一个关于求解k-种产品选址问题的近似算法

对于k-种产品工厂选址问题,有如下描述：存在一组客户和一组可以建立工厂的厂址。现在有k种不同的产品,要求每一个客户必须由k个不同的工厂来提供k种不同的产品,其中每个工厂都只能为客户提供唯一的一种产品。在该问题中,假定建厂费用以及任意两个结点之间的运输费用都为非负,并且任意两个结点之间的运输费用都满足对称和三角不等式关系的性质。问题的要求是要从若干厂址中选择一组厂址来建立工厂,给每个工厂指定一种需要生产的产品,并且给每一个客户提供一组指派使每个客户都能有k个工厂来为其供应这k种不同的产品。对于此类问题,优化目标是最小化建厂费用以及运输费用。论文在假设建厂费用为零的前提下,提出了求解该类问题的一种最坏性能比为3k/2-1的近似算法。     

On the Competitive Ratio for Online Facility Location

We consider the problem of Online Facility Location, where the demand points arrive online and must be assigned irrevocably to an open facility upon arrival. The objective is to minimize the sum of facility and assignment costs. We prove that the competitive ratio for Online Facility Location is Θ . On the negative side, we show that no randomized algorithm can achieve a competitive ratio better than Ω against an oblivious adversary even if the demands lie on a line segment. On the positive side, we present a deterministic algorithm which achieves a competitive ratio of in every metric space. A preliminary version of this work appeared in the Proceedings of the 30th International Colloquium on Automata, Languages and Programming (ICALP 2003), Lecture Notes in Computer Science 2719. This work was done while the author was at the Max-Planck-Institut für Informatik, Saarbrücken, Germany, and was partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM–FT).     

Optimal switch location in mobile communication networks using hybrid genetic algorithms

The optimal positioning of switches in a mobile communication network is an important task, which can save costs and improve the performance of the network. In this paper we propose a model for establishing which are the best nodes of the network for allocating the available switches, and several hybrid genetic algorithms to solve the problem. The proposed model is based on the so-called capacitated p-median problem, which have been previously tackled in the literature. This problem can be split in two subproblems: the selection of the best set of switches, and a terminal assignment problem to evaluate each selection of switches. The hybrid genetic algorithms for solving the problem are formed by a conventional genetic algorithm, with a restricted search, and several local search heuristics. In this work we also develop novel heuristics for solving the terminal assignment problem in a fast and accurate way. Finally, we show that our novel approaches, hybridized with the genetic algorithm, outperform existing algorithms in the literature for the p-median problem.     

一种改进遗传算法在生产车间设备布局中的应用

生产系统的设备布局设计是一个组合优化的问题。具有非线性,N P难等特性,常规方法较难以求解。文章通过创建生产系统设备布局的数学优化模型。引入了小生境技术,保持了种群的多样性。并且利用精英选择机制,自适应交叉和变异概率等手段,在使种群保持多样化的同时,增强了算法的全局和局部搜索能力,协调了遗传算法大范围粗糙搜索和小范围精细搜索之间的平衡,有效改善了早熟和过早收敛问题,并通过实例验证了其有效性。     

A novel grouping harmony search algorithm for the multiple-type access node location problem

In this paper we present a novel grouping harmony search algorithm for the Access Node Location Problem (ANLP) with different types of concentrators. The ANLP is a NP-hard problem where a set of distributed terminals, with distinct rate demands, must be assigned to a variable number of concentrators subject to capacity constraints. We consider the possibility of choosing between different concentrator models is given in order to provide service demand at different cost. The ANLP is relevant in communication networks design, and has been considered before within the design of MPLS networks, for example. The approach we propose to tackle the ANLP problem consists of a hybrid Grouping Harmony Search (GHS) algorithm with a local search method and a technique for repairing unfeasible solutions. Moreover, the presented scheme also includes the adaptation of the GHS to a differential scheme, where each proposed harmony is obtained from the same harmony in the previous iteration. This differential scheme is perfectly adapted to the specifications of the ANLP problem, as it utilizes the grouping concept based on the proximity between nodes, instead of being only based on the grouping concept. This allows for a higher efficiency on the searching process of the algorithm. Extensive Monte Carlo simulations in synthetic instances show that this proposal provides faster convergence rate, less computational complexity and better statistical performance than alternative algorithms for the ANLP, such as grouping genetic algorithms, specially when the size of the scenario increases. We also include practical results for the application of GHS to a real wireless network deployment problem in Bizkaia, northern Spain.     

Planar expropriation problem with non-rigid rectangular facilities

In this paper, we introduce the planar expropriation problem with non-rigid rectangular facilities. The facilities considered in this study are two-dimensional facilities of rectangular shape. Moreover, we allow the facility dimensions to be decision variables and introduce the concept of non-rigid facilities. Based on the geometric properties of such facilities, we developed a new formulation for this continuous covering location model which does not require employing distance measures. This model is intended to determine the location and formation of facilities simultaneously. For solving this new model, we proposed a continuous branch-and-bound framework utilizing linear approximations for the tradeoff curve associated with the facility formation alternatives. Further, we developed new problem generation and bounding strategies suitable for our particular problem structure. Computational experience shows that the branch-and-bound procedure we developed performs better than conventional mixed-integer nonlinear programming solvers BARON and SBB for solving this particular location model.     

