The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to pro...The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.展开更多
It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optima...It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optimal combination under various constraints not only involves numerical calculations but also is an NP-hard combinatorial problem.To solve the problem,an adaptive genetic algorithm based on cluster search,which is divided into two phases,is put forward.In the first phase,according to the density,all individuals can be homogeneously scattered over the whole solution space through crossover and mutation and better individuals are collected as candidate cluster centres.In the second phase,the search is confined to the neighbourhood of some selected possible solutions to accurately solve with cluster radius decreasing slowly,meanwhile all clusters continuously move to better regions until all the peaks in the question space is searched.This algorithm can efficiently solve the combination problem.Taking the optimization on decision-making of aircraft maintenance by the algorithm for an example,maintenance which combines multiple parts or tasks can significantly enhance economic benefit when the halt cost is rather high.展开更多
文摘The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.
基金supported by the National Natural Science Foundation of China(6107901361079014+4 种基金61403198)the National Natural Science Funds and Civil Aviaiton Mutual Funds(U1533128U1233114)the Programs of Natural Science Foundation of China and China Civil Aviation Joint Fund(60939003)the Natural Science Foundation of Jiangsu Province in China(BK2011737)
文摘It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optimal combination under various constraints not only involves numerical calculations but also is an NP-hard combinatorial problem.To solve the problem,an adaptive genetic algorithm based on cluster search,which is divided into two phases,is put forward.In the first phase,according to the density,all individuals can be homogeneously scattered over the whole solution space through crossover and mutation and better individuals are collected as candidate cluster centres.In the second phase,the search is confined to the neighbourhood of some selected possible solutions to accurately solve with cluster radius decreasing slowly,meanwhile all clusters continuously move to better regions until all the peaks in the question space is searched.This algorithm can efficiently solve the combination problem.Taking the optimization on decision-making of aircraft maintenance by the algorithm for an example,maintenance which combines multiple parts or tasks can significantly enhance economic benefit when the halt cost is rather high.
