The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this wor...The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.展开更多
For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfacto...For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfactory degree in application.To acquire a more satisfying solution than the optimistic one to realize the two levels' most profits,this paper considers both levels' satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation.Then,using the duality gap of the lower level as the penalty function,the authors transfer these two levels problem to a single one and propose a corresponding algorithm.Finally,the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.展开更多
The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and ap...The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications in optimal combination and linear programming fields. It can be difficultly solved by the electronic computer in exponential level time. Meanwhile in previous studies deoxyribonucleic acid （DNA） molecular operations usually were used to solve NP-complete continuous path search problems, e.g. HPP, traveling salesman problem, rarely for NP-hard problems with discrete vertices or edges solutions, such as the minimum vertex cover problem, graph coloring problem and so on. In this paper, we present a DNA algorithm for solving the MMP with DNA molecular operations. For an undirected graph with n vertices and m edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions of the MMP in proper length range using O（n^3） time. We extend the application of DNA molecular operations and simultaneously simplify the complexity of the computation.展开更多
基金Projects(61573144,61773165,61673175,61174040)supported by the National Natural Science Foundation of ChinaProject(222201717006)supported by the Fundamental Research Funds for the Central Universities,China
文摘The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.
基金supported by the National Science Foundation of China under Grant No.71171150the National Natural Science Foundation of ChinaTian Yuan Foundation under Grant No.11226226
文摘For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfactory degree in application.To acquire a more satisfying solution than the optimistic one to realize the two levels' most profits,this paper considers both levels' satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation.Then,using the duality gap of the lower level as the penalty function,the authors transfer these two levels problem to a single one and propose a corresponding algorithm.Finally,the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.
文摘The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications in optimal combination and linear programming fields. It can be difficultly solved by the electronic computer in exponential level time. Meanwhile in previous studies deoxyribonucleic acid （DNA） molecular operations usually were used to solve NP-complete continuous path search problems, e.g. HPP, traveling salesman problem, rarely for NP-hard problems with discrete vertices or edges solutions, such as the minimum vertex cover problem, graph coloring problem and so on. In this paper, we present a DNA algorithm for solving the MMP with DNA molecular operations. For an undirected graph with n vertices and m edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions of the MMP in proper length range using O（n^3） time. We extend the application of DNA molecular operations and simultaneously simplify the complexity of the computation.
