A linear-time algorithm for finding approximate shortest common superstrings

Approximate shortest common superstrings for a given setR of strings can be constructed by applying the greedy heuristics for finding a longest Hamiltonian path in the weighted graph that represents the pairwise overlaps between the strings inR. We develop an efficient implementation of this idea using a modified Aho-Corasick string-matching automaton. The resulting common superstring algorithm runs in timeO(n) or in timeO(n min(logm, log¦¦)) depending on whether or not the goto transitions of the Aho-Corasick automaton can be implemented by direct indexing over the alphabet . Heren is the total length of the strings inR andm is the number of such strings. The best previously known method requires timeO(n logm) orO(n logn) depending on the availability of direct indexing.This work was supported by the Academy of Finland.     

An 11/6-approximation algorithm for the network steiner problem

An instance of the Network Steiner Problem consists of an undirected graph with edge lengths and a subset of vertices; the goal is to find a minimum cost Steiner tree of the given subset (i.e., minimum cost subset of edges which spans it). An 11/6-approximation algorithm for this problem is given. The approximate Steiner tree can be computed in the time0(¦V¦ ¦E¦ + ¦S¦⁴), whereV is the vertex set,E is the edge set of the graph, andS is the given subset of vertices.     

On the parameterized complexity of the fixed alphabet shortest common supersequence and longest common subsequence problems

We show that the fixed alphabet shortest common supersequence (SCS) and the fixed alphabet longest common subsequence (LCS) problems parameterized in the number of strings are W[1]-hard. Unless W[1]=FPT, this rules out the existence of algorithms with time complexity of O(f(k)nα) for those problems. Here n is the size of the problem instance, α is constant, k is the number of strings and f is any function of k. The fixed alphabet version of the LCS problem is of particular interest considering the importance of sequence comparison (e.g. multiple sequence alignment) in the fixed length alphabet world of DNA and protein sequences.     

An optimal approximation algorithm for the rectilinearm-center problem

Given a set ofn points on the plane, the rectilinearm-center problem is to findn rectilinear squares covering all thesen points such that the maximum side length of these squares is minimized. In this paper we prove that there is no polynomial-time algorithm with an error ratio < 2 for the rectilinearm-center problem unless NP = P. A polynomial-time approximation algorithm with an error ratio of 2 is also proposed.This research work was partially supported by a grant from the National Science Council of the Republic of China under Grant NSC-77-0408-E007-03.     

An algorithm for the three-dimensional packing problem with asymptotic performance analysis

The three-dimensional packing problem can be stated as follows. Given a list of boxes, each with a given length, width, and height, the problem is to pack these boxes into a rectangular box of fixed-size bottom and unbounded height, so that the height of this packing is minimized. The boxes have to be packed orthogonally and oriented in all three dimensions. We present an approximation algorithm for this problem and show that its asymptotic performance bound is between 2.5 and 2.67. This result answers a question raised by Li and Cheng [5] about the existence of an algorithm for this problem with an asymptotic performance bound less than 2.89. This research was partially supported by FAPESP (proc. 93/0603-1) and by CNPq/ProTeM-CC, project ProComb (proc. 680065/94-6).     

An efficient fault-containing self-stabilizing algorithm for the shortest path problem

Shortest path finding has a variety of applications in transportation and communication. In this paper, we propose a fault-containing self-stabilizing algorithm for the shortest path problem in a distributed system. The improvement made by the proposed algorithm in stabilization times for single-fault situations can demonstrate the desirability of an efficient fault-containing self-stabilizing algorithm. For single-fault situations, the worst-case stabilization time of the proposed algorithm is O(Δ), where Δ is the maximum node degree in the system, and the contamination number of the proposed algorithm is 1.     

改进量子进化算法及其在物流配送路径优化问题中的应用

量子进化算法的性能直接受量子旋转门旋转角计算方法的影响.文中提出一种改进量子进化算法,核心是设计了基于量子比特概率幅比值自适应计算量子旋转门旋转角的新方法,算法具有收敛速度快和全局搜索能力强的特点.通过0/1背包问题分析了新方法中相关参数对算法性能的影响,并应用算法求解物流配送路径优化问题,仿真表明改进量子进化算法性能优于量子进化算法和传统进化算法.     

