An inverse approach to convex ordered median problems in trees

The convex ordered median problem is a generalization of the median, the k-centrum or the center problem. The task of the associated inverse problem is to change edge lengths at minimum cost such that a given vertex becomes an optimal solution of the location problem, i.e., an ordered median. It is shown that the problem is NP-hard even if the underlying network is a tree and the ordered median problem is convex and either the vertex weights are all equal to 1 or the underlying problem is the k-centrum problem. For the special case of the inverse unit weight k-centrum problem a polynomial time algorithm is developed.     

基于非概率可靠性的铁路应急设施选址-路径鲁棒优化

鉴于铁路应急设施选址研究中很难合理估计参数的概率分布或确定其隶属函数的问题,将选址-路径问题与区间非概率可靠性方法结合起来,以复杂网络理论为基础,提出网络节点区间权重的确定方法,同时考虑节点权重、边权及径权区间不确定性的共同作用,构建铁路应急设施选址节点加权网络。基于区间非概率可靠性理论及区间运算规则,提出路径的非概率可靠性度量及最优时间可靠度路径选择方法,建立节点权重、边权及径权均为区间数的非概率可靠性铁路应急设施选址-路径鲁棒优化模型,并给出了求解算法,确定了基于区间模型的铁路应急设施鲁棒选址的最优方案。算例表明,本文的优化方案能更好地保证救援的时间鲁棒性,能有效地规避不确定因素波动对设施选址的长期风险,具有很好的实际应用价值。     

Two-level network design with intermediate facilities: An application to electrical distribution systems

We consider the two-level network design problem with intermediate facilities. This problem consists of designing a minimum cost network respecting some requirements, usually described in terms of the network topology or in terms of a desired flow of commodities between source and destination vertices. Each selected link must receive one of two types of edge facilities and the connection of different edge facilities requires a costly and capacitated vertex facility. We propose a hybrid decomposition approach which heuristically obtains tentative solutions for the vertex facilities number and location and use these solutions to limit the computational burden of a branch-and-cut algorithm. We test our method on instances of the power system secondary distribution network design problem. The results show that the method is efficient both in terms of solution quality and computational times.     

Approximating soft-capacitated facility location problem with uncertainty

In this paper we devise the stochastic and robust approaches to study the soft-capacitated facility location problem with uncertainty. We first present a new stochastic soft-capacitated model called The 2-Stage Soft Capacitated Facility Location Problem and solve it via an approximation algorithm by reducing it to linear-cost version of 2-stage facility location problem and dynamic facility location problem. We then present a novel robust model of soft-capacitated facility location, The Robust Soft Capacitated Facility Location Problem. To solve it, we improve the approximation algorithm proposed by Byrka et al. (LP-rounding algorithms for facility-location problems. CoRR, 2010a) for RFTFL and then treat it similarly as in the stochastic case. The improvement results in an approximation factor of \(\alpha + 4\) for the robust fault-tolerant facility location problem, which is best so far.     

Constrained pairwise and center-star sequences alignment problems

This paper considers the minimax regret vertex 2-sink location problem in a dynamic path network with positive edge lengths and uniform edge capacity. Let \(P\) be an undirected path graph of \(n\) vertices, and the weight (initial supply) of every vertex is known as an interval. The problem is to find two vertices \(x\) and \(y\) as two sinks on the path such that all the weights can evacuate to \(x\) and \(y\) with minimum regret of evacuation time in case of an emergency for any possible weight distribution. We present an \(O(n^3\log n)\) time algorithm.     

Median problems with positive and negative weights on cycles and cacti

This paper deals with facility location problems on graphs with positive and negative vertex weights. We consider two different objective functions: In the first one (MWD) vertices with positive weight are assigned to the closest facility, whereas vertices with negative weight are assigned to the farthest facility. In the second one (WMD) all the vertices are assigned to the nearest facility. For the MWD model it is shown that there exists a finite set of points in the graph which contains the locations of facilities in an optimal solution. Furthermore, algorithms for both models for the 2-median problem on a cycle are developed. The algorithm for the MWD model runs in linear time, whereas the algorithm for the WMD model has a time complexity of  O(n²)\mathcal{O}(n^{2}) .     

