scholarly journals A Decomposition Approach for Stochastic Shortest-Path Network Interdiction with Goal Threshold

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 237 ◽  
Author(s):  
Xiangyu Wei ◽  
Kai Xu ◽  
Peng Jiao ◽  
Quanjun Yin ◽  
Yabing Zha
Keyword(s):  
Shortest Path ◽  
Real World ◽  
Benders Decomposition ◽  
Research Problem ◽  
Resource Consumption ◽  
Network Interdiction ◽  
Master Problem ◽  
Decomposition Approach ◽  
Stochastic Shortest Path ◽  
T Path

Shortest-path network interdiction, where a defender strategically allocates interdiction resource on the arcs or nodes in a network and an attacker traverses the capacitated network along a shortest s-t path from a source to a terminus, is an important research problem with potential real-world impact. In this paper, based on game-theoretic methodologies, we consider a novel stochastic extension of the shortest-path network interdiction problem with goal threshold, abbreviated as SSPIT. The attacker attempts to minimize the length of the shortest path, while the defender attempts to force it to exceed a specific threshold with the least resource consumption. In our model, threshold constraint is introduced as a trade-off between utility maximization and resource consumption, and stochastic cases with some known probability p of successful interdiction are considered. Existing algorithms do not perform well when dealing with threshold and stochastic constraints. To address the NP-hard problem, SSPIT-D, a decomposition approach based on Benders decomposition, was adopted. To optimize the master problem and subproblem iteration, an efficient dual subgraph interdiction algorithm SSPIT-S and a local research based better-response algorithm SSPIT-DL were designed, adding to the SSPIT-D. Numerical experiments on networks of different sizes and attributes were used to illustrate and validate the decomposition approach. The results showed that the dual subgraph and better-response procedure can significantly improve the efficiency and scalability of the decomposition algorithm. In addition, the improved enhancement algorithms are less sensitive and robust to parameters. Furthermore, the application in a real-world road network demonstrates the scalability of our decomposition approach.

A Benders Decomposition Approach for the Multivehicle Production Routing Problem with Order-up-to-Level Policy

2020 ◽  
Author(s):  
Zhenzhen Zhang ◽  
Zhixing Luo ◽  
Roberto Baldacci ◽  
Andrew Lim
Keyword(s):  
Benders Decomposition ◽  
Valid Inequalities ◽  
Planning Horizon ◽  
Set Partitioning ◽  
Master Problem ◽  
Inventory Level ◽  
Inventory Routing ◽  
Routing Problem ◽  
Decomposition Approach ◽  
Production Routing

The production routing problem (PRP) arises in the applications of integrated supply chain which jointly optimize the production, inventory, distribution, and routing decisions. The literature on this problem is quite rare due to its complexity. In this paper, we consider the multivehicle PRP (MVPRP) with order-up-to-level inventory replenishment policy, where every time a customer is visited, the quantity delivered is such that the maximum inventory level is reached. We propose an exact Benders’ decomposition approach to solve the MVPRP, which decomposes the problem as a master problem and a slave problem. The master problem decides whether to produce the product, the quantity to be produced, and the customers to be replenished for every period of the planning horizon. The resulting slave problem decomposes into a capacitated vehicle routing problem for each period of the planning horizon where each problem is solved using an exact algorithm based on the set partitioning model, and the identified feasibility and optimality cuts are added to the master problem to guide the solution process. Valid inequalities and initial optimality cuts are used to strengthen the linear programming relaxation of the master formulation. The exact method is tested on MVPRP instances and on instances of the multivehicle vendor-managed inventory routing problem, a special case of the MVPRP, and the good performance of the proposed approach is demonstrated.

scholarly journals Bi-Layer Shortest-Path Network Interdiction Game for Internet of Things

Sensors ◽  
2020 ◽  
Vol 20 (20) ◽  
pp. 5943
Author(s):  
Jingwen Yan ◽  
Kaiming Xiao ◽  
Cheng Zhu ◽  
Jun Wu ◽  
Guoli Yang ◽  
...  
Keyword(s):  
Internet Of Things ◽  
Shortest Path ◽  
Benders Decomposition ◽  
Random Search ◽  
Single Layer ◽  
Economic Loss ◽  
Physical Layer ◽  
Network Interdiction ◽  
Objective Functions ◽  
Target Node

Network security is a crucial challenge facing Internet-of-Things (IoT) systems worldwide, which leads to serious safety alarms and great economic loss. This paper studies the problem of malicious interdicting network exploitation of IoT systems that are modeled as a bi-layer logical–physical network. In this problem, a virtual attack takes place at the logical layer (the layer of Things), while the physical layer (the layer of Internet) provides concrete support for the attack. In the interdiction problem, the attacker attempts to access a target node on the logical layer with minimal communication cost, but the defender can strategically interdict some key edges on the physical layer given a certain budget of interdiction resources. This setting generalizes the classic single-layer shortest-path network interdiction problem, but brings in nonlinear objective functions, which are notoriously challenging to optimize. We reformulate the model and apply Benders decomposition process to solve this problem. A layer-mapping module is introduced to improve the decomposition algorithm and a random-search process is proposed to accelerate the convergence. Extensive numerical experiments demonstrate the computational efficiency of our methods.

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

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.

Sign in / Sign up

Export Citation Format

Share Document