A Hierarchical Decomposition Framework for Modeling Combinatorial Optimization Problems

Chaieb, Marouene; Jemai, Jaber; Mellouli, Khaled

doi:10.1016/j.procs.2015.08.169

Cited by 8 publications

(5 citation statements)

References 6 publications

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“…As with any other hierarchical solution, we must check that the assembled solution satisfies all the constraints of the original problem [28]. We observe that three of our four constraints cannot be violated due to the design of PC-ILP-each DP is associated with the CS placed closest to it.…”

Section: Repairing An Infeasible Solutionmentioning

confidence: 99%

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PC-ILP: A Fast and Intuitive Method to Place Electric Vehicle Charging Stations in Smart Cities

Bose,

Dutta,

Shrivastava

et al. 2023

Smart Cities

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The widespread use of electric vehicles necessitates meticulous planning for the placement of charging stations (CSs) in already crowded cities so that they can efficiently meet the charging demand while adhering to various real-world constraints such as the total budget, queuing time, electrical regulations, etc. Many classical and metaheuristic-based approaches provide good solutions, but they are not intuitive, and they do not scale well for large cities and complex constraints. Many classical solution techniques often require prohibitive amounts of memory and their solutions are not easily explainable. We analyzed the layouts of the 50 most populous cities of the world and observed that any city can be represented as a composition of five basic primitive shapes (stretched to different extents). Based on this insight, we use results from classical topology to design a new charging station placement algorithm. The first step is a topological clustering algorithm to partition a large city into small clusters and then use precomputed solutions for each basic shape to arrive at a solution for each cluster. These cluster-level solutions are very intuitive and explainable. Then, the next step is to combine the small solutions to arrive at a full solution to the problem. Here, we use a surrogate function and repair-based technique to fix any resultant constraint violations (after all the solutions are combined). The third step is optional, where we show that the second step can be extended to incorporate complex constraints and secondary objective functions. Along with creating a full software suite, we perform an extensive evaluation of the top 50 cities and demonstrate that our method is not only 30 times faster but its solution quality is also 36.62% better than the gold standard in this area—an integer linear programming (ILP) approach with a practical timeout limit.

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Section: Repairing An Infeasible Solutionmentioning

confidence: 99%

“…We rely on a class of approaches that use a hierarchical decomposition framework [26][27][28]. The idea is to break a large problem into much smaller subproblems, solve them, and combine them to form the final solution.…”

Section: Salient Features Of Pc-ilpmentioning

confidence: 99%

PC-ILP: A Fast and Intuitive Method to Place Electric Vehicle Charging Stations in Smart Cities

Bose,

Dutta,

Shrivastava

et al. 2023

Smart Cities

View full text Add to dashboard Cite

show abstract

“…However, for small-and/or medium-sized problems, it is possible to be solved. Hierarchical decomposition is one of the effective methods to solve MUTAPP [8], which decomposes the MUTAPP problem into task assignment and path planning.…”

Section: Related Workmentioning

confidence: 99%

Cooperative Search Method for Multiple UAVs Based on Deep Reinforcement Learning

Gao

Zhang

2022

Sensors

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In this paper, a cooperative search method for multiple UAVs is proposed to solve the problem of low efficiency of multi-UAV task execution by using a cooperative game with incomplete information. To improve search efficiency, CBBA (Consensus-Based Bundle Algorithm) is applied to designate the tasks area for each UAV. Then, Independent Deep Reinforcement Learning (IDRL) is used to solve Nash equilibrium to improve UAVs’ collaborations. The proposed reward function is smartly developed to guide UAVs to fly along the path with higher reward value while avoiding the collisions between UAVs during flights. Finally, extensive experiments are carried out to compare our proposed method with other algorithms. Simulation results show that the proposed method can obtain more rewards in the same period of time as other algorithms.

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“…Moreover, we propose the hierarchical idea to decompose the structures of neural networks. Hierarchical idea occasionally appears in the algorithm designing in combinatorial optimization [10,11,12,13]. Hierarchical optimization usually decomposes optimization problem into two or more sub-problems, which has its own subjective and constrains [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…Hierarchical idea occasionally appears in the algorithm designing in combinatorial optimization [10,11,12,13]. Hierarchical optimization usually decomposes optimization problem into two or more sub-problems, which has its own subjective and constrains [10,11]. Our paper decomposes the fully connected neural network structure into several simple, independent and parallel substructures and finds basis path set for each independent substructure.…”

Section: Introductionmentioning

confidence: 99%

Interpreting the Basis Path Set in Neural Networks

et al. 2021

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Based on basis path set, G-SGD algorithm significantly outperforms conventional SGD algorithm in optimizing ReLU neural networks. However, how the inner mechanism of basis paths work remains mysterious. From the aspect of graph theory, this paper defines basis path, investigates structure properties of basis paths in regular fully connected neural network and interprets the graph representation of basis path set. Moreover, we propose hierarchical algorithm HBPS to find basis path set 𝐵 in fully connected neural network by decomposing the network into several independent and parallel substructures. Algorithm HBPS demands that there doesn't exist shared edges between any two independent substructure paths.

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A Hierarchical Decomposition Framework for Modeling Combinatorial Optimization Problems

Cited by 8 publications

References 6 publications

PC-ILP: A Fast and Intuitive Method to Place Electric Vehicle Charging Stations in Smart Cities

PC-ILP: A Fast and Intuitive Method to Place Electric Vehicle Charging Stations in Smart Cities

Cooperative Search Method for Multiple UAVs Based on Deep Reinforcement Learning

Interpreting the Basis Path Set in Neural Networks

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