数学常规解法与模型解法之思——以排列组合中的典型问题为例

该文以排列组合中的分球入箱、装错信封、传球问题、质点运动问题为典型案例,对比探讨了数学常规解法和模型解法的不同特点,得到结论:两者没有绝对的优劣高低之分,在教学实践中应辩证对待模型解法与常规解法的关系,重视两种解法形态在解题中的作用,只有适合学生的解法才是最优化解法,只有适合学生的解题教学才是最优化解题教学。     

一道二次根式和的最大值解法

一题多解就是启发和引导学生从不同角度,不同思路,运用不同方法和不同的运算过程以解答同一道数学问题的方法,这篇文章旨在探寻一道二次根式和的最大值的解法.     

一人多机的动态配置模型及其解法

本文以机械企业为背景,探讨了一人多机看管问题中的人员配置问题,并采用层次序列法对人员配置数学模型进行了求解,给出了启发式解法,指出了进一步研究的方向。     

一个问题的所有解法

~~一个问题的所有解法@赵汀阳     

反求微分方程的问题

高等数学中有一类已知微分方程的通解反求微分方程的题型,本文对此类问题通过例子,说明其常用解法。     

应急管理中的救援物资调度问题

救援物资的调度安排是应急管理中的一个重要问题,本文利用线性规划中的表上作业法给出了这类问题的一种解法。本文的方法可适用于供需平衡和供需不平衡两种情况,且在求解过程中,选用了比最小元素法效率更高的Vogel法。     

溶液中离子浓度大小比较题型解题新思路

针对溶液中离子浓度大小比较题型的传统解法学生难以掌握的问题,本文提出将溶液中各种离子的浓度计算出来进行比较的新思路.     

一种改进的TSP问题启发式算法

旅行推销商问题(TSP)属于组合优化领域中一个典型的NP Hard问题。本文在最近城市搜索法的基础上,提出一种改进的启发式算法———两端延伸最近城市搜索法,这种方法能够很快得到最优解(近优解),且大大降低了计算复杂度。同时,对TSP问题进行了分类,并给出相应的启发式解法。     

灰色理论在创业初期企业产品组合战略中的运用研究

基于灰色理论的方法和视角分析了灰整数规划的性质和解法,针对创业初期企业资源安排的不确定性和模糊性,探讨了灰色理论在创业初期企业产品组合战略中的运用,并指出它在信息不完备领域中解决模糊问题的可行性和广泛性.     

利用网络推动野生动物保育工作

野生动物因生活环境与人类重叠性很低,所以习性与生活史较不为人所知,人类也因而较不关心他们的存续。这个问题在濒危物种上更为严重,因为数量少,更容易在人类的忽视下,很快就从这个地球上消失,所以必须进行有效的野生动物保育。这个问题在网络发达的今天,找到了适当的解法。不论是网站、博客、脸书、微信,都有一共同特点,就是所有的信息在输进计算机后,弹指之间都能传送到电话线所及之处,与远方的朋友及同行分享和讨论。这会让信息获得充分的利用、共同商议适当的解法。在过去,野生动物遭到残杀,栖息地遭到破坏,需野外生态学家跋山涉水花很多时间到荒僻的地点去了解原因。等到引起政府重视时,物种早已被消灭了。一些物种的生物信息及保育倡导,会因信息传递不易而效果不佳。现在,只要随身携带适当的电子产品,如手机,这些问题在很短的时间内就可以获得相关单位及民众的重视,及早采取应对措施,让动物免于灭绝的厄运及增加人们对它们的了解。     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

A Combined D.C. Optimization—Ellipsoidal Branch-and-Bound Algorithm for Solving Nonconvex Quadratic Programming Problems

In this paper we propose a new branch-and-bound algorithm by using an ellipsoidal partition for minimizing an indefinite quadratic function over a bounded polyhedral convex set which is not necessarily given explicitly by a system of linear inequalities and/or equalities. It is required that for this set there exists an efficient algorithm to verify whether a point is feasible, and to find a violated constraint if this point is not feasible. The algorithm is based upon the fact that the problem of minimizing an indefinite quadratic form over an ellipsoid can be efficiently solved by some available (polynomial and nonpolynomial time) algorithms. In particular, the d.c. (difference of convex functions) algorithm (DCA) with restarting procedure recently introduced by Pham Dinh Tao and L.T. Hoai An is applied to globally solving this problem. DCA is also used for locally solving the nonconvex quadratic program. It is restarted with current best feasible points in the branch-and-bound scheme, and improved them in its turn. The combined DCA-ellipsoidal branch-and-bound algorithm then enhances the convergence: it reduces considerably the upper bound and thereby a lot of ellipsoids can be eliminated from further consideration. Several numerical experiments are given.     

