scholarly journals An Auxiliary Function Method for Global Minimization in Integer Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Hongwei Lin ◽  
Yuping Wang ◽  
Xiaoli Wang
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Function Method ◽  
Original Problem ◽  
Local Minimizer ◽  
Auxiliary Function ◽  
Global Minimizer ◽  
Global Minimization ◽  
Integer Programming Problem ◽  
Effectiveness And Efficiency

An auxiliary function method is proposed for finding the global minimizer of integer programming problem. Firstly, we propose a method to transform the original problem into an integer programming with box constraint, which does not change the properties of the original problem. For the transformed problem, we propose an auxiliary function to escape from the current local minimizer and to get a better one. Then, based on the proposed auxiliary function, a new algorithm to find the global minimizer of integer programming is proposed. At last, numerical results are given to demonstrate the effectiveness and efficiency of the proposed method.

scholarly journals Method for solving a convex integer programming problem

2003 ◽  
Vol 2003 (44) ◽  
pp. 2829-2834 ◽  
Author(s):  
Stefan M. Stefanov
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Assignment Problem ◽  
Original Problem ◽  
Integer Program ◽  
Integer Programming Problem ◽  
Equivalent Problem ◽  
Nonlinear Version ◽  
Convex Integer Programming

We consider a convex integer program which is a nonlinear version of the assignment problem. This problem is reformulated as an equivalent problem. An algorithm for solving the original problem is suggested which is based on solving the simple assignment problem via some of known algorithms.

TWO BI-OBJECTIVE OPTIMIZATION MODELS FOR COMPETITIVE LOCATION PROBLEMS

2006 ◽  
Vol 05 (03) ◽  
pp. 531-543 ◽  
Author(s):  
FENGMEI YANG ◽  
GUOWEI HUA ◽  
HIROSHI INOUE ◽  
JIANMING SHI
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Integer Program ◽  
Location Problems ◽  
Optimization Models ◽  
Competitive Location ◽  
Integer Programming Problem ◽  
Single Objective ◽  
Parametric Integer Programming

This paper deals with two bi-objective models arising from competitive location problems. The first model simultaneously intends to maximize market share and to minimize cost. The second one aims to maximize both profit and the profit margin. We study some of the related properties of the models, examine relations between the models and a single objective parametric integer programming problem, and then show how both bi-objective location problems can be solved through the use of a single objective parametric integer program. Based on this, we propose two methods of obtaining a set of efficient solutions to the problems of fundamental approach. Finally, a numerical example is presented to illustrate the solution techniques.

scholarly journals The Magnetic Bead Computing Model of the 0-1 Integer Programming Problem Based on DNA Cycle Hybridization

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Rujie Xu ◽  
Zhixiang Yin ◽  
Zhen Tang ◽  
Jing Yang ◽  
Jianzhong Cui ◽  
...  
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Magnetic Beads ◽  
Specific Binding ◽  
Optimal Solution ◽  
High Sensitivity ◽  
Magnetic Bead ◽  
Integer Programming Problem ◽  
Computing Model ◽  
Dna Strands

Magnetic beads and magnetic Raman technology substrates have good magnetic response ability and surface-enhanced Raman technology (SERS) activity. Therefore, magnetic beads exhibit high sensitivity in SERS detection. In this paper, DNA cycle hybridization and magnetic bead models are combined to solve 0-1 integer programming problems. First, the model maps the variables to DNA strands with hairpin structures and weights them by the number of hairpin DNA strands. This result can be displayed by the specific binding of streptavidin and biotin. Second, the constraint condition of the 0-1 integer programming problem can be accomplished by detecting the signal intensity of the biological barcode to find the optimal solution. Finally, this model can be used to solve the general 0-1 integer programming problem and has more extensive applications than the previous DNA computing model.

Solving the multi-objective stochastic interval-valued linear fractional integer programming problem

2021 ◽  
pp. 2250022
Author(s):  
Leila Younsi-Abbaci ◽  
Mustapha Moulaï
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Probabilistic Constraints ◽  
Chance Constrained Programming ◽  
Integer Programming Problem ◽  
Objective Functions ◽  
Programming Technique ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Interval Valued

In this paper, we consider a Multi-Objective Stochastic Interval-Valued Linear Fractional Integer Programming problem (MOSIVLFIP). We especially deal with a multi-objective stochastic fractional problem involving an inequality type of constraints, where all quantities on the right side are log-normal random variables, and the objective functions coefficients are fractional intervals. The proposed solving procedure is divided in three steps. In the first one, the probabilistic constraints are converted into deterministic ones by using the chance constrained programming technique. Then, the second step consists of transforming the studied problem objectives on an optimization problem with an interval-valued objective functions. Finally, by introducing the concept of weighted sum method, the equivalent converted problem obtained from the two first steps is transformed into a single objective deterministic fractional problem. The effectiveness of the proposed procedure is illustrated through a numerical example.

Sign in / Sign up

Export Citation Format

Share Document