Finding minimum-cost circulations by canceling negative cycles
Journal of the ACM (JACM)
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
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A complex system by definition is open; its boundaries in accordance with the system's nature must be transparent, and the same time characteristic feature of complex systems is nesting. Following these, paper is consecrated to the new algorithm of the optimal distribution of material, energy or informational fluxes in the big dimensional and complex topological network in normal and emergency situations of functioning. Using the modified genetic algorithm the solution of flux distribution problem is developed. Tree structure is presented in the form of levels which conditions stage-wise operation of algorithm or the presented algorithm is many staged. Algorithm operates in the cycle for separate fragment of each autonomous tree in descending principle. In emergency situations when the integrity of any arc is broken and respectively, the given arc cannot be considered in its structure, or in cases when flow redistribution cannot renovate normal mode of system operation, it becomes necessary to select alternative versions in order to find the best structure. Just in the view of topological flexibility the decomposition of network structures into tree structures and the indispensability of creation of its algorithm are conditioned. With the help of decomposition algorithm the regeneration of new trees and its realization by gates or switches existing at the ends of each arc will be done. Control diagram represents the massif of binary state of the mentioned devices that is given as a recommendation to the dispatcher. Then, using the distribution algorithm of flows the optimum values of flows are determined in conditions of new structures.