The Optimal Flow in Multicommodity Dynamic Problem using Modified Algorithm

The multicommodity flow problem is classical optimization problem where multi commodities transported from sources to sinks subject to different constraints e.g. distance function, demand function with respect to time expanded capacities. Dynamic approach considering time varying flows to resolve the multicommodity flow problem. In this paper, we investigated a time-dependent, stochastic version of min-cost integer multi-commodity flow problem in context of dynamic resource allocation. The stochastic and time dependent dynamic approach uses to resolve the problem considering flow rates changes over time due to certain parameters such as demand function, distance function, conjugation or changing the cost. Linear approximations result in low-quality solutions. Although we will eventually need to use piecewise-linear or hybrid approximation techniques, their quick runtimes can make them respond in the initial piecewise-linear approximation iterations. For this reason, in present work applied an iterative, adaptive dynamic programming approach that influences both non-linear and linear approximations of value function to efficiently tackle this complex problem. The numerical results show that the proposed model gives optimal solution and is computationally useful for large scale problems. It also allows to efficiently manage and optimize the transportation of multicommodity through complex network overtime.