Solving of Discrete Problems of Optimization with Linear-Fractional Objective Function by Branch and Bound Methods

2013 ◽  
Vol 45 (9) ◽  
pp. 77-83
Author(s):  
Oleg A. Iemets ◽  
Oksana A. Chernenko
Keyword(s):  
Objective Function ◽  
Branch And Bound ◽  
Branch And Bound Methods ◽  
Discrete Problems

scholarly journals On derivative based bounding for simplicial branch and bound

2021 ◽  
Author(s):  
Eligius M.T. Hendrix ◽  
Boglarka G. -Tóth ◽  
Frederic Messine ◽  
Leocadio G. Casado
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Branch And Bound ◽  
Partial Derivative ◽  
Interval Arithmetic ◽  
Objective Function Value ◽  
Search Space ◽  
Second Derivative ◽  
Branch And Bound Methods

Simplicial based Global Optimization branch and bound methods require tight bounds on the objective function value. Recently, a renewed interest appears on bound calculation based on Interval Arithmetic by Karhbet and Kearfott (2017) and on exploiting second derivative bounds by Mohand (2021). The investigated question here is how partial derivative ranges can be used to provide bounds of the objective function value over the simplex. Moreover, we provide theoretical properties of how this information can be used from a monotonicity perspective to reduce the search space in simplicial branch and bound.

Branch-and-Bound Methods

2014 ◽  
pp. 39-69
Author(s):  
Iréne Charon ◽  
Olivier Hudry
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Methods

A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs

2022 ◽  
Author(s):  
Vahid Mahmoodian ◽  
Iman Dayarian ◽  
Payman Ghasemi Saghand ◽  
Yu Zhang ◽  
Hadi Charkhgard
Keyword(s):  
Objective Function ◽  
Branch And Bound ◽  
Capacity Allocation ◽  
Branch And Cut ◽  
Nash Bargaining ◽  
Mixed Integer ◽  
Bargaining Solution ◽  
Reliability Optimization ◽  
Criterion Space ◽  
Multiplicative Programs

This study introduces a branch-and-bound algorithm to solve mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). This class of optimization problems arises in many applications, such as finding a Nash bargaining solution (Nash social welfare optimization), capacity allocation markets, reliability optimization, etc. The proposed algorithm applies multiobjective optimization principles to solve MIBL-MMPs exploiting a special characteristic in these problems. That is, taking each multiplicative term in the objective function as a dummy objective function, the projection of an optimal solution of MIBL-MMPs is a nondominated point in the space of dummy objectives. Moreover, several enhancements are applied and adjusted to tighten the bounds and improve the performance of the algorithm. The performance of the algorithm is investigated by 400 randomly generated sample instances of MIBL-MMPs. The obtained result is compared against the outputs of the mixed-integer second order cone programming (SOCP) solver in CPLEX and a state-of-the-art algorithm in the literature for this problem. Our analysis on this comparison shows that the proposed algorithm outperforms the fastest existing method, that is, the SOCP solver, by a factor of 6.54 on average. Summary of Contribution: The scope of this paper is defined over a class of mixed-integer programs, the so-called mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). The importance of MIBL-MMPs is highlighted by the fact that they are encountered in applications, such as Nash bargaining, capacity allocation markets, reliability optimization, etc. The mission of the paper is to introduce a novel and effective criterion space branch-and-cut algorithm to solve MIBL-MMPs by solving a finite number of single-objective mixed-integer linear programs. Starting with an initial set of primal and dual bounds, our proposed approach explores the efficient set of the multiobjective problem counterpart of the MIBL-MMP through a criterion space–based branch-and-cut paradigm and iteratively improves the bounds using a branch-and-bound scheme. The bounds are obtained using novel operations developed based on Chebyshev distance and piecewise McCormick envelopes. An extensive computational study demonstrates the efficacy of the proposed algorithm.

Branch and Bound Methods

2000 ◽  
pp. 205-228
Author(s):  
H. A. Eiselt ◽  
C.-L. Sandblom
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Methods

Branch-and-Bound Methods

2013 ◽  
pp. 39-69
Author(s):  
Irène Charon ◽  
Olivier Hudry
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Methods

Branch-and-Bound Methods

1975 ◽  
pp. 139-176
Author(s):  
Hamdy A. Taha
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Methods

scholarly journals Branch and bound methods based tone injection schemes for PAPR reduction of DCO-OFDM visible light communications

2017 ◽  
Vol 25 (2) ◽  
pp. 595 ◽  
Author(s):  
Yongqiang Hei ◽  
Jiao Liu ◽  
Wentao Li ◽  
Xiaochuan Xu ◽  
Ray T. Chen
Keyword(s):  
Visible Light ◽  
Branch And Bound ◽  
Papr Reduction ◽  
Visible Light Communications ◽  
Branch And Bound Methods
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