scholarly journals An Out Space Accelerating Algorithm for Generalized Affine Multiplicative Programs Problem

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Lei Cai ◽  
Shuai Tang ◽  
Jingben Yin ◽  
Zhisong Hou ◽  
Hongwei Jiao
Keyword(s):  
Branch And Bound ◽  
Original Problem ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Space Region ◽  
Equivalent Problem ◽  
Space Partition ◽  
Space Reduction ◽  
Multiplicative Programs ◽  
New Variables

This paper presents an out space branch-and-bound algorithm for solving generalized affine multiplicative programs problem. Firstly, by introducing new variables and constraints, we transform the original problem into an equivalent nonconvex programs problem. Secondly, by utilizing new linear relaxation technique, we establish the linear relaxation programs problem of the equivalent problem. Thirdly, based on the out space partition and the linear relaxation programs problem, we construct an out space branch-and-bound algorithm. Fourthly, to improve the computational efficiency of the algorithm, an out space reduction operation is employed as an accelerating device for deleting a large part of the investigated out space region. Finally, the global convergence of the algorithm is proved, and numerical results demonstrate the feasibility and effectiveness of the proposed algorithm.

An Optimization Algorithm for a Class of Mathematical Model in Mechanical Engineering

2010 ◽  
Vol 26-28 ◽  
pp. 813-816
Author(s):  
Jing Ben Yin ◽  
Jie Sheng Yan ◽  
Ying Feng Zhao ◽  
Hong Wei Jiao
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Branch And Bound ◽  
Optimization Algorithm ◽  
Mechanical Engineering ◽  
Original Problem ◽  
Relaxation Method ◽  
Linear Relaxation ◽  
Equivalent Problem ◽  
Numerical Examples

In this paper, we develop an algorithm to globally solve a class of mathematical models in system engineering. Firstly, by utilizing equivalent problem and linear relaxation method, a linear relaxation programming of original problem is established. Secondly, by using branch and bound technique, a determined branch and bound algorithm is proposed for globally solving original problem. Finally, the convergence of the proposed algorithm is given and numerical examples showed that the presented algorithm is feasible.

A Feasible Algorithm for a Class of Mathematical Problems in Mechanical System

2010 ◽  
Vol 26-28 ◽  
pp. 1032-1035
Author(s):  
Jing Ben Yin ◽  
Kun Li ◽  
Hong Wei Jiao ◽  
Yong Qiang Chen
Keyword(s):  
Mechanical System ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Mathematical Problem ◽  
Linear Relaxation ◽  
Equivalent Problem ◽  
Mathematical Problems ◽  
Feasible Algorithm ◽  
Bound Theory

In this paper, we proposed an algorithm to globally solve a class of mathematical problems in mechanical system. Firstly, by utilizing equivalent problem and linear relaxation technique, a linear relaxation programming of original mathematical problem is established. Secondly, by using branch and bound theory, a feasible algorithm is proposed for globally solving original problem. Finally, the convergence of the proposed algorithm is proven, and numerical experiments showed that the presented algorithm is feasible.

scholarly journals An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Hongwei Jiao ◽  
Lei Cai ◽  
Zhisong Hou ◽  
Chunyang Bai
Keyword(s):  
Programming Problem ◽  
Computational Efficiency ◽  
Nonconvex Programming ◽  
Optimal Solution ◽  
Space Region ◽  
Effective Algorithm ◽  
Equivalent Problem ◽  
Solution Quality ◽  
Space Partition ◽  
Pruning Technique

In this study, we propose an effective algorithm for globally solving the sum of linear ratios problems. Firstly, by introducing new variables, we transform the initial problem into an equivalent nonconvex programming problem. Secondly, by utilizing direct relaxation, the linear relaxation programming problem of the equivalent problem can be constructed. Thirdly, in order to improve the computational efficiency of the algorithm, an out space pruning technique is derived, which offers a possibility of pruning a large part of the out space region which does not contain the optimal solution of the equivalent problem. Fourthly, based on out space partition, by combining bounding technique and pruning technique, a new out space branch-and-bound algorithm for globally solving the sum of linear ratios problems (SLRP) is designed. Finally, numerical experimental results are presented to demonstrate both computational efficiency and solution quality of the proposed algorithm.

scholarly journals Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Chun-Feng Wang ◽  
Yan-Qin Bai
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Algorithm ◽  
Linearization Method ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Global Optimization Algorithm ◽  
Multiplicative Programming ◽  
Linear Multiplicative Programming ◽  
Pruning Techniques

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm.

