An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.     

A branch and bound algorithm for the robust shortest path problem with interval data

Many real problems can be modelled as robust shortest path problems on interval digraphs, where intervals represent uncertainty about real costs and a robust path is not too far from the shortest path for each possible configuration of the arc costs.A branch and bound algorithm for this problem is presented.     

Practical algorithms for transposition-invariant string-matching

We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transposition-invariant text searching using indel distance. These problems have applications in music comparison and retrieval. We introduce two novel techniques to solve these problems efficiently. The first is based on the branch and bound method, the second on bit-parallelism. Our branch and bound algorithm computes the longest common transposition-invariant subsequence (LCTS) in time O((m²+loglogσ)logσ) in the best case and O((m²+logσ)σ) in the worst case, where m and σ, respectively, are the length of the strings and the size of the alphabet. On the other hand, we show that the same problem can be solved by using bit-parallelism and thus obtain a speedup of O(w/logm) over the classical algorithms, where the computer word has w bits. The advantage of this latter algorithm over the present bit-parallel ones is that it allows the use of more complex distances, including general integer weights. Since our branch and bound method is very flexible, it can be further improved by combining it with other efficient algorithms such as our novel bit-parallel algorithm. We experiment on several combination possibilities and discuss which are the best settings for each of those combinations. Our algorithms are easily extended to other musically relevant cases, such as δ-matching and polyphony (where there are several parallel texts to be considered). We also show how our bit-parallel algorithm is adapted to text searching and illustrate its effectiveness in complex cases where the only known competing method is the use of brute force.     

Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms

We investigate subdivision strategies that can improve the convergence and efficiency of some branch and bound algorithms of global optimization. In particular, a general class of so called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions.     

On the Center of Continuous Maps of Dendrites

The structure and the depth of the center of a continuous map of a dendrite with a closed countable set of branch points of a finite order are studied. It is proved that the center of that map coincides with the closure of the set of periodic points. It is shown also that for an arbitrary natural number n S 2 there are the dendrite X n with a closed countable set of branch points of a finite order and the continuous map f n : X n M X n with n as the depth of the center.     

A statistical model for global optimization by means of select and clone

A statistical model tor giobai optimization is constructed generalizing some properties ofthe Wiener process to the multidimensional case. A new approach, which is similar to the Branch and Bound approach, is proposed to the construction of algorithms based on statistical models. A two dimensional version of the algorithm is implemented, and test results are presented     

未免有浮夸之嫌——且说“弄《水浒》惹大祸”

白驹施彦端一些真实可靠的史料文物中,并无"中进士"、"字耐庵"、"著水浒"之类记载,而一些学者却以"著《水浒》惹大祸"来辩解其无;相距施彦端四五百年之后,居然出现上述内容,而一些学者却以朝廷无力"禁《水浒》"来辩解其有。这些,都未免有浮夸之嫌,实难以此论证"白驹施彦端进士,字耐庵,为〈水浒传〉作者"。     

醇对非离子型表面活性剂浊点的影响

研究了醇对非离子型表面活性剂浊点的影响，发现直链醇的碳原子数小于４时随着其在表面活性剂中含量的增加浊点上升；当碳原子数大于４时，则随着醇含量的增加浊点下降。醇的构型对浊点起着重要作用。     

n个零件在m台机器上加工有停歇时间的计划排序问题

本文就n个零件在m台机器上加工且在每两台机器加工时段之间存在停歇时段,以总加工时间最小为目标的排序问题当零件加工同顺序时进行讨论,给出了m=3时的分支——定界算法,是文[1]方法的推广。     

用支路撕裂法进行大规模模拟电路故障诊断的新算法

本文首先介绍最近出现的一种用支路撕裂法进行的大规模模拟电路的故障诊断算法,讨论了该算法的容差问题。然后将故障预测技术、替代理论和迭加定理运用到支路撕裂法中,得到一个新的故障诊断方程,并给出了一种新的算法。还讨论了算法的并行处理问题。研究结果证明,当连续监测网络时,新算法的在线计算时间和容差问题均较原算法有很大的改进。