具有遗憾值约束的鲁棒供应链网络设计模型研究

考虑不确定性环境,研究战略层次的供应链网络鲁棒设计问题,目标是设计参数发生摄动时,供应链性能能够保持稳健性。基于鲁棒解的定义,建立从上游供应商选择到下游设施选址-需求分配的供应链网络设计鲁棒优化模型;提出确定遗憾值限定系数上限和下限的方法,允许决策者调节鲁棒水平,选择多种供应链网络结构;通过模型分解与协调,设计了供应链节点配置的禁忌搜索算法。算例的计算结果表明了禁忌搜索算法具有良好的收敛特性,以及在处理大规模问题上的优越性;同时也反映了利用鲁棒优化模型进行供应链网络设计,可以有效规避投资风险。     

An improved approximation algorithm for uncapacitated facility location problem with penalties

In this paper, we consider an interesting variant of the classical facility location problem called uncapacitated facility location problem with penalties (UFLWP for short) in which each client is either assigned to an opened facility or rejected by paying a penalty. The UFLWP problem has been effectively used to model the facility location problem with outliers. Three constant approximation algorithms have been obtained (Charikar et al. in Proceedings of the Symposium on Discrete Algorithms, pp. 642–651, 2001; Jain et al. in J. ACM 50(6):795–824, 2003; Xu and Xu in Inf. Process. Lett. 94(3):119–123, 2005), and the best known performance ratio is 2. The only known hardness result is a 1.463-inapproximability result inherited from the uncapacitated facility location problem (Guha and Khuller in J. Algorithms 31(1):228–248, 1999). In this paper, We present a 1.8526-approximation algorithm for the UFLWP problem. Our algorithm significantly reduces the gap between known performance ratio and the inapproximability result. Our algorithm first enhances the primal-dual method for the UFLWP problem (Charikar et al. in Proceedings of the Symposium on Discrete Algorithms, pp. 642–651, 2001) so that outliers can be recognized more efficiently, and then applies a local search heuristic (Charikar and Guha in Proceedings of the 39th IEEE Symposium on Foundations of Computer Science, pp. 378–388, 1999) to further reduce the cost for serving those non-rejected clients. Our algorithm is simple and can be easily implemented. The research of this work was supported in part by NSF through CAREER award CCF-0546509 and grant IIS-0713489. A preliminary version of this paper appeared in the Proceedings of the 11th Annual International Computing and Combinatorics Conference (COCOON’05).     

Approximation strategy-proof mechanisms for obnoxious facility location on a line

In the facility location game on a line, there are some agents who have fixed locations on the line where an obnoxious facility will be placed. The objective is to maximize the social welfare, e.g., the sum of distances from the facility to all agents. On collecting location information, agents may misreport the locations so as to stay far away from the obnoxious facility. In this paper, strategy-proof mechanisms are designed and the approximation ratio is used to measure the performances of the strategy-proof mechanisms. Two objective functions, maximizing the sum of squares of distances (maxSOS) and maximizing the sum of distances (maxSum), have been considered. For maxSOS, a randomized 5/3-approximated strategy-proof mechanism is proposed, and the lower bound of the approximation ratio is proved to be at least 1.042. For maxSum, the lower bound of the approximation ratio of the randomized strategy-proof mechanism is proved to be 1.077. Moreover, a general model is considered that each agent may have multiple locations on the line. For the objective functions maxSum and maxSOS, both deterministic and randomized strategy-proof mechanisms are investigated, and the deterministic mechanisms are shown to be best possible.     

