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 this paper, an efficient extension of network simplex algorithm is presented. In static scheduling problem, where there is no change in situation, the challenge is that the large problems can be solved in a short time. In this paper, the Static Scheduling problem of Automated Guided Vehicles in container terminal is solved by Network Simplex Algorithm (NSA) and NSA+, which extended the stand...

We present a faster implementation of the polynomial time primal simplex algorithm due to Orlin [23]. His algorithm requires O(nm min{log(nC), m log n}) pivots and O(n m · min{log nC, m log n}) time. The bottleneck operations in his algorithm are performing the relabeling operations on nodes, selecting entering arcs for pivots, and performing the pivots. We show how to speed up these operations...

The maximum flow problem (MFP) is a fundamental model in operations research. The network simplex algorithm is one of the most efficient solution methods for MFP in practice. The theoretical properties of established pivot algorithms for MFP is less understood. Variants of the primal simplex and dual simplex methods for MFP have been proven strongly polynomial, but no similar result exists for ...

The minimum cost network flow problem, (MCNFP) constitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex type” category. Similar to the classical dual network simplex algorithm (DNSA), this algorithm starts with a dual feasible tree-solu...

We present a new efficient approach for solving the multicommodity flow problem as a sequence of subproblems, each on a very sparse but connected network. We show that each subproblem can be contracted to a problem on a much smaller graph. We then solve these problems using the simplex method. We test the algorithm on benchmark instances, and show its improvement over the usual simplex algorithm.