scholarly journals A parametric simplex algorithm for biobjective piecewise linear programming problems

2017 ◽  
Vol 13 (2) ◽  
pp. 573-586 ◽  
Author(s):  
Rong Hu ◽  
◽  
Ya-Ping Fang ◽  
Keyword(s):  
Linear Programming ◽  
Piecewise Linear ◽  
Simplex Algorithm ◽  
Linear Programming Problems ◽  
Parametric Simplex Algorithm ◽  
Piecewise Linear Programming

scholarly journals Objective variation simplex algorithm for continuous piecewise linear programming

2017 ◽  
Vol 22 (01) ◽  
pp. 73-82 ◽  
Author(s):  
Yu Bai ◽  
Zhiming Xu ◽  
Xiangming Xi ◽  
Shuning Wang
Keyword(s):  
Linear Programming ◽  
Piecewise Linear ◽  
Simplex Algorithm ◽  
Piecewise Linear Programming

scholarly journals A comparative study of two key algorithms in multiple objective linear programming

2019 ◽  
Vol 13 ◽  
pp. 174830261987042
Author(s):  
Paschal B Nyiam ◽  
Abdellah Salhi
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Objective Space ◽  
Linear Programming Problems ◽  
Outer Approximation Algorithm ◽  
Parametric Simplex Algorithm ◽  
Problem Instances ◽  
Comparative Results

Multiple objective linear programming problems are solved with a variety of algorithms. While these algorithms vary in philosophy and outlook, most of them fall into two broad categories: those that are decision space-based and those that are objective space-based. This paper reports the outcome of a computational investigation of two key representative algorithms, one of each category, namely the parametric simplex algorithm which is a prominent representative of the former and the primal variant of Bensons Outer-approximation algorithm which is a prominent representative of the latter. The paper includes a procedure to compute the most preferred nondominated point which is an important feature in the implementation of these algorithms and their comparison. Computational and comparative results on problem instances ranging from small to medium and large are provided.

Piecewise linear programming via interior points

2000 ◽  
Vol 27 (13) ◽  
pp. 1303-1324 ◽  
Author(s):  
Mario Conrado Cavichia ◽  
Marcos Nereu Arenales
Keyword(s):  
Linear Programming ◽  
Piecewise Linear ◽  
Interior Points ◽  
Piecewise Linear Programming
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