Comparing Algorithms for Minimizing Congestion and Cost in the Multi-Commodity k-Splittable Flow

Abstract

In the k-splittable flow problem, each commodity can only use at most k paths and the key point is to find the suitable transmitting paths for each commodity. To guarantee the efficiency of the network, minimizing congestion is important, but it is not enough, the cost consumed by the network is also needed to minimize. Most researches restrict to congestion or cost, but not the both. In this paper, we consider the bi-objective (minimize congestion, minimize cost) k-splittable problem. We propose three different heuristic algorithms for this problem, 1 A , 2A and 3 A . Each algorithm finds paths for each commodity in a feasible splittable flow, and the only difference between these algorithms is the initial feasible flow. We compare the three algorithms by testing instances, showing that choosing suitable initial feasible flow is important for obtaining good results.

A matheuristic approach for the Quickest Multicommodity k-Splittable Flow Problem

“…The solution with the maximum total routed flow obtained by applying the three strategies is then returned. Jiao et al [31] proposed three heuristics for the bi-objective Multicommodity kSF P minimizing congestion and costs. The strategies differ themselves on the type of relaxation applied to the original problem to obtain an initial solution satisfying the commodity demands.…”

A randomized rounding approach to a k-splittable multicommodity flow problem with lower path flow bounds affording solution quality guarantees

“…Network flow B by the construction of stripping s a network flow conforming to the Kirchoff law, with some commodity emission E in node s(k) and the same absorption E in node t (k) (a negative emission means an actual absorption and vice versa). The value E cannot be negative, since nothing flows into s(k): in flow A the constraint (12) held and the link flows in network flow B are not greater than the respective link flows in network flow A by the construction of stripping. If, in turn, E were positive, network flow B could be decomposed into flows on paths leading from s(k) to t (k), at least one of them being positive, and some flows on loops (circles)-see e.g.…”

“…Once the paths have been chosen, the values of flows along them that maximize the goal function are found as a solution of an auxiliary linear programming problem. An interesting heuristic is proposed in [12]. The authors cope with arbitrary in choosing a particular flow model by defining a bi-criteria model with the twofold goal of minimizing the congestion and minimizing the cost of the transfer.…”