Optimization Algorithm for Solving a Kind of Mathematical Problems

2010 ◽  
Vol 44-47 ◽  
pp. 3423-3426 ◽  
Author(s):  
Hong Wei Jiao ◽  
Kun Li
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Original Problem ◽  
Mathematical Problem ◽  
Relaxation Method ◽  
Linear Relaxation ◽  
Global Optimization Algorithm ◽  
Equivalent Problem ◽  
Numerical Examples ◽  
Mathematical Problems

In this paper, we develop an algorithm to globally solve a kind of mathematical problem. Firstly, by utilizing equivalent problem and linear relaxation method, a linear relaxation programming of original problem is established. Secondly, by using branch and bound technique, a determined global optimization algorithm is proposed for solving equivalent problem. Finally, the convergence of the proposed algorithm is proven and numerical examples showed that the presented algorithm is feasible to solve the kind of mathematical problems.

scholarly journals An Effective Branch and Bound Algorithm for Minimax Linear Fractional Programming

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hong-Wei Jiao ◽  
Feng-Hui Wang ◽  
Yong-Qiang Chen
Keyword(s):  
Branch And Bound ◽  
Fractional Programming ◽  
Optimal Solution ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Feasible Region ◽  
Test Problems ◽  
Linear Fractional Programming ◽  
Successive Refinement ◽  
Global Optimal

An effective branch and bound algorithm is proposed for globally solving minimax linear fractional programming problem (MLFP). In this algorithm, the lower bounds are computed during the branch and bound search by solving a sequence of linear relaxation programming problems (LRP) of the problem (MLFP), which can be derived by using a new linear relaxation bounding technique, and which can be effectively solved by the simplex method. The proposed branch and bound algorithm is convergent to the global optimal solution of the problem (MLFP) through the successive refinement of the feasible region and solutions of a series of the LRP. Numerical results for several test problems are reported to show the feasibility and effectiveness of the proposed algorithm.

scholarly journals An Efficient Branch-and-Bound Algorithm for Globally Solving Minimax Linear Fractional Programming Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Pujun Jia ◽  
Hongwei Jiao ◽  
Dongwei Shi ◽  
Jingben Yin
Keyword(s):  
Programming Problem ◽  
Branch And Bound ◽  
Fractional Programming ◽  
Outer Space ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Wide Range ◽  
Linear Fractional Programming Problem

This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, by introducing auxiliary variables, we first equivalently transform the problem (MLFP) into the problem (EP). By using a new linear relaxation technique, the problem (EP) is reduced to a sequence of linear relaxation problems over the outer space rectangle, which provides the valid lower bound for the optimal value of the problem (EP). Based on the outer space branch-and-bound search and the linear relaxation problem, an outer space branch-and-bound algorithm is constructed for globally solving the problem (MLFP). In addition, the convergence and complexity of the presented algorithm are given. Finally, numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.

scholarly journals A reduced space branch and bound algorithm for a class of sum of ratios problems

2018 ◽  
Vol 16 (1) ◽  
pp. 539-552
Author(s):  
Yingfeng Zhao ◽  
Ting Zhao
Keyword(s):  
Branch And Bound ◽  
Convex Relaxation ◽  
Branch And Bound Algorithm ◽  
Engineering Practice ◽  
Auxiliary Variables ◽  
Equivalent Problem ◽  
Sum Of Ratios ◽  
Relaxation Problem ◽  
Reduction Techniques ◽  
Reduced Space

AbstractSum of ratios problem occurs frequently in various areas of engineering practice and management science, but most solution methods for this kind of problem are often designed for determining local solutions . In this paper, we develop a reduced space branch and bound algorithm for globally solving sum of convex-concave ratios problem. By introducing some auxiliary variables, the initial problem is converted into an equivalent problem where the objective function is linear. Then the convex relaxation problem of the equivalent problem is established by relaxing auxiliary variables only in the outcome space. By integrating some acceleration and reduction techniques into branch and bound scheme, the presented global optimization algorithm is developed for solving these kind of problems. Convergence and optimality of the algorithm are presented and numerical examples taken from some recent literature and MINLPLib are carried out to validate the performance of the proposed algorithm.

scholarly journals An Efficient Algorithm for Solving a Class of Fractional Programming Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yongjian Qiu ◽  
Yuming Zhu ◽  
Jingben Yin
Keyword(s):  
Computational Complexity ◽  
Global Convergence ◽  
Programming Problem ◽  
Branch And Bound ◽  
Fractional Programming ◽  
Financial Engineering ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Optimal Solutions ◽  
Communication Engineering

This paper presents an efficient branch-and-bound algorithm for globally solving a class of fractional programming problems, which are widely used in communication engineering, financial engineering, portfolio optimization, and other fields. Since the kind of fractional programming problems is nonconvex, in which multiple locally optimal solutions generally exist that are not globally optimal, so there are some vital theoretical and computational difficulties. In this paper, first of all, for constructing this algorithm, we propose a novel linearizing method so that the initial fractional programming problem can be converted into a linear relaxation programming problem by utilizing the linearizing method. Secondly, based on the linear relaxation programming problem, a novel branch-and-bound algorithm is designed for the kind of fractional programming problems, the global convergence of the algorithm is proved, and the computational complexity of the algorithm is analysed. Finally, numerical results are reported to indicate the feasibility and effectiveness of the algorithm.

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