scholarly journals A Deterministic Method for Solving the Sum of Linear Ratios Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhenping Wang ◽  
Yonghong Zhang ◽  
Paolo Manfredi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Branch And Bound ◽  
Nonconvex Programming ◽  
Real Life ◽  
Branch And Bound Algorithm ◽  
Separation Technique ◽  
Linear Programming Relaxation ◽  
Deterministic Method ◽  
Linearization Technique

Since the sum of linear ratios problem (SLRP) has many applications in real life, for globally solving it, an efficient branch and bound algorithm is presented in this paper. By utilizing the characteristic of the problem (SLRP), we propose a convex separation technique and a two-part linearization technique, which can be used to generate a sequence of linear programming relaxation of the initial nonconvex programming problem. For improving the convergence speed of this algorithm, a deleting rule is presented. The convergence of this algorithm is established, and some experiments are reported to show the feasibility and efficiency of the proposed algorithm.

scholarly journals The Knowledge of Expert Opinion in Intuitionistic Fuzzy Linear Programming Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
A. Nagoorgani ◽  
J. Kavikumar ◽  
K. Ponnalagu
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Real Life ◽  
Fuzzy Linear Programming ◽  
Limited Resources ◽  
Fuzzy Data ◽  
Intuitionistic Fuzzy ◽  
Competing Demands ◽  
Intuitionistic Fuzzy Data

In real life, information available for certain situations is vague and such uncertainty is unavoidable. One possible solution is to consider the knowledge of experts on the parameters involved as intuitionistic fuzzy data. We examine a linear programming problem in which all the coefficients are intuitionistic in nature. An approach is presented to solve an intuitionistic fuzzy linear programming problem. In this proposed approach, a procedure for allocating limited resources effectively among competing demands is developed. An example is given to highlight the illustrated study.

scholarly journals Historical Load Balance in Distribution Systems Using the Branch and Bound Algorithm

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1219 ◽  
Author(s):  
Jorge Arias ◽  
Maria Calle ◽  
Daniel Turizo ◽  
Javier Guerrero ◽  
John Candelo-Becerra
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Distribution System ◽  
Load Balance ◽  
Distribution Systems ◽  
Branch And Bound Algorithm ◽  
Power Demand ◽  
Planning Tool ◽  
Time Intervals ◽  
Processing Technologies

One of the biggest problems with distribution systems correspond to the load unbalance created by power demand of customers. This becomes a difficult task to solve with conventional methods. Therefore, this paper uses integer linear programming and Branch and Bound algorithm to balance the loads in the three phases of the distribution system, employing stored data of power demand. Results show that the method helps to decrease the unbalance factor in more than 10%, by selecting the phase where a load should be connected. The solution may be used as a planning tool in distribution systems applied to installations with systems for measuring power consumption in different time intervals. Furthermore, in conjunction with communications and processing technologies, the solution could be useful to implement with a smart grid.

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 A Branch and Bound Algorithm for Agile Earth Observation Satellite Scheduling

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Xiaogeng Chu ◽  
Yuning Chen ◽  
Lining Xing
Keyword(s):  
Branch And Bound ◽  
Real Life ◽  
Engineering Application ◽  
Search Space ◽  
Branch And Bound Algorithm ◽  
Temporal Constraint ◽  
Look Ahead ◽  
Combined Use ◽  
Earth Observation Satellite ◽  
Satellite Scheduling

The agile earth observing satellite scheduling (AEOSS) problem consists of scheduling a subset of images among a set of candidates that satisfy imperative constraints and maximize a gain function. In this paper, we consider a new AEOSS model which integrates a time-dependent temporal constraint. To solve this problem, we propose a highly efficient branch and bound algorithm whose effective ingredients include a look-ahead construction method (for generating a high quality initial lower bound) and a combined use of three pruning strategies (which help to prune a large portion of the search space). We conducted computational experiments on a set of test data that were generated with information from real-life scenarios. The results showed that the proposed algorithm is efficient enough for engineering application. In particular, it is able to solve instances with 55 targets to optimality within 164 seconds on average. Furthermore, we carried out additional experiments to analyze the contribution of each key algorithm ingredient.

scholarly journals An effective algorithm for globally solving quadratic programs using parametric linearization technique

2018 ◽  
Vol 16 (1) ◽  
pp. 1300-1312
Author(s):  
Shuai Tang ◽  
Yuzhen Chen ◽  
Yunrui Guo
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Route Optimization ◽  
Linear Programming Relaxation ◽  
Effective Algorithm ◽  
Quadratic Programs ◽  
Parametric Linear Programming ◽  
Quadratic Constraints ◽  
Linearization Technique ◽  
Relaxation Problem

AbstractIn this paper, we present an effective algorithm for globally solving quadratic programs with quadratic constraints, which has wide application in engineering design, engineering optimization, route optimization, etc. By utilizing new parametric linearization technique, we can derive the parametric linear programming relaxation problem of the quadratic programs with quadratic constraints. To improve the computational speed of the proposed algorithm, some interval reduction operations are used to compress the investigated interval. By subsequently partitioning the initial box and solving a sequence of parametric linear programming relaxation problems the proposed algorithm is convergent to the global optimal solution of the initial problem. Finally, compared with some known algorithms, numerical experimental results demonstrate that the proposed algorithm has higher computational efficiency.

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