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.

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.

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 A Review of Piecewise Linearization Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ming-Hua Lin ◽  
John Gunnar Carlsson ◽  
Dongdong Ge ◽  
Jianming Shi ◽  
Jung-Fa Tsai
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Convex Programming Problem ◽  
Nonlinear Programming Problem ◽  
Global Optimal Solution ◽  
Piecewise Linearization ◽  
Linearization Methods ◽  
Global Optimal

Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.

A novel PGSA–PSO hybrid algorithm for structural optimization

2019 ◽  
Vol 37 (1) ◽  
pp. 144-160 ◽  
Author(s):  
Zhengrong Jiang ◽  
Quanpan Lin ◽  
Kairong Shi ◽  
Wenzhi Pan
Keyword(s):  
Structural Optimization ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Initial Growth ◽  
Global Optimal Solution ◽  
Content Type ◽  
Dome Structure ◽  
Global Optimal ◽  
Optimization Efficiency

Purpose The purpose of this paper is to propose a new hybrid algorithm, named improved plant growth simulation algorithm and particle swarm optimization hybrid algorithm (PGSA–PSO hybrid algorithm), for solving structural optimization problems. Design/methodology/approach To further enhance the optimization efficiency and precision of this algorithm, the optimization solution process of PGSA–PSO comprises two steps. First, an excellent initial growth point is selected by PSO. Then, the global optimal solution can be obtained quickly by PGSA and its improved strategy called growth space adjustment strategy. A typical mathematical example is provided to verify the capacity of the new hybrid algorithm to effectively improve the global search capability and search efficiency of PGSA. Moreover, PGSA–PSO is applied to the optimization design of a suspended dome structure. Findings Through typical mathematical example, the improved strategy can improve the optimization efficiency of PGSA considerably, and an initial growth point that falls near the global optimal solution can be obtained. Through the optimization of the pre-stress of a suspended dome structure, compared with other methods, the hybrid algorithm is effective and feasible in structural optimization. Originality/value Through the examples of suspended dome structure, it shows that the optimization efficiency and precision of PGSA–PSO are better than those of other algorithms and methods. PGSA–PSO is effective and feasible in structural optimization problems such as pre-stress optimization, size optimization, shape optimization and even topology optimization.

scholarly journals A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hongwei Jiao ◽  
Yongqiang Chen
Keyword(s):  
Lower Bound ◽  
Optimal Solution ◽  
Global Optimum ◽  
Initial Problem ◽  
Linear Relaxation ◽  
Feasible Region ◽  
Global Optimal Solution ◽  
Optimal Value ◽  
Global Optimal ◽  
Methods Numerical

A new linearizing method is presented for globally solving sum of linear ratios problem with coefficients. By using the linearizing method, linear relaxation programming (LRP) of the sum of linear ratios problem with coefficients is established, which can provide the reliable lower bound of the optimal value of the initial problem. Thus, a branch and bound algorithm for solving the sum of linear ratios problem with coefficients is put forward. By successively partitioning the linear relaxation of the feasible region and solving a series of the LRP, the proposed algorithm is convergent to the global optimal solution of the initial problem. Compared with the known methods, numerical experimental results show that the proposed method has the higher computational efficiency in finding the global optimum of the sum of linear ratios problem with coefficients.

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.

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.

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