关键词： Ant colony optimisation   swarm intelligence   convergence analysis   stability analysis   EigenAnt Algorithm  

摘要： As a variant of Ant Colony Optimization, the EigenAnt algorithm finds the shortest path between a source node and a destination node based on negative feedback in the form of selective pheromone removal that occurs only on the path which is actually chosen for each trip. EigenAnt algorithm also could change quickly to reflect to the dynamic variety of initial pheromone concentrations and path length etc. However, in general, the solution of EigenAnt algorithm is not always convergent. In this paper, we propose an improved EigenAnt (iEigenAnt) algorithm in terms of both negative and positive feedback;that is, selective pheromone updates are decided by smart ants or stupid ones, which depends whether the amount of the pheromone at the selected path increases or not. The system modelled by our algorithm has a unique equilibrium as the shortest path. Besides, using mathematical analysis, we demonstrate that the equilibrium is global asymptotically stable, i.e., stable and convergent. Finally, we also implement the iEigenAnt algorithm under four different cases and apply it on travelling salesman problem problem, the simulation result shows that our iEigenAnt algorithm is faster convergent and more effective compared to the original EigenAnt algorithm, and some combinatorial optimisation problems can be effectively solved based on our iEigenAnt algorithm.

关键词： 数学模型   污染物含量   动态预测   点源污染物  

摘要： 河流污染物含量动态预测对污染物的治理具有重要作用,为了提高污染物预测准确度,设计基于BioWin数学模型的河流污染物含量动态预测算法。根据实际径流情况归类当前污染河流相关参数,根据径流特征估算当前河流污染物实际通量,圈定污染物范围,划分河流污染物来源,并分别提出污染物含量的计算方法,实现污染物含量的动态预测。试验数据表明,该预测算法有效提高了预测准确率,具有实际应用优势。

关键词： 数学形态滤波   自适应多尺度滤波算法   小波阈值滤波   大地电磁信号   噪声压制  

摘要： 针对实测大地电磁信号资料中常出现的强噪声干扰问题,提出一种基于数学形态滤波和小波阈值滤波结合的大地电磁噪声压制方法。首先,利用自适应多尺度形态滤波算法对含噪信号进行初次滤波,以消除脉冲类干扰。然后,对已处理的信号进行小波阈值滤波提取大尺度强噪声轮廓。最后,剔除强噪声干扰重构大地电磁信号。通过仿真实验对比,在不同强度噪声干扰背景下,所提方法的性能优于普通小波阈值方法,能更多地保留大地电磁原始信号的细节特征。实测资料处理结果表明,该方法能有效地抑制大尺度强噪声干扰和基线偏移的影响,改善视电阻率曲线质量,具有较好的应用前景。

关键词： 数学教学   算法教学   计算机算法   教学模式  

摘要： 该文结合教学案例详细阐述了"数学计算机算法教学法"在教学过程中如何展开,将教学内容如何精心设计成计算机流程图,用以表达、描述和讲解数学思想的实际应用、分析解决问题的策略与思路、计算方法与技巧的工程算法。这种教学模式逻辑性较强,结构性较强,将数学与计算机相融合,为当今信息时代下的数学教学方法改革提供了一种可供选择的、实用性强的教学模式。

关键词： 数学算法   计算机   人工智能  

摘要： 数学算法具有科学性、逻辑性与严谨性,能够帮助人工智能技术在发展的过程中,实现技术的不断发展和超越。可以说,数学算法是计算机人工智能发展中不可获取的元素,很多技术环节和系统功能的实现都有赖于数学算法。在分析了数学算法在计算机人工智能中的应用要点后,探讨了数学算法对于计算机人工智能的推动作用。

关键词： Bayesian network (BN)   Parameters learning   Scarce data   CPEL algorithm   Autonomous mission decision-making  

