概率论与数理统计是高等院校理工科专业必修的一门公共基础课程.为进一步落实新工科背景下对概率论与数理统计课程教学的基本要求和高校立德树人根本任务,针对概率论与数理统计课程教学中存在的问题,文章分析了传统"BOPPPS"模式的不足,在坚持以学生发展为中心的教学理念下,构建了新的BOPPPS"6+1"模式,并与SPOC有机结合,提出了基于"SPOC+BOPPPS"的线上线下混合的教学模式,在此基础上对教学内容、教学方法和评价体系进行了改革和实践.教学实践证明,该教学模式在提高课堂教学效率的同时也提升了学生的学习兴趣.

Abstract For the traditional whale optimization algorithm to solve the 0-1 knapsack combinatorial optimization problem, there are shortcomings of insufficient solution energy and easy to fall into local optima. A whale optimization algorithm based on domain search is proposed. This method focuses on the development of global search capabilities in the early stage of the evolution of the whale optimization algorithm, introduces the Lévy flight strategy, and uses a two-stage domain search method to enhance the diversity of the population and avoid the algorithm from falling into local optima; In the later stage, it focuses on the development of local search capabilities, and uses a greedy search method to perform fine search on some high-quality solutions to improve the accuracy of the solutions. Finally, the algorithm is used to conduct two sets of tests on the classic data set: the first group is a small and medium-scale data set, and the second group is a large-scale one. The test results show that the first group can find the optimal solution 100%, the second group has a strong advantage. The results show that the proposed algorithm has good robustness and optimization ability. It’s an effective method to solve the 0-1 knapsack problem.

Threshold segmentation is a commonly used method to deal with image segmentation problems. Aiming at the problems of the traditional maximum inter-class variance method (Otsu) in multi-threshold image segmentation, such as large amount of computation, long computation time and low segmentation accuracy. This paper proposes a two-dimensional Otsu multi-threshold image segmentation algorithm based on hybrid whale optimization algorithm. Firstly, the two-dimensional Otsu single-threshold segmentation method is extended to the two-dimensional Otsu multi-threshold segmentation method to improve the segmentation effect. At the same time, in order to reduce the calculation time and improve the solution accuracy, the new hybrid whale optimization algorithm proposed in this paper is used to calculate the threshold. The test is carried out through a set of classical image threshold segmentation sets, and the widely used image segmentation evaluation standards PSNR and SSIM are used for judgment. The results of this paper are also compared with the results of other novel algorithms, including the results of one-dimensional Otsu multi-threshold segmentation method. The results show that the proposed two-dimensional Otsu single-threshold segmentation improves the segmentation efficiency and quality, it is an effective image segmentation method.

概率论与数理统计是理工科院校重要的专业基础课程,该研究针对传统教学存在的弊端,结合现代教育技术,提出线上线下混合教学模式的改革.教师在教学实践中借助雨课堂智慧教学工具,结合课程网络平台,课前、课后发布课程学习资料给学生开展线上学习,课中面对面讲授、测试辅助学生开展线下学习,通过对课前、课中、课后教学内容的合理设计与具体实施实现线上线下的有效衔接.实践证明,新的教学模式能很好地弥补传统教学的不足,调动了学生学习的积极性,拓宽了学生的知识面,提高了学生分析问题和解决问题的能力.

对于海底数据中心,如何在有限的体积内存放更多的服务器且保证服务器工作过程中向海水中正常快速的散热是一项非常有挑战性的问题.提出了基于对流传热模型的海底数据中心散热优化设计,从数据中心集装箱的外壳材质、外壳结构、放入海底深度及潮汐和季节变化等方面建立数学模型,讨论了集装箱的优化设计,为海底数据中心的外壳散热设计提供了参考.

Aiming at the problem of dynamic flexible job shop scheduling, a multi-step genetic algorithm is proposed. Firstly, special encoding and decoding methods are used according to the characteristics of the problem; then, introducing differential evolution mutation in the mutation process to improve the diversity of the population; at the same time, during the crossover process, in order to ensure the validity of the solution, the group was divided into two groups for pair wise crossover pairing using the random crossover method. Finally, aiming at the actual operation problems of enterprises, the dynamic scheduling in the event of a machine failure and the dynamic scheduling in the case of urgent orders are discussed separately. The test results show that the method proposed in this paper can get a good scheduling scheme and is an effective method for solving dynamic flexible job shop scheduling problems.

In view of the shortcomings of the whale optimization algorithm (WOA), such as slow convergence speed, low accuracy, and easy to fall into local optimum, an improved whale optimization algorithm (IWOA) is proposed. First, the standard WOA is improved from the three aspects of initial population, convergence factor, and mutation operation. At the same time, Gaussian mutation is introduced. Then the nonfixed penalty function method is used to transform the constrained problem into an unconstrained problem. Finally, 13 benchmark problems were used to test the feasibility and effectiveness of the proposed method. Numerical results show that the proposed IWOA has obvious advantages such as stronger global search ability, better stability, faster convergence speed, and higher convergence accuracy; it can be used to effectively solve complex constrained optimization problems.

The problem of finding roots of equations has always been an important research problem in the fields of scientific and engineering calculations. For the standard differential evolution algorithm cannot balance the convergence speed and the accuracy of the solution, an improved differential evolution algorithm is proposed. First, the one-half rule is introduced in the mutation process, that is, half of the individuals perform differential evolutionary mutation, and the other half perform evolutionary strategy reorganization, which increases the diversity of the population and avoids premature convergence of the algorithm; Second, set up an adaptive mutation operator and a crossover operator to prevent the algorithm from falling into the local optimum and improve the accuracy of the solution. Finally, classical high-order algebraic equations and nonlinear equations are selected for testing, and compared with other algorithms. The results show that the improved algorithm has higher solution accuracy and robustness, and has a faster convergence speed. It has outstanding effects in finding roots of equations, and provides an effective method for engineering and scientific calculations.

