develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining...develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.展开更多
In the k-product uncapacitated facility location problem with penalties,we are given a set of demand points where clients are located and a set of potential sites where facilities with unlimited capacities can be open...In the k-product uncapacitated facility location problem with penalties,we are given a set of demand points where clients are located and a set of potential sites where facilities with unlimited capacities can be opened.There are k different kinds of products to be supplied by a set of open facilities.Each open facility can supply only a distinct product with a non-negative fixed cost determined by the product it wants to supply.Each client is either supplied with k kinds of products by a set of k different open facilities or completely rejected.There is a non-negative service cost between each pair of locations and also a penalty cost for each client if its service is rejected.These service costs are assumed to be symmetric and satisfy the triangle inequality.The goal is to select a set of clients to reject their service and then choose a set of facilities to be opened to service the remaining clients so that the total cost of opening facilities,servicing the clients,and the penalty is minimized.We address two different integer programs to describe the problem.Based on the linear programming rounding technique,we propose a(2k+1)-approximation algorithm for this problem.展开更多
In this paper, we study the dynamic facility location problem with submodular penalties （DFLPSP）. We present a combinatorial primal-dual 3-approximation algorithm for the DFLPSP.
The differential evolution algorithm is an evolutionary algorithm for global optimization and the un-capacitated facility location problem (UFL) is one of the classic NP-Hard problems. In this paper, combined with the...The differential evolution algorithm is an evolutionary algorithm for global optimization and the un-capacitated facility location problem (UFL) is one of the classic NP-Hard problems. In this paper, combined with the specific characteristics of the UFL problem, we introduce the activation function to the algorithm for solving UFL problem and name it improved adaptive differential evolution algorithm (IADEA). Next, to improve the efficiency of the algorithm and to alleviate the problem of being stuck in a local optimum, an adaptive operator was added. To test the improvement of our algorithm, we compare the IADEA with the basic differential evolution algorithm by solving typical instances of UFL problem respectively. Moreover, to compare with other heuristic algorithm, we use the hybrid ant colony algorithm to solve the same instances. The computational results show that IADEA improves the performance of the basic DE and it outperforms the hybrid ant colony algorithm.展开更多
We consider the k-level facility location problem with soft capacities （k-LFLPSC）. In the k- LFLPSC, each facility i has a soft capacity ui along with an initial opening cost fi ≥O, i.e., the capacity of facility i...We consider the k-level facility location problem with soft capacities （k-LFLPSC）. In the k- LFLPSC, each facility i has a soft capacity ui along with an initial opening cost fi ≥O, i.e., the capacity of facility i is an integer multiple of ui incurring a cost equals to the corresponding multiple of fi. We firstly propose a new bifactor （ln（1/β）/（1 -β）, 1 ＋ 2/（1 - β））-approximation algorithm for the k-level facility location problem （k-LFLP）, where β∈（0, 1） is a fixed constant. Then, we give a reduction from the k-LFLPSC to the k-LFLP. The reduction together with the above bifactor approximation algorithm for the k-LFLP imply a 5.5053-approximation algorithm for the k-LFLPSC which improves the previous 6-approximation.展开更多
In this paper,we consider the risk-adjusted two-stage stochastic facility location problem with penalties(RSFLPP).Using the monotonicity and positive homogeneity of the risk measure function,we present an LP-roundin...In this paper,we consider the risk-adjusted two-stage stochastic facility location problem with penalties(RSFLPP).Using the monotonicity and positive homogeneity of the risk measure function,we present an LP-rounding-based 6-approximation algorithm.展开更多
In this paper,we study a stochastic version of the fault-tolerant facility location problem.By exploiting the stochastic structure,we propose a 5-approximation algorithm which uses the LP-rounding technique based on t...In this paper,we study a stochastic version of the fault-tolerant facility location problem.By exploiting the stochastic structure,we propose a 5-approximation algorithm which uses the LP-rounding technique based on the revised optimal solution to the linear programming relaxation of the stochastic fault-tolerant facility location problem.展开更多
Capacitated facility location problem(CFLP)is a classical combinatorial optimization problem that has various applications in operations research,theoretical computer science,and management science.In the CFLP,we have...Capacitated facility location problem(CFLP)is a classical combinatorial optimization problem that has various applications in operations research,theoretical computer science,and management science.In the CFLP,we have a potential facilities set and a clients set.Each facility has a certain capacity and an open cost,and each client has a spliitable demand that need to be met.The goal is to open some facilities and assign all clients to these open facilities so that the total cost is as low as possible.The CFLP is NP-hard(non-deterministic polynomial-hard),and a large amount of work has been devoted to designing approximation algorithms for CFLP and its variants.Following this vein,we introduce a new variant of CFLP called capacitated uniform facility location problem with soft penalties(CUFLPSP),in which the demand of each client can be partially rejected by paying penalty costs.As a result,we present a linear programming-rounding(LP-rounding)based 5.5122-approximation algorithm for the CUFLPSP.展开更多
