老板数独的方程求解算法研究

从老板数独的定义建立了与原问题等价的方程组,由该方程组推导出一系列数学性质,包括候选数删除性质、唯一确定法性质、矛盾性质、不变性性质,说明了数独的人工推理规则包含在这些性质之中。利用这些性质提出了求解该方程组的算法。数值实例表明,提出的方法对于不同难度的数独难题都是有效的。     

基于区域序列枚举法的蜂巢数独求解算法研究

蜂巢数独是类似蜂巢难度又高的变形数独,它有着重要的研究意义。由蜂巢数独谜题提出与之等价的线性规划方程组;从方程组出发推导出求解数独算法的性质,如候选数删除性质、矛盾性质、唯一确定性质、枚举不变性质;基于以上性质,提出用区域序列枚举方法求解蜂巢数独。结合实例计算,提出的算法对中度难度级别的蜂巢数独是有效的。     

数独基于规则的逐步枚举算法设计

给出了数独(Sudoku)的6条性质,并在此基础上提出了6条推理规则,然后结合空格填写的一个一组,两个一组及更多个一组的枚举算法,在枚举中进行推理.使推理和枚举结合起来,对有唯一解的数独问题,其求解速度比回溯法快得多,同时也能完成许多数独软件无法进行推理计算的数独难题.用两个数独难题进行验证,表明该方法十分有效.     

数独难度级别划分的权重法研究

给出候选数模式下模仿人工智能求解数独的一系列填数及删减规则,在此基础上提出模仿人工智能的求解算法及数独难度衡量方法。从数独博士5个难度级别中随机抽取各100道题目,采用难度衡量标准重新分级,并将结果与数独博士等级划分标准做相关性检验, 得到Goodman-Kruskal相关系数r=0.82,说明该标准与数独博士的难度划分标准有较强的相关性,并给出随机生成数独题目的算法。通过难度衡量方法与生成算法,可以随机生成5个不同难度的数独谜题。     

用于数独求解的几何粒子群优化算法设计

针对只有唯一解的数独问题(即标准数独),利用改进的几何粒子群优化算法进行求解,将几何粒子群优化算法应用到数独中,解决数独求解过程中存在的局部最优解问题。通过实例讨论求解过程中最佳参数的选择,并得出较理想的结果。实验结果表明,该方法能够有效解决数独问题。     

融合人工求解策略的数独回溯求解法

数独有唯一解,回溯法可以保证获得正确结果。为了提高回溯法求解效率,向前搜索用最基础的人工策略进行求解,这样只需要两三个正确的候选数就可求解成功。基础人工策略求解的结果分为求解成功、求解失败和求解不确定三种情况,只有在求解不确定时才继续向前搜索,从而达到高效剪枝的目的;同时在算法实施方面采用大量位运算,大量9×9数独的实验结果表明对于绝大部分数独,平均计算时间不超过0.15 ms,对于那些极端困难的数独平均求解时间为2 ms;求解一个16×16数独的平均时间为224 ms。通过实验还发现17个提示数的9×9数独数据集在各方面具有较好的分散性,建议作为标准测试用数据集。     

求解分块循环三对角方程组的新算法

分块循环三对角方程组的求解在科学与工程计算中有着广泛的应用.本文根据分块循环三对角矩阵的特殊分解,给出了求解分块循环三对角方程组的一种新算法.该算法含有可以选择的参数矩阵,适当选择这些参数矩阵,可以使得计算精度高于追赶法,甚至当追赶法失效时,由该算法仍可得到一定精度的解.而数值算例的结果与理论分析的结果也吻合.     