The inverse 1-center problem on trees with variable edge lengths under Chebyshev norm and Hamming distance

This paper addresses the problem of modifying the edge lengths of a tree in minimum total cost such that a prespecified vertex becomes the 1-center of the perturbed tree. This problem is called the inverse 1-center problem on trees. We focus on the problem under Chebyshev norm and Hamming distance. From special properties of the objective functions, we can develop combinatorial algorithms to solve the problem. Precisely, if there does not exist any vertex coinciding with the prespecified vertex during the modification of edge lengths, the problem under Chebyshev norm or bottleneck Hamming distance is solvable in \(O(n\log n)\) time, where \(n+1\) is the number of vertices of the tree. Dropping this condition, the problem can be solved in \(O(n^{2})\) time.     

Approximation Algorithms for Certain Network Improvement Problems

We study budget constrained network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V, E), in the edge based upgrading model, it is assumed that each edge e of the given network also has an associated function ce (t) that specifies the cost of upgrading the edge by an amount t. A reduction strategy specifies for each edge e the amount by which the length (e) is to be reduced. In the node based upgrading model, a node v can be upgraded at an expense of c(v). Such an upgrade reduces the delay of each edge incident on v. For a given budget B, the goal is to find an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph (e.g. minimum spanning tree) under the modified edge lengths is the best over all possible strategies which obey the budget constraint.After providing a brief overview of the models and definitions of the various problems considered, we present several new results on the complexity and approximability of network improvement problems.     

Managing consumer returns in high clockspeed industries

In this study, we address control policies to manage the collection of products that have been returned by consumers to retailers after they have been sold. Specifically, we model a consumer returns process where the operational decision of interest is the frequency in which returns are picked up from a collection point and then processed at a centralized location. Returns decay in value over time according to their industry clockspeed. Hence there is an intrinsic tradeoff in the decision – a longer interval between collections not only reduces transportation cost, but also reduces the value of asset recovery.We analyze a stylized model with a single collection point and a centralized returns processing center. Given an asset decay rate and a fixed transportation cost we determine the optimal collection interval. We later expand the analysis to the case of a capacitated returns processing center. We also explore the value of information (number of returns held at the collection point) sharing between a collection point and the central processing facility. We find that the voi is quite sensitive to parametric settings ranging upwards to over 20% with a median value of 5.0%. We find that the voi increases with respect to the asset value decay rate and the rate of returns, while it decreases with respect to the shipping cost.     

Developing and Testing a Facility Location Model for Canadian Nuclear Fuel Waste

The purpose of this paper is to develop and test a facility location model for the siting of a nuclear fuel waste disposal facility in Canada. The model is based on successful Canadian siting processes related to hazardous waste and low level radioactive waste facilities, as well as attributes of facility siting found in the literature. The proposed model was presented to a sample of participants in the federal environmental assessment review of the technical feasibility of the Canadian Nuclear Fuel Waste Disposal Concept (CNFWDC) held throughout Canada in 1990. Results demonstrate that despite the fact that over half of the survey respondents did not support the CNFWDC during the public hearings, the majority favorably rated the proposed facility location model. Components of the model that were tested included siting criteria and goals, decision-making groups, and siting safeguards. On the basis of these results, it is concluded that the siting of a nuclear fuel waste disposal facility must make the decentralization of decision-making authority to local communities and governments a priority.     

Line facility location in weighted regions

In this paper, we present approximation algorithms for solving the line facility location problem in weighted regions. The weighted region setup is a more realistic model for many facility location problems that arise in practical applications. Our algorithms exploit an interesting property of the problem, that could possibly be used for solving other problems in weighted regions.     

Approximation Algorithms for Bounded Facility Location Problems

The bounded k-median problem is to select in an undirected graph G = (V,E) a set S of k vertices such that the distance from any vertex v V to S is at most a given bound d and the average distance from vertices V\S to S is minimized. We present randomized algorithms for several versions of this problem and we prove some inapproximability results. We also study the bounded version of the uncapacitated facility location problem and present extensions of known deterministic algorithms for the unbounded version.     