An improved genetic algorithm with conditional genetic operators and its application to set-covering problem

The genetic algorithm (GA) is a popular, biologically inspired optimization method. However, in the GA there is no rule of thumb to design the GA operators and select GA parameters. Instead, trial-and-error has to be applied. In this paper we present an improved genetic algorithm in which crossover and mutation are performed conditionally instead of probability. Because there are no crossover rate and mutation rate to be selected, the proposed improved GA can be more easily applied to a problem than the conventional genetic algorithms. The proposed improved genetic algorithm is applied to solve the set-covering problem. Experimental studies show that the improved GA produces better results over the conventional one and other methods.     

BEAMR: An exact and approximate model for the p-median problem

The p-median problem is perhaps one of the most well-known location–allocation models in the location science literature. It was originally defined by Hakimi in 1964 and 1965 and involves the location of p facilities on a network in such a manner that the total weighted distance of serving all demand is minimized. This problem has since been the subject of considerable research involving the development of specialized solution approaches as well as the development of many different types of extended model formats. One element of past research that has remained almost constant is the original ReVelle–Swain formulation [ReVelle CS, Swain R. Central facilities location. Geographical Analysis 1970;2:30–42]. With few exceptions as detailed in the paper, virtually no new formulations have been proposed for general use in solving the classic p-median problem. This paper proposes a new model formulation for the p-median problem that contains both exact and approximate features. This new p-median formulation is called Both Exact and Approximate Model Representation (BEAMR). We show that BEAMR can result in a substantially smaller integer-linear formulation for a given application of the p-median problem and can be used to solve for either an exact optimum or a bounded, close to optimal solution. We also present a methodological framework in which the BEAMR model can be used. Computational results for problems found in the OR_library of Beasley [A note on solving large p-median problems. European Journal of Operational Research 1985;21:270–3] indicate that BEAMR not only extends the application frontier for the p-median problem using general-purpose software, but for many problems represents an efficient, competitive solution approach.     

Shuffled frog leaping algorithm and its application to 0/1 knapsack problem

This paper proposes a modified discrete shuffled frog leaping algorithm (MDSFL) to solve 01 knapsack problems. The proposed algorithm includes two important operations: the local search of the ‘particle swarm optimization’ technique; and the competitiveness mixing of information of the ‘shuffled complex evolution’ technique. Different types of knapsack problem instances are generated to test the convergence property of MDSFLA and the result shows that it is very effective in solving small to medium sized knapsack problems. Further, computational experiments with a set of large-scale instances show that MDSFL can be an efficient alternative for solving tightly constrained 01 knapsack problems.     

An almost-linear time and linear space algorithm for the longest common subsequence problem

There are two general approaches to the longest common subsequence problem. The dynamic programming approach takes quadratic time but linear space, while the nondynamic-programming approach takes less time but more space. We propose a new implementation of the latter approach which seems to get the best for both time and space for the DNA application.     

理性遗传算法及其在运动规划中的应用

为提高理性遗传算法遗传信忠的完备性、算法全局收敛性以及算法的整体结构，给出了一个更一般化的理性算子和算法结构，证明了算法的全局收敛性．理论分析和在运动规划问题中的应用结果验证了理性遗传算法的有效性．     

Order relation between intervals and its application to shortest path problem

It is true that intervals are frequently partially ordered and cannot be compared. Nevertheless, varous definitions for ranking intervals have been proposed. In this paper, we propose a new definition for order relation between intervals by introducing a parameter called “a degree between partial and total order”, and apply it to the shortest path problem with arcs represented as intervals. In order to solve this problem, we modify the Dijkstra's algorithm, and propose a new algorithm obtaining some incomparable interval solutions. Finally, a numerical example is shown.     

An approximation algorithm to the k-Steiner Forest problem

Given a graph G$G$, an integer k$k$, and a demand set D={(_s1,_t1),…,(_sl,_tl)}$D=\{(s_1,t_1),\dots ,(s_l,t_l)\}$, the k$k$-Steiner Forest problem finds a forest in graph G$G$ to connect at least k$k$ demands in D$D$ such that the cost of the forest is minimized. This problem was proposed by Hajiaghayi and Jain in SODA’06. Thereafter, using a Lagrangian relaxation technique, Segev et al. gave the first approximation algorithm to this problem in ESA’06, with performance ratio O(n^2/3logl)$O(n^{2/3}logl)$. We give a simpler and faster approximation algorithm to this problem with performance ratio O(n^2/3logk)$O(n^{2/3}logk)$ via greedy approach, improving the previously best known ratio in the literature.     