In this paper,we propose the Priority Facility Location Problem with Outliers(PFLPO),which is a generalization of both the Facility Location Problem with Outliers(FLPO)and Priority Facility Location Problem(PFLP).As o...In this paper,we propose the Priority Facility Location Problem with Outliers(PFLPO),which is a generalization of both the Facility Location Problem with Outliers(FLPO)and Priority Facility Location Problem(PFLP).As our main contribution,we use the technique of primal-dual to provide a 3-approximation algorithm for the PFLPO.We also give two heuristic algorithms.One of them is a greedy-based algorithm and the other is a local search algorithm.Moreover,we compare the experimental results of all the proposed algorithms in order to illustrate their performance.展开更多
In this work, the Lagrangean Relaxation method has been discussed to solve different sizes of capacitated facility location problem (CFLP). A good lower bound has been achieved on the solution of the CFLP considered i...In this work, the Lagrangean Relaxation method has been discussed to solve different sizes of capacitated facility location problem (CFLP). A good lower bound has been achieved on the solution of the CFLP considered in this paper. This lower bound has been improved by using the Volume algorithm. The methods of setting two important parameters in heuristic have been given. The approaches used to gain the lower bound have been explained. The results of this work have been compared with the known results given by Beasley.展开更多
Given m facilities each with an opening cost, n demands, and distance between every demand and facility, the Facility Location problem finds a solution which opens some facilities to connect every demand to an opened ...Given m facilities each with an opening cost, n demands, and distance between every demand and facility, the Facility Location problem finds a solution which opens some facilities to connect every demand to an opened facility such that the total cost of the solution is minimized. The κ-Facility Location problem further requires that the number of opened facilities is at most κ, where κ is a parameter given in the instance of the problem. We consider the Facility Location problems satisfying that for every demand the ratio of the longest distance to facilities and the shortest distance to facilities is at most ω, where ω is a predefined constant. Using the local search approach with scaling technique and error control technique, for any arbitrarily small constant ε 〉 0, we give a polynomial-time approximation algorithm for the ω-constrained Facility Location problem with approximation ratio 1 ＋ √ω ＋ ε, which significantly improves the previous best known ratio （ω ＋ 1）/α for some 1 ≤ α ≤2, and a polynomial-time approximation algorithm for the ω-constrained κ- Facility Location problem with approximation ratio ω ＋ 1 ＋ ε. On the aspect of approximation hardness, we prove that unless NP C DTIME（n^O（log log n））, the ω-constrained Facility Location problem cannot be approximated within 1 ＋ln √ω 1, which slightly improves the previous best known hardness result 1.243 ＋ 0.316 ln（ω - 1）. The experimental results on the standard test instances of Facility Location problem show that our algorithm also has good performance in practice.展开更多
In this paper, we consider the fault-tolerant concave facility location problem （FTCFL） with uniform requirements. By investigating the structure of the FTCFL, we obtain a modified dual-fitting bifactor approximatio...In this paper, we consider the fault-tolerant concave facility location problem （FTCFL） with uniform requirements. By investigating the structure of the FTCFL, we obtain a modified dual-fitting bifactor approximation algorithm. Combining the scaling and greedy argumentation technique, the approximation factor is proved to be 1.52.展开更多
We study the two-stage stochastic facility location problem(2-SFLP)by proposing an LP(location problem)-rounding approximation algorithm with 2.3613 per-scenario bound for this problem,improving the previously best pe...We study the two-stage stochastic facility location problem(2-SFLP)by proposing an LP(location problem)-rounding approximation algorithm with 2.3613 per-scenario bound for this problem,improving the previously best per-scenario bound of 2.4957.展开更多
Layout design problem is to determine a suitable arrangement for the departments so that the total costs associated with the flow among departments become least. Single Row Facility Layout Problem, SRFLP, is one of &l...Layout design problem is to determine a suitable arrangement for the departments so that the total costs associated with the flow among departments become least. Single Row Facility Layout Problem, SRFLP, is one of </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">layout problems that have many practical applications. This problem and its specific scenarios are often used to model many of the raised issues in the field of facility location. SRFLP is an arrangement of </span><i><span style="font-family:Verdana;">n</span></i><span style="font-family:Verdana;"> departments with a specified length in a straight line so that the sum of the weighted distances between the pairs of departments is minimized. This problem is NP-hard. In this paper, first, a lower bound for a special case of SRFLP is presented. Then, a general </span><span style="font-family:Verdana;">case of SRFLP is presented in which some new and real assumptions are added to generate more practical model. Then a lower bound, as well as an algorithm, is proposed for solving the model. Experimental results on some instances in literature show the efficiency of our algorithm.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11371001
文摘develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.