Strategyproof mechanism design for facility location games with weighted agents on a line

Approximation mechanism design without money was first studied in Procaccia and Tennenholtz (2009) by considering a facility location game. In general, a facility is being opened and the cost of an agent is measured by its distance to the facility. In order to achieve a good social cost, a mechanism selects the location of the facility based on the locations reported by agents. It motivates agents to strategically report their locations to get good outcomes for themselves. A mechanism is called strategyproof if no agents could manipulate to get a better outcome by telling lies regardless of any configuration of other agents. The main contribution in this paper is to explore the strategyproof mechanisms without money when agents are distinguishable. There are two main variations on the nature of agents. One is that agents prefer getting closer to the facility, while the other is that agents prefer being far away from the facility. We first consider the model that directly extends the model in Procaccia and Tennenholtz (2009). In particular, we consider the strategyproof mechanisms without money when agents are weighted. We show that the strategyproof mechanisms in the case of unweighted agents are still the best in the weighted cases. We establish tight lower and upper bounds for approximation ratios on the optimal social utility and the minimum utility when agents prefer to stay close to the facility. We then provide the lower and upper bounds on the optimal social utility and lower bound on the minimum distance per weight when agents prefer to stay far away from the facility. We also extend our study in a natural direction where two facilities must be built on a real line. Secondly, we propose an novel threshold based model to distinguish agents. In this model, we present a strategyproof mechanism that leads to optimal solutions in terms of social cost.     

α-鲁棒随机截流选址问题的模型和算法

由于选址决策的长期性,相关参数会随着时间而变化,所以选址问题存在很多不确定因素。本文通过不同的情景来处理截流问题中流量的不确定性,并结合随机优化和鲁棒优化,提出α-鲁棒随机截流选址模型。该模型规定了在各情景下的相对后悔值不超过α的条件下,使截得的流量的期望值最大,该条件称为α-鲁棒约束。本文将该模型建立成为一个线性0-1整数规划,并给出了改进型贪婪算法和拉格朗日启发式算法。最后,本文使用这两种算法对不同规模的截流选址问题进行了研究。     

A unified dual-fitting approximation algorithm for the facility location problems with linear/submodular penalties

In this paper, we study two variants of the classical facility location problem, namely, the facility location problem with linear penalties (FLPLP) and the facility location problem with submodular penalties (FLPSP), respectively. We give a unified dual-fitting based approximation algorithm for these two problems, yielding approximation ratios 2 and 3 respectively.     

Genetic algorithms for optimization of a mine system under uncertainty

The production planning of a mine system associated with mining, processing and refining stages dictates to determine optimal system parameters such as optimal production rates, location of refining facility and the best reconstruction time of production rates. This paper proposes a combination of the chance constrained programming (CCP) and the genetic algorithms (GA) to find the optimal system parameters simultaneously. In generic form the problem is expressed as the maximization of net present value of future cash flows such that the capacity constraint and predefined specifications are satisfied. The blending requirements expressed in the CCP are transformed into deterministic equivalents. A new form of the problem is solved by the GA. The approach was demonstrated on extraction, processing and refining of four iron ore mines with varying reserves, ore qualities, geological and topographic conditions, four mineral processing units and one refining facility. The results showed that the proposed algorithm could be used to determine optimal production rates, the facility location and the best reconstruction time.     

A Bicriterion Maximal Covering Location Formulation Which Considers the Satisfaction of Uncovered Demand

There have been many applications of the maximal covering location problem (MCLP). An underlying assumption of the MCLP is that demand not covered (i.e., not within a prespecified maximal distance of a facility) is not served. This may be an unrealistic assumption in many location planning scenarios, especially in the public sector. For example, in cases such as fire protection or ambulance service, calls not technically covered will still be serviced. The MCLP, however, does not consider the distances or travel times necessary to service such demand. This paper presents a bicriterion locational covering model which explicitly considers the travel distance or time necessary to service demand not within the maximal covering distance of a facility. The model may be used to generate noninferior (Pareto optimal) siting configurations which demonstrate the inherent trade-offs between a siting scheme designed to maximize total coverage and one designed to minimize total travel time for uncovered demand to reach its nearest facility. In addition, it is shown that for any particular weighting scheme on the two objectives, the problem can be solved as a p-median problem; a problem for which several efficient solution methods exist.