为解决概率统计课程在传统教学中存在的问题,该文借助智慧教学工具雨课堂,探讨基于雨课堂的概率统计课程的混合式教学改革,并在教学班级中进行了实践.实践证明,该文提出的教学改革方法能活跃课堂氛围,提高教学质量和学生学习积极性,为雨课堂在高校教学中的应用提供参考.

针对柔性作业车间调度问题(Flexible Job Shop Scheduling Problem,FJSP)的求解特点,提出了一种混合差分进化算法,该方法以最小化最大完工时间为目标,采用双向变异策略,以一定的概率采用差分变异和遗传变异,同时在变异过程中采用特殊的解码方式;在交叉的过程中采用改进的随机变位交叉的方式,提高了算法的性能.最后用该算法对经典算例进行了测试并与已有算法进行了比较,结果表明,提出的方法具有很好的稳定性和鲁棒性,是求解FJSP的一种有效方法.

针对0-1规划问题,提出了一种新的智能优化方法—差分进化算法.首先利用佳点集法产生初始种群,大大提高了种群的多样性.再用牵引法处理约束条件.将进化中的不可行解逐步引入到可行解集,克服了罚函数法选择罚因子的困难,最后对10个0-1规划问题的算例进行测试,并将测试结果与其它算法进行了比较.结果表明:文章提出的算法具有较快的寻优能力和较好的全局搜索能力,是求解0-1规划问题的一种有效方法.

Obtaining more non-dominated solution is very important for the multi-objective problem. This paper developed a new hybrid differential evolution algorithm for solving the multi-objective 0-1 programming problem, which is based on using the good point set method to generate the initial population, the traction method to deal with the constraint conditions, the analytic hierarchy process to design the weights between the objective functions. The proposed algorithm is not only improves the diversity of the population, but also overcomes the difficulty of choosing the penalty factor by the penalty function method. A number of typical multi-objective 0-1 programming problems are tested, and the test results are compared with other algorithms. The results show that the proposed algorithm can find more non-dominated solution for multi-objective 0-1 programming problems. It is an effective method to solve the multi-objective 0-1 programming problem.

In the function optimization,in order to overcome the shortcomings of Differential Evolution Algorithm including precocious,slow convergence speed,easily falling into local optimum value,a Differential Evolution Algorithm Based on Powell Search Method is proposed.The Powell search method and the differential evolution algorithm are used alternately.The group optimized by the differential evolution algorithm has a certain probability to participate in the Powell search.By using the advantage of Powell search method including high precision,fast convergence speed and strong local search ability,the disadvantages of differential evolution algorithm is avoided effectively.Through the test of 10 classical functions,the simulation results show that the proposed algorithm outperforms the standard differential evolution algorithm in terms of convergence speed and convergence precision.

Aiming at the NP hard problem of portfolio optimization, an improved differential evolution algorithm is proposed. In this algorithm, the mutation operator and crossover operator are set up adaptively, and then according to the characteristics of the mutation itself, two kinds of mutation operators with global search ability and local search ability are improved .The improved algorithm can improve the convergence speed and ensure the precision of the algorithm. Through five stocks of the same type and 20 different types of stocks for empirical analysis, the results show that the proposed algorithm has a certain guiding role in solving the problem of portfolio optimization.

A discrete differential evolution algorithm is proposed for solving traveling salesman problem(TSP)in this article. In the algorithm,on the one hand,the differential evolution algorithm with a new coding method is used to solve a discrete TSP, which is often used to solve problems on a continuous domain. On the other hand,the 2-OPT algorithm is also introduced;the new algorithm combined the global search with the local search effectively. The classical TSP has been tested,the simulation results show that the proposed algorithm has strong stability and it is an effective method for solving TSP.

在高校应用型转型发展期,积极推行课程教学模式改革,将翻转课堂教学模式引入《概率论与数理统计》教学中,实践证明,翻转课堂教学模式对培养学生自主学习能力和主观能动性有着积极的意义,是值得推行的一种新型教学模式.

Integration of Science Education and Humanities Education is a trend of educational development is the need of social development. This paper analyzes the historical roots of Chinese education and proposes ways inevitable in today’s technological advances, scientific and humanistic education integration.

Absolute value equations $$ Ax - |x| = b $$ are non-differentiable hard problems. Many linear and quadratic programming problems can ultimately be converted into absolute value equation problems so research on solving an absolute value problem has important practical and theoretical significance. An improved adaptive differential evolution algorithm was proposed to solve the absolute value equations in this paper. The algorithm combined global search ability and local search ability, using an adaptive quadratic mutation operation and crossover operation. Numerical results show that the improved algorithm can quickly find the solutions of these equations.

Combining with the characteristics of linear algebra course, this paper proposed the introduction of the mathematical software MATLAB into classroom teaching, and used examples to prove that, the application of the software in classroom teaching can visualize abstract contents, enhance the contact between lin-ear algebra and practical problems, foster students' mathematical thinking ability and numerical calculation ability, and improve teaching effectiveness.

基于差分进化算法的基本原理,采用马尔可夫链分析了该算法的收敛性,论证了该算法能以概率1收敛到全局最优解.利用该算法对3个经典函数进行了数值仿真,结果表明,该算法能够快而有效地收敛到问题的最优解,说明了文章所得结论的正确性.