基金supported by the National Natural Science Foundation of China(No.11971252)。
文摘In the k-product uncapacitated facility location problem with penalties,we are given a set of demand points where clients are located and a set of potential sites where facilities with unlimited capacities can be opened.There are k different kinds of products to be supplied by a set of open facilities.Each open facility can supply only a distinct product with a non-negative fixed cost determined by the product it wants to supply.Each client is either supplied with k kinds of products by a set of k different open facilities or completely rejected.There is a non-negative service cost between each pair of locations and also a penalty cost for each client if its service is rejected.These service costs are assumed to be symmetric and satisfy the triangle inequality.The goal is to select a set of clients to reject their service and then choose a set of facilities to be opened to service the remaining clients so that the total cost of opening facilities,servicing the clients,and the penalty is minimized.We address two different integer programs to describe the problem.Based on the linear programming rounding technique,we propose a(2k+1)-approximation algorithm for this problem.
基金Supported in part by Hebei Province Department of Education Fund under Grant No.Z2012017the National Natural Science Foundation of China under Grant No.11371001 and 11201013
文摘In this paper, we study the dynamic facility location problem with submodular penalties （DFLPSP）. We present a combinatorial primal-dual 3-approximation algorithm for the DFLPSP.
文摘The differential evolution algorithm is an evolutionary algorithm for global optimization and the un-capacitated facility location problem (UFL) is one of the classic NP-Hard problems. In this paper, combined with the specific characteristics of the UFL problem, we introduce the activation function to the algorithm for solving UFL problem and name it improved adaptive differential evolution algorithm (IADEA). Next, to improve the efficiency of the algorithm and to alleviate the problem of being stuck in a local optimum, an adaptive operator was added. To test the improvement of our algorithm, we compare the IADEA with the basic differential evolution algorithm by solving typical instances of UFL problem respectively. Moreover, to compare with other heuristic algorithm, we use the hybrid ant colony algorithm to solve the same instances. The computational results show that IADEA improves the performance of the basic DE and it outperforms the hybrid ant colony algorithm.
基金supported in part by Natural Science Foundation of China under Grant No.11501412supported by Natural Science Foundation of China under Grant No.11531014
文摘We consider the k-level facility location problem with soft capacities （k-LFLPSC）. In the k- LFLPSC, each facility i has a soft capacity ui along with an initial opening cost fi ≥O, i.e., the capacity of facility i is an integer multiple of ui incurring a cost equals to the corresponding multiple of fi. We firstly propose a new bifactor （ln（1/β）/（1 -β）, 1 ＋ 2/（1 - β））-approximation algorithm for the k-level facility location problem （k-LFLP）, where β∈（0, 1） is a fixed constant. Then, we give a reduction from the k-LFLPSC to the k-LFLP. The reduction together with the above bifactor approximation algorithm for the k-LFLP imply a 5.5053-approximation algorithm for the k-LFLPSC which improves the previous 6-approximation.
基金This work was supported by Scientific Research Common Program of Beijing Municipal Commission of Education(No.KM201210005033)and China Scholarship CouncilThe authors would like to thank the two anonymous referees for many helpful suggestions.
文摘In this paper,we consider the risk-adjusted two-stage stochastic facility location problem with penalties(RSFLPP).Using the monotonicity and positive homogeneity of the risk measure function,we present an LP-rounding-based 6-approximation algorithm.
基金C.Wu was supported by National Natural Science Foundation of China(Grant No.11071268)D.Xu was supported by National Natural Science Foundation of China(Grant No.11371001)+2 种基金Scientific Research Common Program of Beijing Municipal Commission of Education(Grant No.KM201210005033)China Scholarship Council.J.Shu was supported by National Natural Science Foundation of China(Grant Nos.70801014,71171047,and 71222103)The authors would like to thank the two anonymous referees for many helpful suggestions.
文摘In this paper,we study a stochastic version of the fault-tolerant facility location problem.By exploiting the stochastic structure,we propose a 5-approximation algorithm which uses the LP-rounding technique based on the revised optimal solution to the linear programming relaxation of the stochastic fault-tolerant facility location problem.
基金supported by the National Natural Science Foundation of China(Nos.11971349,12071442,12371320,and 12371318).
文摘Capacitated facility location problem(CFLP)is a classical combinatorial optimization problem that has various applications in operations research,theoretical computer science,and management science.In the CFLP,we have a potential facilities set and a clients set.Each facility has a certain capacity and an open cost,and each client has a spliitable demand that need to be met.The goal is to open some facilities and assign all clients to these open facilities so that the total cost is as low as possible.The CFLP is NP-hard(non-deterministic polynomial-hard),and a large amount of work has been devoted to designing approximation algorithms for CFLP and its variants.Following this vein,we introduce a new variant of CFLP called capacitated uniform facility location problem with soft penalties(CUFLPSP),in which the demand of each client can be partially rejected by paying penalty costs.As a result,we present a linear programming-rounding(LP-rounding)based 5.5122-approximation algorithm for the CUFLPSP.