多重群体遗传算法在多选择背包问题中的应用

在解决多选择背包问题中，引入了多重群体遗传算法作为求解方法，根据此问题的特点，制定了具体的杂交、变异方法，设计了遗传算法。在算法中以目标函数加惩罚函数为适应值评价函数，采用新陈代谢的跨世代选择策略，以更好地保持进化过程中的遗传多样性。实践表明，引入了多重群体遗传算法之后，求解此问题效率有明显的改善与提高。     

Primal–Dual Algorithms for Connected Facility Location Problems

We consider the Connected Facility Location problem. We are given a graph $G = (V,E)$ with costs $\{c_e\}$ on the edges, a set of facilities $\F \subseteq V$, and a set of clients $\D \subseteq V$. Facility $i$ has a facility opening cost $f_i$ and client $j$ has $d_j$ units of demand. We are also given a parameter $M\geq 1$. A solution opens some facilities, say $F$, assigns each client $j$ to an open facility $i(j)$, and connects the open facilities by a Steiner tree $T$. The total cost incurred is ${\sum}_{i\in F} f_i+ sum_{j\in\D} d_jc_{i(j)j}+M\sum_{e\in T}c_e$. We want a solution of minimum cost. A special case of this problem is when all opening costs are 0 and facilities may be opened anywhere, i.e., $\F=V$. If we know a facility $v$ that is open, then the problem becomes a special case of the single-sink buy-at-bulk problem with two cable types, also known as the rent-or-buy problem. We give the first primal–dual algorithms for these problems and achieve the best known approximation guarantees. We give an 8.55-approximation algorithm for the connected facility location problem and a 4.55-approximation algorithm for the rent-or-buy problem. Previously the best approximation factors for these problems were 10.66 and 9.001, respectively. Further, these results were not combinatorial—they were obtained by solving an exponential size linear rogramming relaxation. Our algorithm integrates the primal–dual approaches for the facility location problem and the Steiner tree problem. We also consider the connected $k$-median problem and give a constant-factor approximation by using our primal–dual algorithm for connected facility location. We generalize our results to an edge capacitated variant of these problems and give a constant-factor approximation for these variants.     

基于遗传算法求解TSP问题的一种算法

主要研究了用遗传算法求解TSP问题.阐述了简单遗传算法的设计方法、基本原理和基本步骤.描述了简单遗传算法在TSP问题中的应用现状.根据种群个体的多样性和分布情况,提出了判定遗传算法的截止代数.简单遗传算法具有易于陷入局部最优解、收敛速度慢的特点,针对这些特点,通过改进交叉算子,加入初始化启发信息,提高了遗传算法解的精度和收敛性.     

基于遗传算法的八数码问题的设计及实现

介绍了遗传算法（GA）在八数码问题中的应用。首先介绍了八数码问题及遗传算法的相关知识,分析了求解八数码问题的传统解决方案;然后给出了八数码问题的遗传算法模型,并对此模型进行了算法的设计,即确定编码的表示、选择算子、交叉算子、变异算子及适应度函数;最后把此算法运用到基于八数码问题的拼图游戏求解过程的动态演示上。文中对此算法进行了多角度试验,试验表明采用遗传算法解决八数码问题是有效的、稳定的,具有较高的搜索效率。     

Online chasing problems for regular polygons

We consider a server location problem with only one server to move. In this paper we assume that a request is given as a region and that the service can be done anywhere inside the region. Namely, for each request an online algorithm chooses an arbitrary point in the region and moves the server there. Note that if every request is a single point and the server must exactly go there in the given order as conventional server problems, there is no choice for the online player and the problem is trivial. Our main result shows that if the region is a regular n-gon, the competitive ratio of the greedy algorithm is for odd n, and for even n. In particular for a square region, the greedy algorithm turns out to be optimal.     

大规模突发事件应急设施选址模型及算法

大规模突发事件下应急物资的需求量巨大以及对资源持续需求的特点,考虑设施选址的公平性、效率性及成本等因素,基于多级覆盖和覆盖衰减思想,提出一类应急设施多目标多重覆盖衰减选址模型。基于MATLAB7.0设计贪婪算法、上升算法、遗传算法程序对模型进行求解,以25组不同规模的算例验证了模型的性能和算法的有效性。数值模拟结果表明,该模型较之传统覆盖选址模型可以为需求点提供更高的覆盖满意度;当目标权系数取不同值时对选址结果产生较大影响;对三个算法性能进行比较,遗传算法最优,上升算法次之,贪婪算法最差,上升算法适于求解中小规模的选址问题,而遗传算法更适合于大规模选址问题的求解。     

SLP和遗传算法结合在车间设备布局中的应用

用经典的系统布置设计结合遗传算法求解车间设备布局,以高效率获得满意的设计结果,弥补传统SLP设计过程中手工操作的繁琐迭代、易受主观影响、结果不稳定等缺点。并且通过对遗传算法的改进,增强了算法的全局和局部搜索能力。最后,通过实例验证了其有效性。     

The vendor location problem

The vendor location problem is the problem of locating a given number of vendors and determining the number of vehicles and the service zones necessary for each vendor to achieve at least a given profit. We consider two versions of the problem with different objectives: maximizing the total profit and maximizing the demand covered. The demand and profit generated by a demand point are functions of the distance to the vendor. We propose integer programming models for both versions of the vendor location problem. We then prove that both are strongly NP-hard and we derive several families of valid inequalities to strengthen our formulations. We report the outcomes of a computational study where we investigate the effect of valid inequalities in reducing the duality gaps and the solution times for the vendor location problem.