scholarly journals A Primal-Dual Interior-Point Method for Facility Layout Problem with Relative-Positioning Constraints

Algorithms ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 60
Author(s):  
Shunichi Ohmori ◽  
Kazuho Yoshimoto
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Facility Layout ◽  
Optimal Solution ◽  
Point Method ◽  
Interior Point Algorithm ◽  
Relative Positioning ◽  
Layout Problem ◽  
Facility Layout Problem ◽  
Primal Dual

We consider the facility layout problem (FLP) in which we find the arrangements of departments with the smallest material handling cost that can be expressed as the product of distance times flows between departments. It is known that FLP can be formulated as a linear programming problem if the relative positioning of departments is specified, and, thus, can be solved to optimality. In this paper, we describe a custom interior-point algorithm for solving FLP with relative positioning constraints (FLPRC) that is much faster than the standard methods used in the general-purpose solver. We build a compact formation of FLPRC and its duals, which enables us to establish the optimal condition very quickly. We use this optimality condition to implement the primal-dual interior-point method with an efficient Newton step computation that exploit special structure of a Hessian. We confirm effectiveness of our proposed model through applications to several well-known benchmark data sets. Our algorithm shows much faster speed for finding the optimal solution.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

Feasibility issues in a primal-dual interior-point method for linear programming

1990 ◽  
Vol 49 (1-3) ◽  
pp. 145-162 ◽  
Author(s):  
Irvin J. Lustig
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Primal Dual

scholarly journals An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
John Machacek ◽  
Shafiu Jibrin
Keyword(s):  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Point Method ◽  
Feasible Region ◽  
Test Problems ◽  
Analytic Centers ◽  
Semidefinite Programs

We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.

scholarly journals Evaluation of Transfer Capability based on Load Supplying Capability Calculation Using Primal-Dual Interior Point Method

2000 ◽  
Vol 120 (8-9) ◽  
pp. 1175-1181
Author(s):  
Min-Hwa Jeong ◽  
Junji Kubokawa ◽  
Naoto Yorino ◽  
Hiroshi Sasaki ◽  
Byongjun Lee ◽  
...  
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Transfer Capability ◽  
Primal Dual

scholarly journals Improved Primal–Dual Interior-Point Method Using the Lawson-Norm for Inverse Problems

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 41053-41061
Author(s):  
Wenjing Shang ◽  
Wei Xue ◽  
Yingsong Li ◽  
Yidong Xu
Keyword(s):  
Inverse Problems ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Primal Dual

A primal-dual interior-point method for iterative feedback tuning

1999 ◽  
Vol 32 (2) ◽  
pp. 4654-4658 ◽  
Author(s):  
Anders Hansson ◽  
Khalid El-Awady ◽  
Bo Wahlberg
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Primal Dual ◽  
Iterative Feedback

Primal-Dual Interior-Point Method for an Optimization Problem Related to the Modeling of Atmospheric Organic Aerosols

2006 ◽  
Vol 130 (3) ◽  
pp. 377-409 ◽  
Author(s):  
N. R. Amundson ◽  
A. Caboussat ◽  
J. W. He ◽  
J. H. Seinfeld
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problem ◽  
Organic Aerosols ◽  
Point Method ◽  
Primal Dual
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