One-machine scheduling to minimize mean tardiness with minimum number tardy

In this paper the one-machine scheduling problem with the objective of minimizing the mean tardiness subject to maintaining a prescribed number of tardy jobs is analysed. An algorithm for solving this problem is presented. It is proved that the schedule generated by the proposed algorithm is indeed optimal.     

An iterated greedy algorithm for the flowshop scheduling problem with blocking

This paper proposes an iterated greedy algorithm for solving the blocking flowshop scheduling problem for makespan minimization. Moreover, it presents an improved NEH-based heuristic, which is used as the initial solution procedure for the iterated greedy algorithm. The effectiveness of both procedures was tested on some of Taillard’s benchmark instances that are considered to be blocking flowshop instances. The experimental evaluation showed the efficiency of the proposed algorithm, in spite of its simple structure, in comparison with a state-of-the-art algorithm. In addition, new best solutions for Taillard’s instances are reported for this problem, which can be used as a basis of comparison in future studies.     

用混合遗传算法求解物流配送路径优化问题的研究

论文建立了物流配送路径优化问题的数学模型,并针对遗传算法在局部搜索能力方面的不足,提出将爬山算法与遗传算法相结合,从而构造了求解物流配送路径优化问题的混合遗传算法,并进行了实验计算。计算结果表明,用混合遗传算法求解物流配送路径优化问题,可以在一定程度上克服遗传算法在局部搜索能力方面的不足和爬山算法在全局搜索能力方面的不足,从而得到质量较高的解。     

组合拍卖竞胜标确定问题的混沌搜索算法

组合拍卖能够提高拍卖的效率,还能降低竞标人的风险. 但竞胜标确定问题是一个NP 难题. 在分析该问题特性的基础上,设计了一种嵌入优先适合启发式规则的混沌搜索算法. 与 传统算法相比,该算法具有实现方便,寻优效果好的优点. 实例计算结果表明了算法在解决该 问题的有效性和广阔的应用前景.     

Approximate and Exact Algorithms for Constrained (Un) Weighted Two-dimensional Two-staged Cutting Stock Problems

In this paper we propose two algorithms for solving both unweighted and weighted constrained two-dimensional two-staged cutting stock problems. The problem is called two-staged cutting problem because each produced (sub)optimal cutting pattern is realized by using two cut-phases. In the first cut-phase, the current stock rectangle is slit down its width (resp. length) into a set of vertical (resp. horizontal) strips and, in the second cut-phase, each of these strips is taken individually and chopped across its length (resp. width).First, we develop an approximate algorithm for the problem. The original problem is reduced to a series of single bounded knapsack problems and solved by applying a dynamic programming procedure. Second, we propose an exact algorithm tailored especially for the constrained two-staged cutting problem. The algorithm starts with an initial (feasible) lower bound computed by applying the proposed approximate algorithm. Then, by exploiting dynamic programming properties, we obtain good lower and upper bounds which lead to significant branching cuts. Extensive computational testing on problem instances from the literature shows the effectiveness of the proposed approximate and exact approaches.     

A hard clustering approach to the part family formation problem

The part family problem in group technology can be stated as the problem of finding the best grouping of parts into families such that the parts within each family are as similar to each other as possible. In this paper, the part family formation problem is considered. The problem is cast into a hard clustering model, and the k-means algorithm is proposed for solving it. Preliminary computational experience on the algorithm is very encouraging and it shows that real-life problems of large sizes can efficiently be handled by this approach.     

投资项目集合选择问题的非线性规划模型与解法研究

基于项目集合选择问题的定义,给出了项目集合选择问题求解的一般步骤。依据投资方案组合选择问题的非线性特性,构建了投资项目集合选择问题的非线性规划模型,在此模型的基础上提出了基于外点法求解此类问题的改进贪婪搜索算法。研究了采用surrogate松弛模型确定初始点和运用改进的贪婪算法搜索最优解的具体实现方法,给出了实现算法的具体步骤。     

有限缓冲区的多节点订单接受模型与算法

订单接受问题广泛存在于生产管理中,而现有多节点订单接受问题中大多不考虑缓冲区约束对订单接受的影响。针对这一问题,以缓冲区约束的多节点生产为背景,建立了订单接受模型。利用改进NEH算法、离散和声搜索算法和变邻域搜索的混合算法对模型进行求解。实验结果显示,当问题规模较小时,算法取得较好的计算效果。问题规模较大时,求解效果一般。缓冲区的大小对订单完工时间影响较小,与无限缓冲区的计算结果相似。混合算法具有较好的求解速度,能够有效求解问题模型。