An Algorithmic Solution to the Minimax Resource Allocation Problem with Multimodal Functions

The problem of allocation is one of the most widely investigated topics in the area of mathematical optimization because of its broad applicability to different classes of real world problems. The basic idea is that, given some type of resource whose total amount is N, we want to partition and allocate the total resource over n activities to minimize some objective function, F, whose value represents the "cost" of the allocation. As can be seen from various research results in this area, the procedures to solve discrete and continuous resource allocation problems can be significantly different. One obvious basic difference is that the discrete problem can be exactly solved by exhaustive enumeration, while the continuous problem cannot.