Improved Adaptive Differential Evolution Algorithm for the Un-Capacitated Facility Location Problem

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.

Research Progress and Trends of Urban Public Facilities' Location

Urban development in China has recently encountered various problems,and many of these problems have been caused by uneven distribution of public facilities in different districts,so it is signifi cant to choose reasonable locations for urban public facilities. Current researches on location of urban public facilities in China cover various aspects,involve different units,show diverse features,and make outstanding contributions. However,these researches have also obvious limitations. The future study on public facilities' location will focus on specifi c application of the model in different cities,or better consider characteristics of the city.

Method to Evaluate the Location of Aged Care Facilitiesin Urban Areas Focusing on the Equity in Terms ofUsers’Accessibility

The present study developed and tested a method to evaluate the location of aged care facilities from the viewpoint of whether they are equitably located for users,using the improved Median Share Ratio(MSR).By evaluating the current location of aged care facilities,it is possible to extract the districts which are short of facilities.The evaluation method was applied to Chofu and Kiyose Cities in Tokyo Metropolis,Japan,and the evaluation result of weighting and that of not weighting by elderly population were compared and discussed.Consequently,adopting the evaluation method with weighting by elderly population,it is possible to adequately examine the districts where new aged care facilities should be constructed.From this evidence,it is significant to evaluate the location of aged care facilities,using the improved MSR with weighting by elderly population in the study.

Facility location model for a remanufacturing logistics network

First a remanufactming logistics network is con- structed, in which the structure of both the forward logistics and the reverse logistics are of two levels and all the logistics facilities are capacitated. Both the remanufactming products and the new products can be used to meet the demands of customers. Moreover, it is assumed that homogeneous facilities can be designed together into integrated ones, based on which a mixed integer nonlinear programming （MINLP） facility location model of the remanufacturing logistics network with six types of facilities to be sited is built. Then an algorithm based on enumeration for the model is given. The feasible combinations of binary variables are searched by enumeration, and the remaining sub-problems are solved by the LP solver. Finally, the validities of the model and the algorithm are illustrated by means of an example. The result of the sensitivity analysis of parameters indicates that the integration of homogeneous facilities may influence the optimal solution of the problem to a certain degree.

Collaborative planning approach for anti-bioterrorism emergency facility location based on aerodynamics

To smooth the correlation process from bio-virus diffusion to emergency relief response,the Gaussian plume model is used to describe the diffusion of dangerous sources,where the bio-virus concentration at any given point in affected areas can be calculated.And the toxic load rule is introduced to define the borderline of the dangerous area at different levels.Combined with this,different emergency levels of different demand points in dangerous areas are confirmed using fuzzy clustering,which allows demand points at the same emergency level to cluster in a group.Some effective emergency relief centers are chosen from the candidate hospitals which are located in different emergency level affected areas by set covering.Bioterrorism experiments which were conducted in Nanjing,Jiangsu province are simulated,and the results indicate that the novel method can be used efficiently by decision makers during an actual anti-bioterrorism relief.

Optimization of Charging/Battery-Swap Station Location of Electric Vehicles with an Improved Genetic Algorithm-Based Model

The joint location planning of charging/battery-swap facilities for electric vehicles is a complex problem.Considering the differences between these two modes of power replenishment,we constructed a joint location-planning model to minimize construction and operation costs,user costs,and user satisfaction-related penalty costs.We designed an improved genetic algorithm that changes the crossover rate using the fitness value,memorizes,and transfers excellent genes.In addition,the present model addresses the problem of“premature convergence”in conventional genetic algorithms.A simulated example revealed that our proposed model could provide a basis for optimized location planning of charging/battery-swapping facilities at different levels under different charging modes with an improved computing efficiency.The example also proved that meeting more demand for power supply of electric vehicles does not necessarily mean increasing the sites of charging/battery-swap stations.Instead,optimizing the level and location planning of charging/battery-swap stations can maximize the investment profit.The proposed model can provide a reference for the government and enterprises to better plan the location of charging/battery-swap facilities.Hence,it is of both theoretical and practical value.

Approximation Algorithms for the Priority Facility Location Problem with Penalties

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.

Reliability Analysis of Facility Systems Subject to Edge Failures: Based on the Uncapacitated Fixed-Charge Location Problem

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.

A Review of the Discrete Facility Location Problem

In this paper we attempt to classify discrete facility location problems in the right perspective and propose discrete facility location problems that include： median problems, covering problems, center problems, multi-commodities problems and dynamic problems on the basis of former research by other scholars. We consider vehicle muting location problems, inventory-location problems and hub problems as a recent research field of discrete facility location problems according to literature from the last 10 years.

Reliable Facility Systems Design Subject to Edge Failures: Based on the Uncapacitated Fixed-Charge Location Problem

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.

A Multi-Objective Obnoxious Facility Location Modelon a Plane

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.

Implementing Lagrangean Decomposition Technique to Acquire an Adequate Lower Boundon the Facility Location Problem Solution

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.

Facility Location Problem with Different Type of Clients

This paper proposes a new model of facility location problem referred to as k-product uncapacitated facility location problem with multi-type clients. The k-product uncapacitated facility location problem with multi- type clients consists of two set of sites, one is the set of demand points where clients are located and the other is the set of sites where facilities of unlimited capacities can be set up to serve the clients. Each facility can provide only one kind of products. Each client needs to be served by a set of facilities depending on which products it needs. Each facility can be set up only for one of the k products with a non-negative fixed cost determined by the product it is designated to provide. There is also a nonnegative cost of shipping goods between each pair of locations. The problem is to determine the set of facilities to be set up and to find an assignment of each client to a set of facilities so that the sum of the setup costs and the shipping costs is minimized. Under the assumption that the setting costs is zero and the shipping costs are in facilities centered metric space, it is shown that the problem with two kinds of clients is NP-complete. Furthermore a heuristic algorithm with worst case performance ratio not more than 2-1/k is presented for any integer k.

