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
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
A facility system can be modeled by a connected graph in which the vertices represent entities such as suppliers, distribution centers or customers and the edges represent facilities such as the paths of goods or info...A facility system can be modeled by a connected graph in which the vertices represent entities such as suppliers, distribution centers or customers and the edges represent facilities such as the paths of goods or information. The efficiency, and hence the reliability, of a facility system is to a large degree adversely affected by the edge failures in the network. Such failures may be caused by various natural disasters or terrorist attacks. In this paper, we consider facility systems’ reliability analysis based on the classical uncapacitated fixed-charge location problem when subject to edge failures. For an existing facility system, we formulate two models based on deterministic case and stochastic case to measure the loss in efficiency due to edge failures and give computational results and reliability envelopes for a specific example.展开更多
The reliability of facility location problem has aroused wide concern recently. Many researchers focus on reliable and robust facility systems design under component failures and have obtained promising performance. H...The reliability of facility location problem has aroused wide concern recently. Many researchers focus on reliable and robust facility systems design under component failures and have obtained promising performance. However, the target and reliability of a facility system are to a large degree adversely affected by the edge failures in the network, which remains a deep study. In this paper, we focus on facility systems’ reliability subject to edge failures. For a facility location system, we formulate two models based on classical uncapacitated fixed-charge location problem under deterministic and stochastic cases. For a specific example, location decisions and the comparison of reliability under different location models are given. Extensive experiments verify that significant improvements in reliability can be attained simply by increasing the amount of operating cost.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
In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing f...In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing facility points;2) Maximize the minimum distance from the facility to be located to the existing facility points;3) Maximize the number of existing facility points covered. Area restriction concept has been incor-porated so that the facility to be located should be within certain restricted area. The model developed here is a class of maximal covering problem, that is covering maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region Two types of compromise solution methods have been designed to get a satisfactory solution of the multi-objective problem. A transformed non- linear programming algorithm has been designed for the proposed non-linear model. Rectilinear dis-tance norm has been considered as the distance measure as it is more appropriate to various realistic situa-tions. A numerical example has been presented to illustrate the solution algorithm.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
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
The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence;attempts to integrate th...The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence;attempts to integrate these two decisions have been limited. Multi-objective location-routing problem (MLRP) is combined with the facility location and the vehicle routing decision and satisfied the different objectives. Due to the problem complexity, simultaneous solution methods are limited, which are given in different objectives with conflicts in functions satisfied. Two kinds of optimal mathematical models are proposed for the solution of MLRP. Three methods have been emphatically developed for MLRP. MGA architecture makes it possible to search the solution space efficiently, which provides a path for searching the solution with two-objective LRP. At last the practical proof is given by random analysis for regional distribution with nine cities.展开更多
The reliability of facility location problems has been received wide attention for several decades. Researchers formulate varied models to optimize the reliability of location decisions. But the most of such studies a...The reliability of facility location problems has been received wide attention for several decades. Researchers formulate varied models to optimize the reliability of location decisions. But the most of such studies are not practical since the models are too ideal. In this paper, based on the classical uncapacitated fixed-charge location problem (UFLP) and some supply constraints from the reality, we distinguish deterministic facility failure and stochastic facility failure cases to formulate models to measure the reliability of a system. The computational results and reliability envelopes for a specific example are also given.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.
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
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
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 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.
文摘A facility system can be modeled by a connected graph in which the vertices represent entities such as suppliers, distribution centers or customers and the edges represent facilities such as the paths of goods or information. The efficiency, and hence the reliability, of a facility system is to a large degree adversely affected by the edge failures in the network. Such failures may be caused by various natural disasters or terrorist attacks. In this paper, we consider facility systems’ reliability analysis based on the classical uncapacitated fixed-charge location problem when subject to edge failures. For an existing facility system, we formulate two models based on deterministic case and stochastic case to measure the loss in efficiency due to edge failures and give computational results and reliability envelopes for a specific example.
文摘The reliability of facility location problem has aroused wide concern recently. Many researchers focus on reliable and robust facility systems design under component failures and have obtained promising performance. However, the target and reliability of a facility system are to a large degree adversely affected by the edge failures in the network, which remains a deep study. In this paper, we focus on facility systems’ reliability subject to edge failures. For a facility location system, we formulate two models based on classical uncapacitated fixed-charge location problem under deterministic and stochastic cases. For a specific example, location decisions and the comparison of reliability under different location models are given. Extensive experiments verify that significant improvements in reliability can be attained simply by increasing the amount of operating cost.
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.
文摘In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing facility points;2) Maximize the minimum distance from the facility to be located to the existing facility points;3) Maximize the number of existing facility points covered. Area restriction concept has been incor-porated so that the facility to be located should be within certain restricted area. The model developed here is a class of maximal covering problem, that is covering maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region Two types of compromise solution methods have been designed to get a satisfactory solution of the multi-objective problem. A transformed non- linear programming algorithm has been designed for the proposed non-linear model. Rectilinear dis-tance norm has been considered as the distance measure as it is more appropriate to various realistic situa-tions. A numerical example has been presented to illustrate the solution algorithm.
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.
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.
文摘The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence;attempts to integrate these two decisions have been limited. Multi-objective location-routing problem (MLRP) is combined with the facility location and the vehicle routing decision and satisfied the different objectives. Due to the problem complexity, simultaneous solution methods are limited, which are given in different objectives with conflicts in functions satisfied. Two kinds of optimal mathematical models are proposed for the solution of MLRP. Three methods have been emphatically developed for MLRP. MGA architecture makes it possible to search the solution space efficiently, which provides a path for searching the solution with two-objective LRP. At last the practical proof is given by random analysis for regional distribution with nine cities.
文摘The reliability of facility location problems has been received wide attention for several decades. Researchers formulate varied models to optimize the reliability of location decisions. But the most of such studies are not practical since the models are too ideal. In this paper, based on the classical uncapacitated fixed-charge location problem (UFLP) and some supply constraints from the reality, we distinguish deterministic facility failure and stochastic facility failure cases to formulate models to measure the reliability of a system. The computational results and reliability envelopes for a specific example are also given.
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.
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.
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.