基金supported by the Beijing Municipal Natural Science Foundation(No.Z220004)the National Natural Science Foundation of China(Nos.12371321,12171051,and 12171052)the Research Innovation Fund for College Students of Beijing University of Posts and Telecommunications.
文摘In this paper,we propose the Priority Facility Location Problem with Outliers(PFLPO),which is a generalization of both the Facility Location Problem with Outliers(FLPO)and Priority Facility Location Problem(PFLP).As our main contribution,we use the technique of primal-dual to provide a 3-approximation algorithm for the PFLPO.We also give two heuristic algorithms.One of them is a greedy-based algorithm and the other is a local search algorithm.Moreover,we compare the experimental results of all the proposed algorithms in order to illustrate their performance.
文摘In this work, the Lagrangean Relaxation method has been discussed to solve different sizes of capacitated facility location problem (CFLP). A good lower bound has been achieved on the solution of the CFLP considered in this paper. This lower bound has been improved by using the Volume algorithm. The methods of setting two important parameters in heuristic have been given. The approaches used to gain the lower bound have been explained. The results of this work have been compared with the known results given by Beasley.
基金Supported by the National Natural Science Foundation of China for Distinguished Young Scholars under Grant No. 60325206the National Natural Science Foundation of China for Major International (Regional) Joint Research Project under Grant No. 60310213the National Natural Science Foundation of China under Grant No. 60573024.
文摘Given m facilities each with an opening cost, n demands, and distance between every demand and facility, the Facility Location problem finds a solution which opens some facilities to connect every demand to an opened facility such that the total cost of the solution is minimized. The κ-Facility Location problem further requires that the number of opened facilities is at most κ, where κ is a parameter given in the instance of the problem. We consider the Facility Location problems satisfying that for every demand the ratio of the longest distance to facilities and the shortest distance to facilities is at most ω, where ω is a predefined constant. Using the local search approach with scaling technique and error control technique, for any arbitrarily small constant ε 〉 0, we give a polynomial-time approximation algorithm for the ω-constrained Facility Location problem with approximation ratio 1 ＋ √ω ＋ ε, which significantly improves the previous best known ratio （ω ＋ 1）/α for some 1 ≤ α ≤2, and a polynomial-time approximation algorithm for the ω-constrained κ- Facility Location problem with approximation ratio ω ＋ 1 ＋ ε. On the aspect of approximation hardness, we prove that unless NP C DTIME（n^O（log log n））, the ω-constrained Facility Location problem cannot be approximated within 1 ＋ln √ω 1, which slightly improves the previous best known hardness result 1.243 ＋ 0.316 ln（ω - 1）. The experimental results on the standard test instances of Facility Location problem show that our algorithm also has good performance in practice.
基金Supported by the National Natural Science Foundation of China (No. 60773185, 11071268, 10871144)Beijing Natural Science Foundation (No. 1102001)
文摘In this paper, we consider the fault-tolerant concave facility location problem （FTCFL） with uniform requirements. By investigating the structure of the FTCFL, we obtain a modified dual-fitting bifactor approximation algorithm. Combining the scaling and greedy argumentation technique, the approximation factor is proved to be 1.52.
基金supported by National Natural Science Foundation of China (Grant No. 11371001)the Natural Sciences and Engineering Research Council of Canada (Grant No. 283106)China Scholarship Council
文摘We study the two-stage stochastic facility location problem(2-SFLP)by proposing an LP(location problem)-rounding approximation algorithm with 2.3613 per-scenario bound for this problem,improving the previously best per-scenario bound of 2.4957.
文摘Layout design problem is to determine a suitable arrangement for the departments so that the total costs associated with the flow among departments become least. Single Row Facility Layout Problem, SRFLP, is one of </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">layout problems that have many practical applications. This problem and its specific scenarios are often used to model many of the raised issues in the field of facility location. SRFLP is an arrangement of </span><i><span style="font-family:Verdana;">n</span></i><span style="font-family:Verdana;"> departments with a specified length in a straight line so that the sum of the weighted distances between the pairs of departments is minimized. This problem is NP-hard. In this paper, first, a lower bound for a special case of SRFLP is presented. Then, a general </span><span style="font-family:Verdana;">case of SRFLP is presented in which some new and real assumptions are added to generate more practical model. Then a lower bound, as well as an algorithm, is proposed for solving the model. Experimental results on some instances in literature show the efficiency of our algorithm.
