scholarly journals A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Xue-Gang Zhou ◽  
Bing-Yuan Cao
Keyword(s):  
Linear Programming ◽  
Nonconvex Programming ◽  
Optimal Solution ◽  
Linearization Method ◽  
Global Optimal Solution ◽  
Natural Logarithm ◽  
Lower Bounding ◽  
Linear Programming Problems ◽  
Global Optimal ◽  
Logarithm Function

A new two-part parametric linearization technique is proposed globally to a class of nonconvex programming problems (NPP). Firstly, a two-part parametric linearization method is adopted to construct the underestimator of objective and constraint functions, by utilizing a transformation and a parametric linear upper bounding function (LUBF) and a linear lower bounding function (LLBF) of a natural logarithm function and an exponential function witheas the base, respectively. Then, a sequence of relaxation lower linear programming problems, which are embedded in a branch-and-bound algorithm, are derived in an initial nonconvex programming problem. The proposed algorithm is converged to global optimal solution by means of a subsequent solution to a series of linear programming problems. Finally, some examples are given to illustrate the feasibility of the presented algorithm.

Optimization Method for Globally Solving a Kind of Multiplicative Problems with Coefficients

2011 ◽  
Vol 467-469 ◽  
pp. 526-530 ◽  
Author(s):  
Hong Wei Jiao ◽  
Jing Ben Yin ◽  
Yun Rui Guo
Keyword(s):  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Linearization Method ◽  
Equivalent Transformation ◽  
Engineering System ◽  
Linear Programming Problems ◽  
Global Optimal ◽  
Multiplicative Problems

Multiplicative problems are a kind of difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, system, finance, economics, and other fields. In this paper, an optimization method is proposed to globally solve a class of multiplicative problems with coefficients. Firstly, by utilizing equivalent transformation and linearization method, a linear relaxation programming problem is established. Secondly, by using branch and bound technique, a determined algorithm is proposed for solving equivalent problem. Finally, the proposed algorithm is convergent to the global optimal solution of original problem by means of the subsequent solutions of a series of linear programming problems.

A Deterministic Method for a Class of Fractional Programming Problems with Coefficients

2011 ◽  
Vol 467-469 ◽  
pp. 531-536
Author(s):  
Jing Ben Yin ◽  
Kun Li
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Deterministic Algorithm ◽  
Linear Relaxation ◽  
Convex Programming Problem ◽  
Global Optimal Solution ◽  
Deterministic Method ◽  
Equivalent Problem ◽  
Linear Programming Problems ◽  
Global Optimal

The sum of linear fractional functions problem has attracted the interest of researchers and practitioners for a number of years. Since these types of optimization problems are non-convex, various specialized algorithms have been proposed for globally solving these problems. However, these algorithms are only for the case that sum of linear ratios problem without coefficients, and may be difficult to be solved. In this paper, a deterministic algorithm is proposed for globally solving the sum of linear fractional functions problem with coefficients. By utilizing an equivalent problem and linear relaxation technique, the initial non-convex programming problem is reduced to a sequence of linear relaxation programming problems. The proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems.

scholarly journals Global Optimization for the Sum of Concave-Convex Ratios Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
XueGang Zhou ◽  
JiHui Yang
Keyword(s):  
Convex Programming ◽  
Convex Set ◽  
Nonconvex Programming ◽  
Compact Convex ◽  
Optimal Solution ◽  
Global Optimal Solution ◽  
Equivalent Problem ◽  
Linearization Technique ◽  
Compact Convex Set ◽  
Global Optimal

This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

scholarly journals An Effective Global Optimization Algorithm for Quadratic Programs with Quadratic Constraints

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 424
Author(s):  
Dongwei Shi ◽  
Jingben Yin ◽  
Chunyang Bai
Keyword(s):  
Numerical Experiments ◽  
Optimal Solution ◽  
Linearization Method ◽  
Linear Programming Relaxation ◽  
Global Optimization Algorithm ◽  
Quadratic Programs ◽  
Global Optimal Solution ◽  
Quadratic Constraints ◽  
Relaxation Problem ◽  
Global Optimal

This paper will present an effective algorithm for globally solving quadratic programs with quadratic constraints. In this algorithm, we propose a new linearization method for establishing the linear programming relaxation problem of quadratic programs with quadratic constraints. The proposed algorithm converges with the global optimal solution of the initial problem, and numerical experiments show the computational efficiency of the proposed algorithm.

AO-BBO: A Novel Optimization Algorithm and Its Application in Plant Drug Extraction

2019 ◽  
Vol 19 (2) ◽  
pp. 139-145 ◽  
Author(s):  
Bote Lv ◽  
Juan Chen ◽  
Boyan Liu ◽  
Cuiying Dong
Keyword(s):  
Optimization Algorithm ◽  
Learning Strategy ◽  
Optimal Solution ◽  
Population Diversity ◽  
Global Optimal Solution ◽  
Plant Medicine ◽  
Suitability Index ◽  
Sensing Model ◽  
Local Optimal Solution ◽  
Global Optimal

<P>Introduction: It is well-known that the biogeography-based optimization (BBO) algorithm lacks searching power in some circumstances. </P><P> Material & Methods: In order to address this issue, an adaptive opposition-based biogeography-based optimization algorithm (AO-BBO) is proposed. Based on the BBO algorithm and opposite learning strategy, this algorithm chooses different opposite learning probabilities for each individual according to the habitat suitability index (HSI), so as to avoid elite individuals from returning to local optimal solution. Meanwhile, the proposed method is tested in 9 benchmark functions respectively. </P><P> Result: The results show that the improved AO-BBO algorithm can improve the population diversity better and enhance the search ability of the global optimal solution. The global exploration capability, convergence rate and convergence accuracy have been significantly improved. Eventually, the algorithm is applied to the parameter optimization of soft-sensing model in plant medicine extraction rate. Conclusion: The simulation results show that the model obtained by this method has higher prediction accuracy and generalization ability.</P>

scholarly journals Best Proximity Point Results in Complex Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Pranati Maity
Keyword(s):  
Minimum Distance ◽  
Metric Spaces ◽  
Optimal Solution ◽  
Global Optimal Solution ◽  
Complex Valued Metric Space ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Global Optimal ◽  
Metric Function ◽  
Complex Valued

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

Sign in / Sign up

Export Citation Format

Share Document