竞选算法及其在函数全局最优化问题中的应用

竞选算法是借鉴人类竞选活动中所蕴涵的优化思想而建立的一种优化算法,其搜索机制模拟的是竞选人在整个竞选过程中追求最高支持率的行为。介绍了算法的基本思想、基本原理和计算步骤,并将竞选算法应用于求解函数的全局最优解。通过对标准测试函数优化的数值实验结果表明,竞选算法可快速搜索到函数的全局最优解,并具有较好的稳定性。     

Mean analysis of an online algorithm for the vertex cover problem

In 2005, Demange and Paschos proposed in [M. Demange, V.Th. Paschos, On-line vertex-covering, Theoret. Comput. Sci. 332 (2005) 83-108] an online algorithm (noted LR here) for the classical vertex cover problem. They shown that, for any graph of maximum degree Δ, LR constructs a vertex cover whose size is at most Δ times the optimal one (this bound is tight in the worst case).Very recently, two of the present authors have shown in [F. Delbot, C. Laforest, A better list heuristic for vertex cover, Inform. Process. Lett. 107 (2008) 125-127] that LR has interesting properties (it is a good “list algorithm” and it can easily be distributed). In addition, LR has good experimental behavior in spite of its Δ approximation (or competitive) ratio and the fact that it can be executed without the knowledge of the full instance at the beginning.In this paper we analyze it deeper and we show that LR has good “average” performances: we prove that its mean approximation ratio is strictly less than 2 for any graph and is equal to 1+e−2≈1.13 in paths. LR is then a very interesting algorithm for constructing small vertex covers, despite its bad worst case behavior.     

自适应布谷鸟算法及其在化工优化中的应用

动态优化问题广泛存在于化工自动控制过程中,对其求解是化工过程工业发展的一个不可忽视的环节。群智能算法求解此类优化问题时不可避免地存在后期收敛速度慢、求解精度的不高等不足,这一直是一个研究热点。针对新兴的布谷鸟算法与以上问题,提出一种变步长自适应布谷鸟搜索算法(VSACS),将基本布谷鸟搜索(CS)算法中的随机步长改进成根据迭代次数自适应调整的步长。通过15个标准测试函数的测试,结果验证了改进的算法有较快的收敛速度和较高的求解精度。最后将改进的算法用于批示反应器、管式反应器、生物反应器等3个典型的化工动态优化问题中,获得了满意的实验结果,同时也进一步表明该算法的有效性。     

背包问题混合遗传算法在电力恢复中的应用

文章把电力系统的负荷恢复问题建模为带众多约束条件的0-1背包问题,并设计了一种将贪心算法与改进遗传算法结合起来的改进混合遗传算法来对此问题进行求解.该算法的主要特点是具有群体爬山性和利用了郭涛算子的非凸组合技术使算法具有搜索的遍历性.采用此算法可以得到负荷恢复的某一阶段可恢复的最大的负荷量.求解的过程保证了求得的解是满足系统的约束条件,所以系统的负荷恢复过程是安全的.算例的结果表明了该算法的有效性.     

改进自组织迁移算法及其在Bump 问题中的应用

提出了改进自组织迁移算法（Improved Self-Organizing Migrating Algorithm,ISOMA）。该算法通过在迁移过程中引入差分迁移方式来增加种群的多样性,将迁移的方向由原来的正方向扩展到正负两方向以提高算法的搜索能力,对步长进行自适应调整进一步平衡算法的勘探和开采能力。利用该算法来求解高维约束问题——BUMP 问题,计算结果表明新算法的有效性。     

改进的麻雀搜索优化算法及其应用

麻雀搜索算法SSA在求解目标函数最优解时,存在种群多样性不丰富,易陷于局部最优,多维函数求解精度差等问题,针对这些问题提出改进的麻雀搜索算法ISSA。首先,利用反向学习策略初始化种群,增加种群多样性;然后,对步长因子进行动态调整,提高算法的求解精度;最后,在侦查预警的麻雀位置更新公式中引入Levy飞行,提高算法寻优能力和跳出局部极值的能力。将ISSA、SSA和其他算法在8个测试函数上进行求解,并进行秩和检验,仿真结果表明,ISSA具有更高的寻优性能。还将ISSA应用到认知无线电的频谱分配中,实验结果表明,ISSA的系统效益和公平性优于其他算法,验证了ISSA在实际应用中的可行性。