Global Optimization of Nonconvex MINLP by a Hybrid Branch-and-Bound and Revised General Benders Decomposition Approach

2003 ◽  
Vol 42 (3) ◽  
pp. 528-539 ◽  
Author(s):  
Yushan Zhu ◽  
Takahito Kuno
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Benders Decomposition ◽  
Decomposition Approach

scholarly journals The electric location-routing problem with heterogeneous fleet: Formulation and Benders decomposition approach

2021 ◽  
Vol 131 ◽  
pp. 105251
Author(s):  
Hatice Çalık ◽  
Ammar Oulamara ◽  
Caroline Prodhon ◽  
Said Salhi
Keyword(s):  
Benders Decomposition ◽  
Location Routing Problem ◽  
Routing Problem ◽  
Decomposition Approach ◽  
Heterogeneous Fleet ◽  
Location Routing

scholarly journals A tailored Benders decomposition approach for last-mile delivery with autonomous robots

2021 ◽  
Author(s):  
Laurent Alfandari ◽  
Ivana Ljubić ◽  
Marcos de Melo da Silva
Keyword(s):  
Benders Decomposition ◽  
Autonomous Robots ◽  
Decomposition Approach ◽  
Last Mile ◽  
Last Mile Delivery

Wind Power Investment: A Benders Decomposition Approach

2012 ◽  
Vol 27 (1) ◽  
pp. 433-441 ◽  
Author(s):  
Luis Baringo ◽  
Antonio J. Conejo
Keyword(s):  
Wind Power ◽  
Benders Decomposition ◽  
Decomposition Approach

A Benders decomposition approach to transmission expansion planning considering energy storage

Energy ◽  
2016 ◽  
Vol 112 ◽  
pp. 795-803 ◽  
Author(s):  
C.A.G. MacRae ◽  
A.T. Ernst ◽  
M. Ozlen
Keyword(s):  
Energy Storage ◽  
Benders Decomposition ◽  
Decomposition Approach ◽  
Expansion Planning ◽  
Transmission Expansion Planning ◽  
Transmission Expansion

The Star Degree Centrality Problem: A Decomposition Approach

2021 ◽  
Author(s):  
Mustafa C. Camur ◽  
Thomas Sharkey ◽  
Chrysafis Vogiatzis
Keyword(s):  
Integer Programming ◽  
Large Scale ◽  
Benders Decomposition ◽  
Open Neighborhood ◽  
Decomposition Algorithm ◽  
Solution Time ◽  
Set Cover ◽  
Degree Centrality ◽  
Decomposition Approach ◽  
Acceleration Techniques

We consider the problem of identifying the induced star with the largest cardinality open neighborhood in a graph. This problem, also known as the star degree centrality (SDC) problem, is shown to be [Formula: see text]-complete. In this work, we first propose a new integer programming (IP) formulation, which has a smaller number of constraints and nonzero coefficients in them than the existing formulation in the literature. We present classes of networks in which the problem is solvable in polynomial time and offer a new proof of [Formula: see text]-completeness that shows the problem remains [Formula: see text]-complete for both bipartite and split graphs. In addition, we propose a decomposition framework that is suitable for both the existing and our formulations. We implement several acceleration techniques in this framework, motivated by techniques used in Benders decomposition. We test our approaches on networks generated based on the Barabási–Albert, Erdös–Rényi, and Watts–Strogatz models. Our decomposition approach outperforms solving the IP formulations in most of the instances in terms of both solution time and quality; this is especially true for larger and denser graphs. We then test the decomposition algorithm on large-scale protein–protein interaction networks, for which SDC is shown to be an important centrality metric. Summary of Contribution: In this study, we first introduce a new integer programming (NIP) formulation for the star degree centrality (SDC) problem in which the goal is to identify the induced star with the largest open neighborhood. We then show that, although the SDC can be efficiently solved in tree graphs, it remains [Formula: see text]-complete in both split and bipartite graphs via a reduction performed from the set cover problem. In addition, we implement a decomposition algorithm motivated by Benders decomposition together with several acceleration techniques to both the NIP formulation and the existing formulation in the literature. Our experimental results indicate that the decomposition implementation on the NIP is the best solution method in terms of both solution time and quality.

scholarly journals A Global Optimization Algorithm for Sum of Linear Ratios Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yuelin Gao ◽  
Siqiao Jin
Keyword(s):  
Global Optimization ◽  
Lower Bound ◽  
Programming Problem ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Bilinear Programming ◽  
Global Optimization Algorithm ◽  
Product Function ◽  
Optimal Value

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

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