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Research on The Layout Optimization Problem of Computational Power Network (CPN) Based on Greedy Algorithm and QUBO Model

Zhenhua Wen, Nuohan Zhang, Jinglai Wu, Aizimaitijiang Aihemaiti, Chuhan Feng, Zhuowei Li

Published Apr 12, 2024• 0 citations
Publisher

Abstract

To address the problem, we need to deploy two edge servers in a specific area to maximize the computational demand of the coverage. The problem can be transformed into a maximum coverage problem where the goal is to select a set of locations to deploy edge servers such that the total computational demand being covered is maximized. To solve this problem, we use a greedy algorithm. For quantum computing, the problem can be modeled as a quadratic unconstrained binary optimization (QUBO) problem. The solution process involves calculating the coverage area and computational requirements of possible server locations, constructing a QUBO model, solving the model using a solver and simulator, and parsing the results to obtain the optimal server deployment locations. The final result is the coordinate locations of the edge servers with optimized coverage of computational demands and the corresponding amount of coverage computational demands.

DOI
10.1109/ictech63197.2024.00059

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To address the problem, we need to deploy two edge servers in a specific area to maximize the computational demand of the coverage. The problem can be transformed into a maximum coverage problem where the goal is to select a set of locations to deploy edge servers such that the total computational demand being covered is maximized. To solve this problem, we use a greedy algorithm. For quantum computing, the problem can be modeled as a quadratic unconstrained binary optimization (QUBO) problem. The solution process involves calculating the coverage area and computational requirements of possible server locations, constructing a QUBO model, solving the model using a solver and simulator, and parsing the results to obtain the optimal server deployment locations. The final result is the coordinate locations of the edge servers with optimized coverage of computational demands and the corresponding amount of coverage computational demands.
The core of this article is to construct an effective QUBO model to solve the problem of cloud edge end computing resource allocation, including two key scenarios: optimization of server maximum computing demand coverage and optimization of cloud edge server computing network layout. Each scenario provides a detailed description of the model's process from analysis, establishment to solution, overcoming several major difficulties in establishing a QUBO model, including using binary variables to express the objective function, transforming the objective function into QUBO expressions, and transforming inequality constraints. A scheme for the number of constraint relaxation factors is introduced, which effectively reduces the number of quantum bits and computational complexity. Finally, statistical analysis of the solution results, non parametric testing based on data characteristics, and detailed analysis are conducted, demonstrating the potential application of the QUBO model and quantum computing in dealing with complex combinatorial optimization problems. During the solving process, China's first optical quantum computing power cloud platform and corresponding quantum computing library Kaiwu SDK were utilized for research. Multiple solvers were used and their performance was compared to select the best performing taboo search solver, and then detailed results were calculated. The final results were fully visualized to make them more intuitive. The results indicate that quantum computing can provide an efficient, accurate, and stable solution for cloud edge end computing resource allocation. Through these studies, this article not only confirms the efficiency of quantum computing in solving specific optimization problems, but also provides some experience and reference for exploring the application of quantum computing in a wider field.
Edge computing is a promising technology that offers a superior user experience and enables various innovative Internet of Things applications. In this paper, we present a mixed-integer linear programming (MILP) model for optimal edge server placement and workload allocation, which is known to be NP-hard. To this end, we explore the possibility of addressing this computationally challenging problem using quantum computing. However, existing quantum solvers are limited to solving unconstrained binary programming problems. To overcome this obstacle, we propose a hybrid quantum-classical solution that decomposes the original problem into a quadratic unconstrained binary optimization (QUBO) problem and a linear program (LP) subproblem. The QUBO problem can be solved by a quantum solver, while the LP subproblem can be solved using traditional LP solvers. Our numerical experiments demonstrate the practicality of leveraging quantum supremacy to solve complex optimization problems in edge computing.
Edge computing is a promising technology that offers a superior user experience and enables various innovative Internet of Things applications. In this paper, we present a mixed-integer linear programming (MILP) model for optimal edge server placement and workload allocation, which is known to be NP-hard. To this end, we explore the possibility of addressing this computationally challenging problem using quantum computing. However, existing quantum solvers are limited to solving unconstrained binary programming problems. To overcome this obstacle, we propose a hybrid quantum-classical solution that decomposes the original problem into a quadratic unconstrained binary optimization (QUBO) problem and a linear program (LP) subproblem. The QUBO problem can be solved by a quantum solver, while the LP subproblem can be solved using traditional LP solvers. Our numerical experiments demonstrate the practicality of leveraging quantum supremacy to solve complex optimization problems in edge computing.
The digital transformation that Telecommunications and ICT domains are crossing today, is posing several new challenges to Telecom Operators. These challenges require solving complex problems such as: dimensioning and scheduling of virtual/real resources in data centers; automating real-time management/control and orchestration of networks processes; optimizing energy consumption; and overall, ensuring networks and services stability. These problems are usually tackled with methods and algorithms that find suboptimal solutions, for computational efficiency reasons. In this work, we consider a Virtual Data Center scenario where virtual machine consolidation must be performed with joint minimization of network/servers power consumption. For this scenario, we provide an ILP model, the equivalent binary model and the steps towards the equivalent Quadratic Unconstrained Binary Optimization (QUBO) model that is suitable for being solved by means of quantum optimization algorithms. Finally, we compare the computational complexity of classical and quantum solvers from a theoretical perspective.
We provide efficient quadratic unconstrained binary optimization (QUBO) formulations for the Dominating Set and Edge Cover combinatorial problems suitable for adiabatic quantum computers, which are viewed as a real-world enhanced model of simulated annealing (e.g. a type of genetic algorithm with quantum tunneling). The number of qubits (dimension of QUBO matrices) required to solve these set cover problems are O(n + n lg n) and O(m + n lg n) respectively, where n is the number of vertices and m is the number of edges. We also extend our formulations for the Minimum Vertex-Weighted Dominating Set problem and the Minimum Edge-Weighted Edge Cover problem. Experimental results for the Dominating Set and Edge Cover problems using a D-Wave Systems quantum computer with 1098 active qubit-coupled processors are also provided for a selection of known common graphs.
The Maximal Covering Location Problem (MCLP) is an NP-hard Combinatorial Optimization Problem (COP) that aims to determine the optimal facility placements that maximize total coverage. It is characterized by both equality and inequality constraints, which ensure correct coverage but significantly increase the complexity of exploring the solution space as instance size grows. Hybrid quantum-classical approaches might offer a promising alternative to classical optimization methods by enabling the exploration of complex energy landscapes through quantum superposition and probabilistic sampling. In this work, the MCLP is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model, where constraint embedding plays a critical role in solution quality. In particular, Unbalanced Penalization (UP) is employed as an alternative to the Slack Variables (SV) for handling inequality constraints without increasing the number of variables. This study focuses on QAOA and one of its variants, the WS-QAOA, which leverages a biased initial state derived from a continuous relaxation of the problem. Additionally, a linear ramp (LR) parameter schedule is incorporated to reduce optimization complexity. The performance of these techniques is evaluated both individually and in combination, as a function of circuit depth ppp and problem size. Results show that the combined approach of UP, LR, and WS-QAOA consistently improves solution quality and feasibility metrics, while maintaining robust performance as the problem size increases, highlighting its potential within hybrid quantum-classical optimization frameworks.