重大突发事件应急设施多重覆盖选址模型及算法

为了解决应对重大突发事件过程中应急需求的多点同时需求和多次需求问题,本文研究了应对重大突发事件的应急服务设施布局中的覆盖问题:针对重大突发事件应急响应的特点,引入最大临界距离和最小临界距离的概念,在阶梯型覆盖质量水平的基础上,建立了多重数量和质量覆盖模型。模型的优化目标是满足需求点的多次覆盖需求和多需求点同时需求的要求条件下,覆盖的人口期望最大,并用改进的遗传算法进行求解;最后给出的算例证明了模型和算法的有效性,从而应急设施的多重覆盖选址模型能够为有效应对重大突发事件的应急设施选址决策提供参考依据。     

双层级医疗设施选址问题及禁忌搜索算法

分级诊疗有利于充分利用已有的医疗资源,是医疗卫生体制改革的重要内容,因而在医疗设施选址时需要考虑医疗机构的层级性。本文以两个层级的医疗设施作为选址研究对象,建立了双层级多样流的混合整数规划模型。针对该模型的特点,设计了一种基于禁忌搜索的算法确定最优选址策略。最后,以上海市某区社区卫生服务中心以及区域医疗中心为研究对象,给出相应两个层级医疗设施的选址方案,并对相关参数对选址结果的影响进行了分析。算法求解结果为有就医需求的居民提供指派,使该区域的医疗资源利用率得到了提高,医疗设施配置也更加合理均衡。     

求解无容量设施选址问题的拉格朗日蝙蝠算法

无容量设施选址问题(Uncapacitated Facility Location Problem,UFLP)是一类经典的组合优化问题,被证明是一种NP-hard问题,易于描述却难于求解.首先根据UFLP的数学模型及其具体特征,重新设计了蝙蝠算法的操作算子,给出了求解UFLP的蝙蝠算法.其次构建出三种可行化方法,并将其与求解UFLP的蝙蝠算法和拉格朗日松弛算法相结合,设计了求解该问题的拉格朗日蝙蝠算法.最后通过仿真实例和与其他算法进行比较的方式,验证了该混合算法用来求解UFLP的可行性,是解决离散型问题的一种有效方式.     

一类应急服务设施选址问题的模型及算法

在分析城市应急服务设施选址问题基础上,建立了限定期条件下应急服务设施选址问题的数学模型,提出了一种基于遗传算法的应急服务设施选址模型的有效算法,并通过算例分析验证了该方法的有效性.     

基于人工蜂群算法的配送中心选址问题求解

采用人工蜂群算法对配送中心选址问题进行求解,给出食物源的编码方法,通过整数规范化,使算法能在整数空间内对问题进行求解.应用算法进行了仿真实验,并将结果与其它一些启发式算法进行了比较和分析.计算结果表明人工蜂群算法可以有效求解配送中心选址问题,同时也为算法求解其它一些组合优化问题提供了有益思路.     

半讨厌型设施选址问题的模型与算法

研究了结合网络和平面模型的半讨厌型设施的选址问题.半讨厌型设施结合了讨厌型设施与喜爱型设施的性质,一方面由于这些设施对人们带来很多副作用,人们想要远离他们以避免遭到污染,但同时人们又希望距离设施不要过远,因此建立0-1整数模型,在保证所有人使用该设施的距离不超过既定距离的基础上,使污染范围最小.由于该问题是NP困难问题,本为给出了启发式算法,通过算例进行了比较分析,证明了算法的有效性.     

改进的蝗虫优化算法在双目标应急物资中心选址问题中的应用

近年来世界各地频发灾情疫情等紧急事件,严重影响人民的生活物资保障。在这种情况下,急需建立应急物资中心来缓解燃眉之急。该类问题通常面临资源稀缺并且时间相对紧迫的处境,因此需要在短时间内获得合理的应急设施选址方案来提升服务的质量和效率。本文对应急物资中心选址问题展开研究,提出一种考虑后续运输成本以及有概率发生紧急事件而导致无法正常运送物资的双目标离散选址模型,并为此设计一种二进制多目标蝗虫优化算法。该算法采用模糊关联熵系数来引导迭代更新,同时为其添加外部档案,最优解选择机制和竞争决策机制来提升算法性能。多次数值实验表明该算法的计算效率和求解质量较高,可作为应急物资中心选址问题的一种可行且有效的算法。     