摘要： In this paper, a constrained parameter evolutionary learning (CPEL) algorithm for Bayesian network (BN) parameters learning under scarce data is proposed, which can be applied to UAV autonomous mission decision-making. In detail, firstly qualitative domain knowledge is employed into BN parameters learning process to reduce the parameter search space where two types of qualitative domain knowledge with experts' confidence are presented;and then evolutionary strategy is introduced into the process to avoid the problem that classical learning technique falls into local optimum easily in which the special encoding for the BN parameters is presented and some evolutionary strategies are discussed. Moreover, the global convergence of the proposed algorithm is proven. According to numerical experiments, it's demonstrated that the CPEL algorithm has better accuracy and timeliness performance than the classical EM algorithm under the same condition. Additionally, a case study of the proposed algorithm in UAV autonomous mission decision-making has been conducted, showing that CPEL algorithm can satisfy the need of UAV autonomous mission decision-making in a complex dynamic environment.

关键词： Aircraft maintenance scheduling   Hangar parking layout planning   Mixed-integer linear programming   Event-based model   Rolling horizon approach  

摘要： An aircraft hangar maintenance scheduling problem is studied, motivated by the aircraft heavy maintenance conducted in a hangar operated by an independent maintenance service company. The aircraft hangar maintenance scheduling problem in such context consists of determining a maintenance schedule with minimum penalty costs in fulfilling maintenance requests, and a series of hangar parking plans aligned with the maintenance schedule through the planning period. A mixed-integer linear programming (MILP) mathematical model, integrating the interrelations between the maintenance schedule and aircraft parking layout plans, is presented at first. In the model, the variation of parking capacity of the maintenance hangar and the blocking of the aircraft rolling in and out path are considered. Secondly, the model is enhanced by narrowing down the domain of the time-related decision variables to the possible rolling in and out operations time of each maintenance request. Thirdly, to obtain good quality feasible solutions for large scale instances, a rolling horizon approach incorporating the enhanced mathematical model is presented. The results of computational experiments are reported, showing: (i) the effectiveness of the event-based discrete time MILP model and (ii) the scalability of the rolling horizon approach that is able to provide good feasible solutions for large size instances covering a long planning period. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Mathematical programming  

摘要： This paper addresses one of the most challenging issues in designing an efficient and sustainable ridesharing service: ridesharing market design. We formulate it as a fair cost allocation problem through the lens of the cooperative game theory. A special property of the cooperative ridesharing game is that its characteristic function values are calculated by solving an optimization problem. Several concepts of fairness are investigated and special attention is paid to a solution concept named nucleolus, which aims to minimize the maximum dissatisfaction in the system. Due to its computational intractability, we break the problem into a master-subproblem structure and two subproblems are developed to generate constraints for the master problem. We propose a coalition generation procedure to find the nucleolus and approximate nucleolus of the game. Experimental results showed that when the game has a non-empty core, in the approximate nucleolus scheme the coalitions are computed only when it is necessary and the approximate procedure produces the actual nucleolus. And when the game has an empty core, the approximate nucleolus is close to the actual one. Regardless of the emptiness of the game, our algorithm needs to generate only a small fraction (1.6%) of the total coalition constraints to compute the approximate nucleolus. The proposed model and results nicely fit systems operated by autonomous vehicles. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Unrelated parallel machine scheduling   Scheduling with a common server   Simulated annealing   Tabu search   Sequence-dependent setup times   Dispatching rule  

摘要： Parallel machine scheduling problems with common servers have many industrial applications. In this paper, we study a generalized problem of scheduling with a common server, which is the unrelated parallel machine scheduling problem with sequence-dependent setup times and machine eligibility restrictions. The objective function involves the minimization of the total weighted tardiness. A mixed integer linear programming (MILP) model is proposed to solve this complex problem. Due to the NP hardness of the problem, tabu search (TS) and simulated annealing (SA) algorithms are proposed. The initial solutions of the algorithms are obtained by a modified apparent tardiness cost with setups (ATCS) dispatching rule. The proposed algorithms are compared using a randomly generated data set. (C) 2018 Elsevier Ltd. All rights reserved.