A network simplex algorithm is described for the minimum-cost network flow problem on a generalized network with the additional constraint that there exist sets of arcs which must carry equal amounts of flow. This problem can be modeled as a linear programming problem and solved using the standard simplex algorithm. However, due to the structure of the problem, more efficient algorithms are pos...

We introduce a new network simplex pivot rule for the shortest path simplex algorithm. This new pivot rule chooses a subset of non-basic arcs to enter into the basis simultaneously. We call to this operation multiple pivot. We show that a shortest path simplex algorithm with this pivot rule makes O(n) multiple pivots and runs in O(nm) time. This new pivot rule is based on the new concept of pse...

augmented downhill simplex method (adsm) is introduced here, that is a heuristic combination of downhill simplex method (dsm) with random search algorithm. in fact, dsm is an interpretable nonlinear local optimization method. however, it is a local exploitation algorithm; so, it can be trapped in a local minimum. in contrast, random search is a global exploration, but less efficient. here, rand...

In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which causes the infinite loop in the algorithm, does not occur in the network simplex algorithm associated with the maximum flow problem.

In this paper a hybrid algorithm based on exploration power of the Genetic algorithms and exploitation capability of Nelder Mead simplex is presented for global optimization of multi-variable functions. Some modifications are imposed on genetic algorithm to improve its capability and efficiency while being hybridized with Simplex method. Benchmark test examples of structural optimization with a...

In this paper, we suggest a new pivot rule for the primal simplex algorithm for the minimum cost flow problem, known as the network simplex algorithm. Due to degeneracy, cycling may occur in the network simplex algorithm. By maintaining strongly feasible bases due to Cunningham [1976, 1979], cycling can be prevented but without restrictions on the entering variable, the algorithm can still perf...

We study the number of pivots required by the primal network simplex algorithm to solve the minimum-cost circulation problem. We propose a pivot selection rule with a.bound -r -° on the number of pivots, for an nvertex network. This is the first known subexponential bound. The network simplex algorithm with this rule can be implemented. to run in n ogn) /2 + 0(l) tine." In the special case of p...

Recently, a new Dual Network Exterior-Point Simplex Algorithm (DNEPSA) for the Minimum Cost Network Flow Problem (MCNFP) has been developed. In extensive computational studies, DNEPSA performed better than the classical Dual Network Simplex Algorithm (DNSA). In this paper, we present for the first time how to utilize the dynamic trees data structure in the DNEPSA algorithm, in order to achieve ...