The Problem of Scheduling Parallel Computations of Multibody Dynamic Analysis Is NP-Hard

1996 ◽  
Author(s):  
Jin-Fan Liu ◽  
Karim A. Abdel-Malek
Keyword(s):  
Dynamic Analysis ◽  
Spanning Tree ◽  
Minimum Weight ◽  
Computational Cost ◽  
Parallel Computations ◽  
Np Hard ◽  
Multibody Dynamic ◽  
Np Hard Problem ◽  
Np Complete ◽  
Minimum Weight Spanning Tree

Abstract A formulation of a graph problem for scheduling parallel computations of multibody dynamic analysis is presented. The complexity of scheduling parallel computations for a multibody dynamic analysis is studied. The problem of finding a shortest critical branch spanning tree is described and transformed to a minimum radius spanning tree, which is solved by an algorithm of polynomial complexity. The problems of shortest critical branch minimum weight spanning tree (SCBMWST) and the minimum weight shortest critical branch spanning tree (MWSCBST) are also presented. Both problems are shown to be NP-hard by proving that the bounded critical branch bounded weight spanning tree (BCBBWST) problem is NP-complete. It is also shown that the minimum computational cost spanning tree (MCCST) is at least as hard as SCBMWST or MWSCBST problems, hence itself an NP-hard problem. A heuristic approach to solving these problems is developed and implemented, and simulation results are discussed.

scholarly journals On the Problem of Scheduling Parallel Computations of Multibody Dynamic Analysis

1999 ◽  
Vol 121 (3) ◽  
pp. 370-376 ◽  
Author(s):  
J. F. Liu ◽  
K. A. Abdel-Malek
Keyword(s):  
Dynamic Analysis ◽  
Spanning Tree ◽  
Minimum Weight ◽  
Computational Cost ◽  
Parallel Computations ◽  
Np Hard ◽  
Multibody Dynamic ◽  
Np Hard Problem ◽  
Np Complete ◽  
Minimum Weight Spanning Tree

A formulation of a graph problem for scheduling parallel computations of multibody dynamic analysis is presented. The complexity of scheduling parallel computations for a multibody dynamic analysis is studied. The problem of finding a shortest critical branch spanning tree is described and transformed to a minimum radius spanning tree, which is solved by an algorithm of polynomial complexity. The problems of shortest critical branch minimum weight spanning tree (SCBMWST) and the minimum weight shortest critical branch spanning tree (MWSCBST) are also presented. Both problems are shown to be NP-hard by proving that the bounded critical branch bounded weight spanning tree (BCBBWST) problem is NP-complete. It is also shown that the minimum computational cost spanning tree (MCCST) is at least as hard as SCBMWST or MWSCBST problems, hence itself an NP-hard problem. A heuristic approach to solving these problems is developed and implemented, and simulation results are discussed.

Multibody Dynamic Analysis of a 6-DOF Parallel Robot

2001 ◽  
Author(s):  
Miguel Almonacid ◽  
Sunil K. Agrawal ◽  
Rafael Aracil ◽  
Roque J. Saltarén
Keyword(s):  
Dynamic Analysis ◽  
Virtual Work ◽  
Computational Cost ◽  
Parallel Robot ◽  
Principle Of Virtual Work ◽  
Singularity Problem ◽  
Multibody Dynamic ◽  
Six Degree Of Freedom ◽  
Stewart Gough Platform ◽  
3D Surfaces

Abstract This paper presents the dynamic analysis of a six-degree of freedom (dof) parallel robot based on multibody dynamics. The robot is also known as Stewart-Gough platform. The inverse and forward dynamic analysis is presented based on the Newton-Euler formulation with the imposition of the constraints through Lagrange multipliers and the application of the principle of virtual work. The singularity problem within the workspace is also focused and 3D surfaces where the robot reach singular configurations are shown. Finally, simulations for the inverse and forward dynamic of the robot have been carried out showing the computational cost.

Mutation reduction in software mutation testing using firefly optimization algorithm

2020 ◽  
Vol 54 (4) ◽  
pp. 461-480
Author(s):  
Nasrin Shomali ◽  
Bahman Arasteh
Keyword(s):  
Optimization Algorithm ◽  
Computational Cost ◽  
Mutation Testing ◽  
Hard Problem ◽  
Np Hard ◽  
Content Type ◽  
Mutation Operators ◽  
Np Hard Problem ◽  
Firefly Optimization ◽  
Firefly Optimization Algorithm

PurposeFor delivering high-quality software applications, proper testing is required. A software test will function successfully if it can find more software faults. The traditional method of assessing the quality and effectiveness of a test suite is mutation testing. One of the main drawbacks of mutation testing is its computational cost. The research problem of this study is the high computational cost of the mutation test. Reducing the time and cost of the mutation test is the main goal of this study.Design/methodology/approachWith regard to the 80–20 rule, 80% of the faults are found in 20% of the fault-prone code of a program. The proposed method statically analyzes the source code of the program to identify the fault-prone locations of the program. Identifying the fault-prone (complex) paths of a program is an NP-hard problem. In the proposed method, a firefly optimization algorithm is used for identifying the most fault-prone paths of a program; then, the mutation operators are injected only on the identified fault-prone instructions.FindingsThe source codes of five traditional benchmark programs were used for evaluating the effectiveness of the proposed method to reduce the mutant number. The proposed method was implemented in Matlab. The mutation injection operations were carried out by MuJava, and the output was investigated. The results confirm that the proposed method considerably reduces the number of mutants, and consequently, the cost of software mutation-test.Originality/valueThe proposed method avoids the mutation of nonfault-prone (simple) codes of the program, and consequently, the number of mutants considerably is reduced. In a program with n branch instructions (if instruction), there are 2n execution paths (test paths) that the data and codes into each of these paths can be considered as a target of mutation. Identifying the error-prone (complex) paths of a program is an NP-hard problem. In the proposed method, a firefly optimization algorithm as a heuristic algorithm is used for identifying the most error-prone paths of a program; then, the mutation operators (faults) are injected only on the identified fault-prone instructions.

Is optimal solution of every NP-complete or NP-hard problem determined from its characteristic for DNA-based computing

Biosystems ◽  
2005 ◽  
Vol 80 (1) ◽  
pp. 71-82 ◽  
Author(s):  
Minyi Guo ◽  
Weng-Long Chang ◽  
Machael Ho ◽  
Jian Lu ◽  
Jiannong Cao
Keyword(s):  
Optimal Solution ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Np Complete
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