We consider a capacitated location-allocation problem in the presence of k connections on the horizontal line barrier. The objective is to locate a set of new facilities among a set of existing facilities and to alloc...We consider a capacitated location-allocation problem in the presence of k connections on the horizontal line barrier. The objective is to locate a set of new facilities among a set of existing facilities and to allocate an optimal number of existing facilities to each new facility in order to satisfy their demands such that the summation of the weighted rectilinear barrier distances from new facilities to existing facilities is minimized. The proposed problem is designed as a mixed-integer nonlinear programming model. To show the efficiency of the model, a numerical example is provided. It is worth noting that the global optimal solution is obtained.展开更多
In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such fa...In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil;the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers;and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.展开更多
In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondo...In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondominated during the evolutionary process,thus leading to the failure of producing offspring toward Pareto-optimal front with diversity.Can we find a more effective way to select nondominated solutions and resolve this issue?To answer this critical question,this work proposes to evolve solutions through line complex rather than solution points in Euclidean space.First,Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum ones.Besides position vectors of the solution points,momentum vectors are used to extend the comparability of nondominated solutions and enhance selection pressure.Then,a new distance function designed for high-dimensional space is proposed to replace Euclidean distance as a more effective distancebased estimator.Based on them,a novel many-objective evolutionary algorithm(MaOEA)is proposed by integrating a line complex-based environmental selection strategy into the NSGAⅢframework.The proposed algorithm is compared with the state of the art on widely used benchmark problems with up to 15 objectives.Experimental results demonstrate its superior competitiveness in solving MaOPs.展开更多
Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to clarify some amb...Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to clarify some ambiguity, we sharpen the definition of PL minimal surfaces, and prove a technical lemma on the Plateau problem in the hyperbolic space.展开更多
文摘We consider a capacitated location-allocation problem in the presence of k connections on the horizontal line barrier. The objective is to locate a set of new facilities among a set of existing facilities and to allocate an optimal number of existing facilities to each new facility in order to satisfy their demands such that the summation of the weighted rectilinear barrier distances from new facilities to existing facilities is minimized. The proposed problem is designed as a mixed-integer nonlinear programming model. To show the efficiency of the model, a numerical example is provided. It is worth noting that the global optimal solution is obtained.
文摘In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil;the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers;and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.
基金supported in part by the National Natural Science Foundation of China(51775385)the Natural Science Foundation of Shanghai(23ZR1466000)+3 种基金the Shanghai Industrial Collaborative Science and Technology Innovation Project(2021-cyxt2-kj10)the Innovation Program of Shanghai Municipal Education Commission(202101070007E00098)the Innovation Project of Engineering Research Center of Integration and Application of Digital Learning Technology of MOE(1221046)the Program to Cultivate Middle-Aged and Young Cadre Teacher of Jiangsu Province。
文摘In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondominated during the evolutionary process,thus leading to the failure of producing offspring toward Pareto-optimal front with diversity.Can we find a more effective way to select nondominated solutions and resolve this issue?To answer this critical question,this work proposes to evolve solutions through line complex rather than solution points in Euclidean space.First,Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum ones.Besides position vectors of the solution points,momentum vectors are used to extend the comparability of nondominated solutions and enhance selection pressure.Then,a new distance function designed for high-dimensional space is proposed to replace Euclidean distance as a more effective distancebased estimator.Based on them,a novel many-objective evolutionary algorithm(MaOEA)is proposed by integrating a line complex-based environmental selection strategy into the NSGAⅢframework.The proposed algorithm is compared with the state of the art on widely used benchmark problems with up to 15 objectives.Experimental results demonstrate its superior competitiveness in solving MaOPs.
基金the Centennial fellowship of the Graduate School at Princeton University
文摘Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to clarify some ambiguity, we sharpen the definition of PL minimal surfaces, and prove a technical lemma on the Plateau problem in the hyperbolic space.