基于Benders分解算法的反恐应急设施选址-定容-分配问题

反恐应急设施的合理布局和资源配置可缩短救援到达时间并提高应急效率。对已有反恐应急设施选址研究拓展,进一步考虑设施容量有限的情形,并将袭击前后关于应急设施的选址、定容和救援物资分配问题进行集成考虑。将该问题构造为三层规划模型,上中下各层规划分别对应袭击前的选址定容问题、袭击时的袭击点选择问题和袭击后的救援物资分配问题。利用下层规划的对偶变换转化为双层规划,并设计Benders分解算法求解。最后,结合南疆交通网络进行仿真分析,验证了模型和算法的有效性。     

给定限期条件下应急选址问题的量子竞争决策算法

为求解给定期限条件的应急设施选址问题,本文提出了一种量子竞争决策算法.将量子个体作为博弈者参与到竞争决策中,利用量子位、叠加态等理论提高竞争群体多样性,缩小群体规模,加快优化速度;基于进化博弈论中博弈者学习和策略调整的机制,实现竞争者学习和自演化的目的,增强算法的寻优能力.实验结果表明算法的可行性和有效性.     

范数下无容量限制设施选址逆问题的求解方法

一个优化问题的逆问题是这样一类问题,在给定该优化问题的一个可行解时,通过最小化目标函数中参数的改变量(在某个范数下)使得该可行解成为改变参数后的该优化问题的最优解。对于本是NP-难问题的无容量限制设施选址问题,证明了其逆问题仍是NP-难的。研究了使用经典的行生成算法对无容量限制设施选址的逆问题进行计算,并给出了求得逆问题上下界的启发式方法。两种方法分别基于对子问题的线性松弛求解给出上界和利用邻域搜索以及设置迭代循环次数的方式给出下界。数值结果表明线性松弛法得到的上界与最优值差距较小,但求解效率提升不大;而启发式方法得到的下界与最优值差距极小,极大地提高了求解该逆问题的效率。     

An improved Benders decomposition algorithm for the tree of hubs location problem

The tree of hubs location problem is a particularly hard variant of the so called hub location problems. When solving this problem by a Benders decomposition approach, it is necessary to deal with both optimality and feasibility cuts. While modern implementations of the Benders decomposition method rely on Pareto-optimal optimality cuts or on rendering feasibility cuts based on minimal infeasible subsystems, a new cut selection scheme is devised here under the guiding principle of extracting useful information even when facing infeasible subproblems. The proposed algorithm outperforms two other modern variants of the method and it is capable of optimally solving instances five times larger than the ones previously reported on the literature.     

An improved origin-based algorithm for solving the combined distribution and assignment problem

This paper is to further study the origin-based (OB) algorithm for solving the combined distribution and assignment (CDA) problem, where the trip distribution follows a gravity model and the traffic assignment is a user-equilibrium model. Recently, the OB algorithm has shown to be superior to the Frank–Wolfe (FW) algorithm for the traffic assignment (TA) problem and better than the Evans’ algorithm for the CDA problem in both computational time and solution accuracy. In this paper, a modified origin–destination (OD) flow update strategy proposed by Huang and Lam [Huang, H.J., Lam, W.H.K., 1992. Modified Evans’ algorithms for solving the combined trip distribution and assignment problem. Transportation Research B 26 (4), 325–337] for CDA with the Evans’ algorithm is adopted to improve the OB algorithm for solving the CDA problem. Convergence proof of the improved OB algorithm is provided along with some preliminary computational results to demonstrate the effect of the modified OD flow update strategy embedded in the OB algorithm.     

An exact algorithm for solving the bilevel facility interdiction and fortification problem

We present an exact approach for solving the $r$-interdiction median problem with fortification. Our approach consists of solving a greedy heuristic and a set cover problem iteratively that guarantees to find an optimal solution upon termination. The greedy heuristic obtains a feasible solution to the problem, and the set cover problem is solved to verify optimality of the solution and to provide a direction for improvement if not optimal. We demonstrate the performance of the algorithm in a computational study.     

An acceleration of Erlenkotter-Körkel’s algorithms for the uncapacitated facility location problem

This contribution is focused on an acceleration of branch and bound algorithms for the uncapacitated facility location problem. Our approach is based on the well-known Erlenkotters’ procedures and Körkels’ multi-ascent and multi-adjustment algorithms, which have proved to be the efficient tools for solving the large-sized instances of the uncapacitated facility location problem. These two original approaches were examined and a thorough analysis of their performance revealed how each particular procedure contributes to the computational time of the whole algorithms. These analyses helped us to focus our effort on the most frequent procedures. The unique contribution of this paper is a new dual ascent procedure. This procedure leads to considerable acceleration of the lower bound computation process and reduces the resulting computational time. To demonstrate more efficient performance of amended algorithms we present the results of extensive numerical experiments.     

