Queen problems are unstructured problems, whose solution scheme can be applied in the actual job scheduling. As for the n-queen problem, backtracking algorithm is considered as an effective approach when the value of ...Queen problems are unstructured problems, whose solution scheme can be applied in the actual job scheduling. As for the n-queen problem, backtracking algorithm is considered as an effective approach when the value of n is small. However, in case the value of n is large, the phenomenon of combination explosion is expected to occur. In order to solve the aforementioned problem, queen problems are firstly converted into the problem of function optimization with constraints, and then the corresponding mathematical model is established. Afterwards, the n-queen problem is solved by constructing the genetic operators and adaption functions using the integer coding based on the population search technology of the evolutionary computation. The experimental results demonstrate that the proposed algorithm is endowed with rapid calculation speed and high efficiency, and the model presents simple structure and is readily implemented.展开更多
With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four di...With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four discrete optimization models are proposed for different parties involved in the management system： government,highway agent,con- tractor and the common users.These four optimal decision models are formulated as linear integer programming problems with binary decision variables.The objective function and constraints are based on the pavement performance and prediction model using the pavement condition index （PCI）.Numerical experiments are carried out with the data from a highway system in Sichuan Province which show the feasibility and effectiveness of the proposed models.展开更多
The circle geometric constraint model （CGCM） was put forward for resolving the open-pit mine ore-matching problems （OMOMP）. By adopting the approaches of graph theory, block model of blasted piles was abstracted i...The circle geometric constraint model （CGCM） was put forward for resolving the open-pit mine ore-matching problems （OMOMP）. By adopting the approaches of graph theory, block model of blasted piles was abstracted into a set of nodes and directed edges, which were connected together with other nodes in the range of circle constraints, to describe the mining sequence. Also, the constructing method of CGCM was introduced in detail. The algorithm of CGCM has been realized in the DIM1NE system, and applied to a short-term （5 d） program calculation for ore-matching of a cement limestone mine in Hebei Province, China. The applications show that CGCM can well describe the mining sequence of ore blocks and its mining geometric constraints in the process of mining blasted piles. This model, which is applicable for resolving OMOMP under complicated geometric constraints with accurate results, provides effective ways to solve the problems of open-pit ore-matching.展开更多
This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player ...This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player the average ranking of his partners in all matches is as close as possible to the average ranking of his opponents in all matches. One of the variations of the basic model provides that each matchup is fair and competitive. We also give models for the case when the number of players is 4n<span style="font-family:;" "=""> </span><span style="font-family:;" "="">+</span><span style="font-family:;" "=""> </span><span style="font-family:;" "="">2, and thus one of the matches has to be singles. Our models were implemented and tested using optimization software AMPL. Computational results along with schedules for some typical situations are also given the paper.</span>展开更多
Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show th...Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.展开更多
集电系统拓扑优化是大型海上风电场规划建设的核心问题,本质上是一个涉及多约束、多目标的复杂混合整数优化问题。针对该问题,提出了一种基于大语言模型(large language model,LLM)辅助的大型海上风电场集电系统拓扑优化方法。首先,基...集电系统拓扑优化是大型海上风电场规划建设的核心问题,本质上是一个涉及多约束、多目标的复杂混合整数优化问题。针对该问题,提出了一种基于大语言模型(large language model,LLM)辅助的大型海上风电场集电系统拓扑优化方法。首先,基于大语言模型辅助对风电机组群进行聚类,通过链式提示法使LLM理解优化目标,并利用LLM将大型海上风电场分割为若干小型区域,以降低优化问题维度,提升求解速度和质量。然后,构建集电系统拓扑优化模型,基于混合整数线性规划求解器,获得海上风电场的最优集电系统拓扑设计方案。最后,利用1个含有75台风电机组的大型海上风电场系统进行方法性能验证,仿真结果表明:与传统优化技术相比,所提方法获得的聚类风机数量更加均衡,在考虑拓扑功率损耗的同时,生成的拓扑方案经济性最优。LLM在集电系统拓扑辅助优化中具有较高的有效性,为海上风电场集电系统拓扑设计优化提供了一种新思路。展开更多
文摘Queen problems are unstructured problems, whose solution scheme can be applied in the actual job scheduling. As for the n-queen problem, backtracking algorithm is considered as an effective approach when the value of n is small. However, in case the value of n is large, the phenomenon of combination explosion is expected to occur. In order to solve the aforementioned problem, queen problems are firstly converted into the problem of function optimization with constraints, and then the corresponding mathematical model is established. Afterwards, the n-queen problem is solved by constructing the genetic operators and adaption functions using the integer coding based on the population search technology of the evolutionary computation. The experimental results demonstrate that the proposed algorithm is endowed with rapid calculation speed and high efficiency, and the model presents simple structure and is readily implemented.