Capacitated Dynamic Facility Location Problem Based on Tabu Search Algorithm

Facility location problem is a kind of NP-Hard combinational problem.Considering ever-changing demand sites,demand quantity and releasing cost,we formulate a model combining tabu search and FCM(fuzzy clustering method) to solve the capacitated dynamic facility location problem.Some results are achieved and they show that the proposed method is effective.

Probabilistic Distance, Capacity Clustering Location Model of a Semi-Obnoxious Facility, a Real Case of Tafo, Kumasi, Ghana

The collection of solid waste from third class communities in most devel-oping countries is by skip containers, however, the location of these facilities has been done arbitrary without any mathematical considerations as to the number of customers the facility is serving, the distance one has to travel to access it and thereby making some of these residences to dump their refuse in gutters, streams and even burn them. In this paper we proposed an improved probabilistic distance, capacity clustering location model which takes into consideration the weight of solid waste from a customer and the capacity of the skip container to locate the skip container to serve a required number of customers based on the capacity constraint of the container. The model was applied on a real world situation and compared with the existing practice in terms of average distance customers had to travel to access the facility. Our results gave a well shorter average travel distance by customers, gave a number of skip containers needed in an area based on their waste generation per capita.

Facility Location Decisions Based on Driving Distances on Spherical Surface

Facility location problems are concerned with the location of one or more facilities in a way that optimizes a certain objective such as minimizing transportation cost, providing equitable service to customers, capturing the largest market share, etc. Many facility location decisions involving distance objective functions on Spherical Surface have been approached using algorithmic, metaheuristic algorithms, branch-and-bound algorithm, approximation algorithms, simulation, heuristic techniques, and decomposition method. These approaches are most based on Euclidean distance or Great circle distance functions. However, if the location points are widely separated, the difference between driving distance, Euclidean distance and Great circle distance may be significant and this may lead to significant variations in the locations of the corresponding optimal source points. This paper presents a framework and algorithm to use driving distances on spherical surface and explores its use as a facility location decision tool and helps companies assess the optimal locations of facilities.

Optimum Location of Field Hospitals for COVID-19: A Nonlinear Binary Metaheuristic Algorithm

Determining the optimum location of facilities is critical in many fields,particularly in healthcare.This study proposes the application of a suitable location model for field hospitals during the novel coronavirus 2019(COVID-19)pandemic.The used model is the most appropriate among the three most common location models utilized to solve healthcare problems(the set covering model,the maximal covering model,and the P-median model).The proposed nonlinear binary constrained model is a slight modification of the maximal covering model with a set of nonlinear constraints.The model is used to determine the optimum location of field hospitals for COVID-19 risk reduction.The designed mathematical model and the solution method are used to deploy field hospitals in eight governorates in Upper Egypt.In this case study,a discrete binary gaining–sharing knowledge-based optimization(DBGSK)algorithm is proposed.The DBGSK algorithm is based on how humans acquire and share knowledge throughout their life.The DBGSK algorithm mainly depends on two junior and senior binary stages.These two stages enable DBGSK to explore and exploit the search space efficiently and effectively,and thus it can solve problems in binary space.

Optimization of Medical Supply Chains and Forward Store Locations for Recurrent Homecare Patient Demand with Periodic Interruptions

Robust and cost-effective distribution is critical to any home delivery network growing company, both to meet demand under normal conditions and to adapt to temporary disruptions. Home healthcare is anticipated to be a rapidly growing modality of healthcare, itself the largest industry in the US and rife with optimization needs in areas such as logistics, scheduling, and supply chains. We develop two mixed integer programming models to optimize forward storage locations in the supply chain of a national consumable medical supplies company with consistent monthly repeating demand, temporary disruption of facility operations, and remote international manufacturers. Modified p-median single and multi-echelon models are used to determine optimal locations of warehouses and distribution facilities that minimize total transportation cost, with 13% savings in one application (approximately $1.4 million annually). Sensitivity analyses to a range of scenarios suggest that the optimal solution is robust across a number of potential scenarios.

A Criteria Model for Budgeting and Assessing Industrial Sites Location in Developing Economy

Industrial sites are selected in many of the developing countries without taking into consideration some pertinent criteria that are directly affecting the sustainability of such industries in the locations after commissioning. Industries are located in some areas based on political influence rather than facility availability that support industry＇s productivity. In this study a criteria model was developed for assessing the present industrial site locations based on predetermined influencing factors called criteria. In the model provision was made for the sorting out of deficient influencing factors for the purpose of upgrading them to the minimum level required called benchmark through periodical allocation of appropriate funds. In validating the model, identified industrial sites located in selected States of Nigeria were surveyed. Data were collected on factors such as power supply, marketability and raw malerial availability which were considered influential to the sustainability of industry＇s site in the respective areas. Data were analysed for the criteria identified along the line of industrial categories which included large-, medium-, and small-scales. Benchmarks, as well as levels of criteria in the respective regions were determined using statistical weighted averages and the results were used as input to the model. The output results of the model showed that none of the industrial sites located in the selected six States of the South-Western Nigeria were productivity supportive. However, a good performance was achieved in a site with a budget of S13 million （US Dollars） for the upgrading of the deficient facilities in the next three years.

Research on Location-Routing Problem with Empirical Analysis for Regional Logistics Distribution

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.