinated operations. The sequentially coordinated operations are suggested to distribute computational burden and yet to make the optimal 24 energy management of multi-microgrids possible. The sequential operations are mathematically modeled to find the optimal operation conditions and illustrated with physical interpretation of how to achieve optimal energy management in the cooperative multi-microgrid community. This global electric energy optimization of the cooperative community is realized by the ancillary internal trading between the microgrids in the cooperative community which reduces the extra cost from unnecessary external trading by adjusting the electric energy production amounts of combined heat and power (CHP) generators and amounts of both internal and external electric energy trading of the cooperative community. A simulation study is also conducted to validate the proposed mathematical energy management models.
OPEN ACCESSEnergies 2015, 8 8372
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