基金Project supported by the National Natural Science Foundation of China (Grant No.70671064)
文摘With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four discrete optimization models are proposed for different parties involved in the management system： government,highway agent,con- tractor and the common users.These four optimal decision models are formulated as linear integer programming problems with binary decision variables.The objective function and constraints are based on the pavement performance and prediction model using the pavement condition index （PCI）.Numerical experiments are carried out with the data from a highway system in Sichuan Province which show the feasibility and effectiveness of the proposed models.
基金Project(2011AA060407) supported by the National High Technology Research and Development Program of ChinaProject(51074073) supported by the National Natural Science Foundation of China
文摘The circle geometric constraint model （CGCM） was put forward for resolving the open-pit mine ore-matching problems （OMOMP）. By adopting the approaches of graph theory, block model of blasted piles was abstracted into a set of nodes and directed edges, which were connected together with other nodes in the range of circle constraints, to describe the mining sequence. Also, the constructing method of CGCM was introduced in detail. The algorithm of CGCM has been realized in the DIM1NE system, and applied to a short-term （5 d） program calculation for ore-matching of a cement limestone mine in Hebei Province, China. The applications show that CGCM can well describe the mining sequence of ore blocks and its mining geometric constraints in the process of mining blasted piles. This model, which is applicable for resolving OMOMP under complicated geometric constraints with accurate results, provides effective ways to solve the problems of open-pit ore-matching.
文摘This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player the average ranking of his partners in all matches is as close as possible to the average ranking of his opponents in all matches. One of the variations of the basic model provides that each matchup is fair and competitive. We also give models for the case when the number of players is 4n<span style="font-family:;" "=""> </span><span style="font-family:;" "="">+</span><span style="font-family:;" "=""> </span><span style="font-family:;" "="">2, and thus one of the matches has to be singles. Our models were implemented and tested using optimization software AMPL. Computational results along with schedules for some typical situations are also given the paper.</span>
文摘Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.
文摘集电系统拓扑优化是大型海上风电场规划建设的核心问题,本质上是一个涉及多约束、多目标的复杂混合整数优化问题。针对该问题,提出了一种基于大语言模型(large language model,LLM)辅助的大型海上风电场集电系统拓扑优化方法。首先,基于大语言模型辅助对风电机组群进行聚类,通过链式提示法使LLM理解优化目标,并利用LLM将大型海上风电场分割为若干小型区域,以降低优化问题维度,提升求解速度和质量。然后,构建集电系统拓扑优化模型,基于混合整数线性规划求解器,获得海上风电场的最优集电系统拓扑设计方案。最后,利用1个含有75台风电机组的大型海上风电场系统进行方法性能验证,仿真结果表明:与传统优化技术相比,所提方法获得的聚类风机数量更加均衡,在考虑拓扑功率损耗的同时,生成的拓扑方案经济性最优。LLM在集电系统拓扑辅助优化中具有较高的有效性,为海上风电场集电系统拓扑设计优化提供了一种新思路。