加权范数下矩阵方程组的对称解及其最佳逼近

应用复合最速下降法,给出了求解矩阵方程组[(AXB=E,CXD=F)]加权范数下对称解及最佳逼近问题的迭代解法。对任意给定的初始矩阵,该迭代算法能够在有限步迭代计算之后得到矩阵方程组的对称解,并且在上述解集合中也可给出指定矩阵的最佳逼近矩阵。     

基于单应矩阵的相对位姿改进算法

从单应矩阵恢复相对位姿在视觉导航、视觉伺服应用中具有重要价值,证明了单应矩阵的新性质,并利用该性质改进了基于单应矩阵分解的相对位姿估计算法。与已有算法相比,该算法的候选解个数减半,并扩大了适用范围。理论分析、合成数据和真实数据测试均表明,改进方法使从候选解中筛选出唯一解的运算时间减少了50%,提高了位姿估计的总体运算效率。     

一类Lyapunov型矩阵方程组的中心对称解及其最佳逼近

建立了求矩阵方程组AiXBi＋GiXDi=Fi（i=1,2）的中心对称解的迭代算法.使用该方法不仅可以判断矩阵方程组是否有中心对称解,而且在有中心对称解时,还能够在有限步迭代计算之后得到矩阵方程组的极小范数中心对称解.同时,也能够在矩阵方程组的中心对称解集合中求得给定矩阵的最佳逼近.     

基于遗传算法求解数独难题

为了求解数独难题,首先将其转化成一个组合优化问题。然后,提出一个在编码、初始化、交叉、变异、局部搜索等方面具有特点的遗传算法来求解它。实验结果表明,对于所有难度等级的数独难题,算法都是有效的。     

Parallel analysis of rotationally periodic structures

A parallel finite element solution algorithm for analysing large rotationally periodic structures on MIMD parallel computer systems is described. For a rotationally periodic structure, the global stiffness matrix under the corresponding symmetric coordinate system is periodic, i.e. possesses isomorphic properties, so that the global equation system can be transformed into a number of smaller equation systems which are fully decoupled. These decoupled equation systems then can be solved simultaneously on a multiprocessor parallel computer. The algorithm also generates the decoupled equation systems in parallel, without explicitly assembling the global stiffness matrix of the structure. A prototype implementation of the algorithm on an array of transputers is presented, and the efficiency of the program is also studied in this paper. Finally, a numerical example is given to demonstrate the speedup of the program.     

Solving nonlinear systems with least significant bit accuracy

We give an algorithm for constructing an inclusion of the solution of a system of nonlinear equations. In contrast to existing methods, the algorithm does not require properties which are difficult to verify such as the non-singularity of a matrix. In fact this latter property is demonstrated by the algorithm itself. The highly accurate computational results are obtained in terms of a residue of first or higher order of the system.     

An evolutionary-based hyper-heuristic approach for the Jawbreaker puzzle

In this paper a hyper-heuristic algorithm is designed and developed for its application to the Jawbreaker puzzle. Jawbreaker is an addictive game consisting in a matrix of colored balls, that must be cleared by popping sets of balls of the same color. This puzzle is perfect to be solved by applying hyper-heuristics algorithms, since many different low-level heuristics are available, and they can be applied in a sequential fashion to solve the puzzle. We detail a set of low-level heuristics and a global search procedure (evolutionary algorithm) that conforms to a robust hyper-heuristic, able to solve very difficult instances of the Jawbreaker puzzle. We test the proposed hyper-heuristic approach in Jawbreaker puzzles of different size and difficulty, with excellent results.     

Solving cross-matching puzzles using intelligent genetic algorithms

Cross-matching puzzles are logic based games being played with numbers, letters or symbols that present combinational problems. A cross-matching puzzle consists of three tables: solution table, detection table, and control table. The puzzle can be solved by superposing the detection and control tables. For the solution of the cross-matching puzzle, a depth first search method can be used, but by expanding the size of the puzzle, computing time can be increased. Hence, the genetic algorithm, which is one of the most common optimization algorithms, was used to solve cross-matching puzzles. The multi-layer genetic algorithm was improved for the solution of cross-matching puzzles, but the results of the multi-layer genetic algorithm were not good enough because of the expanding size of the puzzle. Therefore, in this study, the genetic algorithm was improved in an intelligent way due to the structure of the puzzle. The obtained results showed that an intelligent genetic algorithm can be used to solve cross-matching puzzles.