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 Global Optimization for Generalized Linear Multiplicative Programming Using Convex Relaxation

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yingfeng Zhao ◽  
Ting Zhao
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Recent Literature ◽  
Convex Relaxation ◽  
Relaxation Method ◽  
Engineering Practice ◽  
Multiplicative Programming ◽  
Wide Range ◽  
Linear Multiplicative Programming ◽  
Convergence And Optimality

Applications of generalized linear multiplicative programming problems (LMP) can be frequently found in various areas of engineering practice and management science. In this paper, we present a simple global optimization algorithm for solving linear multiplicative programming problem (LMP). The algorithm is developed by a fusion of a new convex relaxation method and the branch and bound scheme with some accelerating techniques. Global convergence and optimality of the algorithm are also presented and extensive computational results are reported on a wide range of problems from recent literature and GLOBALLib. Numerical experiments show that the proposed algorithm with a new convex relaxation method is more efficient than usual branch and bound algorithm that used linear relaxation for solving the LMP.

scholarly journals A new branch and bound algorithm for minimax ratios problems

2017 ◽  
Vol 15 (1) ◽  
pp. 840-851 ◽  
Author(s):  
Yingfeng Zhao ◽  
Sanyang Liu ◽  
Hongwei Jiao
Keyword(s):  
Programming Problem ◽  
Branch And Bound ◽  
Convex Relaxation ◽  
Numerical Test ◽  
Auxiliary Variable ◽  
Branch And Bound Algorithm ◽  
Computational Performance ◽  
Minimax Fractional Programming ◽  
Convexity And Concavity ◽  
Algorithm Scheme

Abstract This study presents an efficient branch and bound algorithm for globally solving the minimax fractional programming problem (MFP). By introducing an auxiliary variable, an equivalent problem is firstly constructed and the convex relaxation programming problem is then established by utilizing convexity and concavity of functions in the problem. Other than usual branch and bound algorithm, an adapted partition skill and a practical reduction technique performed only in an unidimensional interval are incorporated into the algorithm scheme to significantly improve the computational performance. The global convergence is proved. Finally, some comparative experiments and a randomized numerical test are carried out to demonstrate the efficiency and robustness of the proposed algorithm.

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.

Unit Commitment Solution by Branch and Bound Algorithm

2020 ◽  
Author(s):  
Bishaljit Paul ◽  
Sushovan Goswami ◽  
Dipu Mistry ◽  
Chandan Kumar Chanda
Keyword(s):  
Branch And Bound ◽  
Unit Commitment ◽  
Branch And Bound Algorithm

scholarly journals Identification of mechanical properties of arteries with certification of global optimality

2021 ◽  
Author(s):  
Jan-Lucas Gade ◽  
Carl-Johan Thore ◽  
Jonas Stålhand
Keyword(s):  
Global Solution ◽  
Branch And Bound ◽  
Clinical Data ◽  
Minimization Problem ◽  
Branch And Bound Algorithm ◽  
Stationary Points ◽  
Model Parameters ◽  
Global Optimality ◽  
Clinical Value ◽  
Non Linear

AbstractIn this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.

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