An efficient approach to updating simplex multipliers in the simplex algorithm
نویسندگان
چکیده
The simplex algorithm computes the simplex multipliers by solving a system (or two triangular systems) at each iteration. This note offers an efficient approach to updating the simplex multipliers in conjunction with the Bartels-Golub and Forrest-Tomlin updates for LU factors of the basis. It only solves one triangular system. The approach was implemented within and tested against MINOS 5.51 on 129 problems from Netlib, Kennington and BPMPD. Computational results show that the new approach improves simplex implementations.
منابع مشابه
An Efficient Extension of Network Simplex Algorithm
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...
متن کاملAugmented Downhill Simplex a Modified Heuristic Optimization Method
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...
متن کاملScheduling in Container Terminals using Network Simplex Algorithm
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 the Network Simplex Algorithm (NSA). The algorithm is based on graph model and their performances are at least 100 times faster than traditional si...
متن کاملOptimizing the Static and Dynamic Scheduling problem of Automated Guided Vehicles in Container Terminals
The Minimum Cost Flow (MCF) problem is a well-known problem in the area of network optimisation. To tackle this problem, Network Simplex Algorithm (NSA) is the fastest solution method. NSA has three extensions, namely Network Simplex plus Algorithm (NSA+), Dynamic Network Simplex Algorithm (DNSA) and Dynamic Network Simplex plus Algorithm (DNSA+). The objectives of the research reported in this...
متن کاملA new network simplex algorithm to reduce consecutive degenerate pivots and prevent stalling
It is well known that in operations research, degeneracy can cause a cycle in a network simplex algorithm which can be prevented by maintaining strong feasible bases in each pivot. Also, in a network consists of n arcs and m nodes, not considering any new conditions on the entering variable, the upper bound of consecutive degenerate pivots is equal $left( begin{array}{c} n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Program.
دوره 114 شماره
صفحات -
تاریخ انتشار 2008