An ensemble of discrete differential evolution algorithms for solving the generalized traveling salesman problem

In this paper, an ensemble of discrete differential evolution algorithms with parallel populations is presented. In a single populated discrete differential evolution (DDE) algorithm, the destruction and construction (DC) procedure is employed to generate the mutant population whereas the trial population is obtained through a crossover operator. The performance of the DDE algorithm is substantially affected by the parameters of DC procedure as well as the choice of crossover operator. In order to enable the DDE algorithm to make use of different parameter values and crossover operators simultaneously, we propose an ensemble of DDE (eDDE) algorithms where each parameter set and crossover operator is assigned to one of the parallel populations. Each parallel parent population does not only compete with offspring population generated by its own population but also the offspring populations generated by all other parallel populations which use different parameter settings and crossover operators. As an application area, the well-known generalized traveling salesman problem (GTSP) is chosen, where the set of nodes is divided into clusters so that the objective is to find a tour with minimum cost passing through exactly one node from each cluster. The experimental results show that none of the single populated variants was effective in solving all the GTSP instances whereas the eDDE performed substantially better than the single populated variants on a set of problem instances. Furthermore, through the experimental analysis of results, the performance of the eDDE algorithm is also compared against the best performing algorithms from the literature. Ultimately, all of the best known averaged solutions for larger instances are further improved by the eDDE algorithm.     

An optimization approach for ambulance location and the districting of the response segments on highways

In this paper we present a method to optimize the configuration and operation of emergency medical systems on highways. Different from the approaches studied in the previous papers, the present method can support two combined configuration decisions: the location of ambulance bases along the highway and the districting of the response segments. For example, this method can be used to make decisions regarding the optimal location and coverage areas of ambulances in order to minimize mean user response time or remedy an imbalance in ambulance workloads within the system. The approach is based on embedding a well-known spatially distributed queueing model (hypercube model) into a hybrid genetic algorithm to optimize the decisions involved. To illustrate the application of the proposed method, we utilize two case studies on Brazilian highways and validate the findings via a discrete event simulation model.     

An Evolutionary Approach for the Design and Scheduling of Electroplating Facilities

This paper tackles the Cyclic Hoists Scheduling Problem. This problem is often encountered in electroplating facilities when mass production is required. Then a repetitive sequence of moves is searched for the hoists. We more precisely deal with a global optimization problem that simultaneously considers the design and the scheduling of such production lines. It consists in studying systems integrating several transportation resources, called hoists, by minimizing the cycle time, while minimizing the number of hoists used. To achieve these goals, we use an evolutionary approach. The encoding of one solution is based on the representation of the empty moves of the hoists. To evaluate each individual, we propose a linear programming model. This one both verifies the satisfaction of constraints and provides the best cycle time for the considered number of hoists. This contribution describes a promising approach to solving a simple version of this problem, namely cyclic hoist scheduling, based on Evolutionary Algorithms (EAs), which is an optimization method inspired by biological evolution models. The issues of solution encoding and specialised genetic operators with a repair procedure of the infeasible solutions are discussed. Some results are presented with benchmark examples.      

Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems

An algorithm for solving a nonsingular symmetric system of linear equations with a saddle point is examined. This algorithm has two constant iteration parameters and is an extension of the algorithm of Hermitian and skew-Hermitian splitting iterations (the HSS algorithm). Analytical formulas are derived for the optimal values of the iteration parameters. The formulation of the optimization problem is a classical one for the saddle-point problems. The results obtained are sharp.     

An extension of the Tau numerical algorithm for the solution of linear and nonlinear Lane–Emden equations

The purpose of this paper is to present a numerical algorithm for solving the Lane–Emden equations as singular initial value problems. The proposed algorithm is based on an operational Tau method (OTM). The main idea behind the OTM is to convert the desired problem to some operational matrices. Firstly, we use a special integral operator and convert the Lane–Emden equations to integral equations. Then, we use OTM to linearize the integral equations to some operational matrices and convert the problem to an algebraic system. The concepts, properties, and advantages of OTM and its application for solving Lane–Emden equations are presented. Some orthogonal polynomials are also used to reduce the volume of computations. Finally, several experiments of Lane–Emden equations including linear and nonlinear terms are given to illustrate the validity and efficiency of the proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd.