A Two‐Phase Support Method for Solving Linear Programs: Numerical Experiments

Abstract

We develop a single artificial variable technique to initialize the primal support method for solving linear programs with bounded variables. We first recall the full artificial basis technique, then we will present the proposed algorithm. In order to study the performances of the suggested algorithm, an implementation under the MATLAB programming language has been developed. Finally, we carry out an experimental study about CPU time and iterations number on a large set of the NETLIB test problems. These test problems are practical linear programs modelling various real-life problems arising from several fields such as oil refinery, audit staff scheduling, airline scheduling, industrial production and allocation, image restoration, multisector economic planning, and data fitting. It has been shown that our approach is competitive with our implementation of the primal simplex method and the primal simplex algorithm implemented in the known open-source LP solver LP_SOLVE.

A new method with hybrid direction for linear programming

“…The obtained numerical results on randomly generated test problems and some instances of a linear optimal control problem arising in a scheduling inventory application show that our algorithm is competitive with PSM and AMHD. In a future work, we will apply some crash procedure like that presented in Reference 20 in order to initialize our algorithm with a good initial SFS, then we will compare its performance with the simplex algorithm on netlib test problems 19…”

“…In this work, we propose an algorithm based on a new hybrid direction. This algorithm uses a suboptimality criterion in order to obtain a suboptimal solution and it uses the long step rule in order to change the current support 16 . Hence, the updating formula given in References 2,3 is a special case of our formula.…”

A successive linear approximation algorithm for the global minimization of a concave quadratic program

“…We have executed the different solvers on a PC with microprocessor Intel Core i7-4790, CPU @3.60 Ghz and 8GO of RAM, running under the Windows 10 operating system. For solving the intermediate linear programs, the simplex algorithm (Dantzig 1963) or the algorithms presented in Bentobache and Bibi (2012), Bibi and Bentobache (2015), Bentobache and Bibi (2016) can be used. However, we have used the barrier interior-point algorithm implemented in CPLEX12.8, which is known for its efficiency and robustness (function "cplexlp" with the parameter "lpmethod" set to 4) and we used the function "cplexqp" for finding the maximum of f on R n .…”

Minimizing Test Frequencies for Linear Analog Circuits: New Models and Efficient Solution Methods

“…Therefore, we can find an optimal solution using LP algorithms such as the primal or dual simplex method [14], the support method [15], the hybrid direction algorithm [19], etc. However, it is more efficient to transform the SCP-C1P into a min-cost network flow problem [10].…”