scholarly journals Enhanced method of fast re-routing with load balancing in software-defined networks

2017 ◽  
Vol 68 (6) ◽  
pp. 444-454 ◽  
Author(s):  
Oleksandr Lemeshko ◽  
Oleksandra Yeremenko
Keyword(s):  
Load Balancing ◽  
Traffic Engineering ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Iterative Solution ◽  
Efficiency And Effectiveness ◽  
Communication Links ◽  
Linear Optimization Problems ◽  
Level Method ◽  
Upper Level

AbstractA two-level method of fast re-routing with load balancing in a software-defined network (SDN) is proposed. The novelty of the method consists, firstly, in the introduction of a two-level hierarchy of calculating the routing variables responsible for the formation of the primary and backup paths, and secondly, in ensuring a balanced load of the communication links of the network, which meets the requirements of the traffic engineering concept. The method provides implementation of link, node, path, and bandwidth protection schemes for fast re-routing in SDN. The separation in accordance with the interaction prediction principle along two hierarchical levels of the calculation functions of the primary (lower level) and backup (upper level) routes allowed to abandon the initial sufficiently large and nonlinear optimization problem by transiting to the iterative solution of linear optimization problems of half the dimension. The analysis of the proposed method confirmed its efficiency and effectiveness in terms of obtaining optimal solutions for ensuring balanced load of communication links and implementing the required network element protection schemes for fast re-routing in SDN.

SIMULATION OBJECTIVES OF FUZZY LINEAR PROGRAMMING WITH AN α-LEVEL METHOD OF λ-CONTINUE

2019 ◽  
Vol 6 (2) ◽  
pp. 71-76
Author(s):  
Alevtina Jur'evna Shatalova ◽  
Konstantin Andreevich Lebedev Konstantin Andreevich
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Investment Project ◽  
Fuzzy Linear Programming ◽  
Distribution Law ◽  
Linear Optimization Problems ◽  
Level Method

The article describes an approach that allows to formally describe the arising uncertainties in linear optimization problems. The generalized parametric alpha-level method of lambda-continuation of the fuzzy linear programming problem is considered. The model offers two methods that take into account the expansion of the binary fuzzy ratio (“strong” and “weak”). After the condition is formed taking into account the incoming quantities in the form of fuzzy numbers (the objective function and the system of constraints), the optimal solution (the value of the objective function) for each alpha and lambda is calculated using the simplex method implemented in Mathcad. On its basis, a mathematical model is built that will take into account the random values of alpha and lambda with a uniform distribution law. The paper presents a description of the simulation study, which confirms the conclusions about the possibilities of the method. Using the proposed theory, the decision-maker receives more information showing the behavior of the system with small changes in the input parameters to make more informed conclusions about the choice of financing of an investment project. The developed method of simulation of fuzzy estimation can be applied to other economic models with the appropriate necessary modification, for example, to assess the creditworthiness of the enterprise.

Multirow Intersection Cuts Based on the Infinity Norm

2021 ◽  
Author(s):  
Álinson S. Xavier ◽  
Ricardo Fukasawa ◽  
Laurent Poirrier
Keyword(s):  
Optimization Problems ◽  
Valid Inequalities ◽  
Linear Optimization ◽  
Computational Cost ◽  
General Purpose ◽  
Mixed Integer ◽  
Infinity Norm ◽  
Intersection Cuts ◽  
Linear Optimization Problems ◽  
Mixed Integer Linear Optimization

When generating multirow intersection cuts for mixed-integer linear optimization problems, an important practical question is deciding which intersection cuts to use. Even when restricted to cuts that are facet defining for the corner relaxation, the number of potential candidates is still very large, especially for instances of large size. In this paper, we introduce a subset of intersection cuts based on the infinity norm that is very small, works for relaxations having arbitrary number of rows and, unlike many subclasses studied in the literature, takes into account the entire data from the simplex tableau. We describe an algorithm for generating these inequalities and run extensive computational experiments in order to evaluate their practical effectiveness in real-world instances. We conclude that this subset of inequalities yields, in terms of gap closure, around 50% of the benefits of using all valid inequalities for the corner relaxation simultaneously, but at a small fraction of the computational cost, and with a very small number of cuts. Summary of Contribution: Cutting planes are one of the most important techniques used by modern mixed-integer linear programming solvers when solving a variety of challenging operations research problems. The paper advances the state of the art on general-purpose multirow intersection cuts by proposing a practical and computationally friendly method to generate them.

scholarly journals A new proximity function generating the best known iteration bounds for both large-update and small-update interior-point methods

2007 ◽  
Vol 49 (2) ◽  
pp. 259-270 ◽  
Author(s):  
Keyvan Aminis ◽  
Arash Haseli
Keyword(s):  
Interior Point ◽  
Interior Point Methods ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Point Of View ◽  
Theory And Practice ◽  
Theoretical Point ◽  
Barrier Functions ◽  
Iteration Bound ◽  
Linear Optimization Problems

AbstractInterior-Point Methods (IPMs) are not only very effective in practice for solving linear optimization problems but also have polynomial-time complexity. Despite the practical efficiency of large-update algorithms, from a theoretical point of view, these algorithms have a weaker iteration bound with respect to small-update algorithms. In fact, there is a significant gap between theory and practice for large-update algorithms. By introducing self-regular barrier functions, Peng, Roos and Terlaky improved this gap up to a factor of log n. However, checking these self-regular functions is not simple and proofs of theorems involving these functions are very complicated. Roos el al. by presenting a new class of barrier functions which are not necessarily self-regular, achieved very good results through some much simpler theorems. In this paper we introduce a new kernel function in this class which yields the best known complexity bound, both for large-update and small-update methods.

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