Locating Emergency Facilities Using the Weighted k-median Problem: A Graph-metaheuristic Approach

An efficient approach is presented for addressing the problem of finding the optimal facilities location in conjunction with the k-median method. First the region to be investigated is meshed and an incidence graph is constructed to obtain connectivity properties of meshes. Then shortest route trees (SRTs) are rooted from nodes of the generated graph. Subsequently, in order to divide the nodes of graph or the studied region into optimal k subregions, k-median approach is utilized. The weights of the nodes are considered as the risk factors such as population, seismic and topographic conditions for locating facilities in the high-risk zones to better facilitation. For finding the optimal facility locations, a recently developed meta-heuristic algorithm that is called Colliding Bodies Optimization (CBO) is used. The performance of the proposed method is investigated through different alternatives for minimizing the cost of the weighted k-median problem. As a case study, the Mazandaran province in Iran is considered and the above graph-metaheuristic approach is utilized for locating the facilities

Automatic Domain Decomposition in Finite Element Method – A Comparative Study

In this paper, an automatic data clustering approach is presented using some concepts of the graph theory. Some Cluster Validity Index (CVI) is mentioned, and DB Index is defined as the objective function of meta-heuristic algorithms. Six Finite Element meshes are decomposed containing two- and three- dimensional types that comprise simple and complex meshes. Six meta-heuristic algorithms are utilized to determine the optimal number of clusters and minimize the decomposition problem. Finally, corresponding statistical results are compared

Solution Methods for the \u3cem\u3ep\u3c/em\u3e-Median Problem: An Annotated Bibliography

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network

A Domain Aware Genetic Algorithm for the p-Median Problem

The p-median problem is an NP-complete combinatorial optimization problem often used in the fields of facility location and clustering. Given a graph with n nodes and an integer p \u3c n, the p-median problem seeks a set of p medians such that the sum of the distances of the n nodes from their nearest median is minimized. This dissertation develops a genetic algorithm that generates solutions to the p-median problem that improves on previously published genetic algorithms by implementing operators that exploit domain specific information. More specifically, this GA explores the following: (1) The advantages of using good solutions generated using extant heuristics in the initial generation of chromosomes. (2) The effectiveness of a crossover operation that exchanges centers in the same neighborhood rather than exchanging arbitrarily chosen subsets of centers. (3) The efficacy of using a biased mutation operator that favors replacing existing medians from less fit chromosomes with non-median nodes from the same neighborhood as the median being replaced. Using published problem sets with known solutions, this dissertation examines solutions identified by the new genetic algorithm in order to determine the accuracy, efficiency and performance characteristics of the new algorithm. In addition, it tests the contribution of each of the algorithm\u27s operators by systematically controlling for all the other factors. The results of the analysis showed that integrating operators that exploited domain specific information did have an overall positive impact on the genetic algorithm. In addition, the results showed that using a structured initial population had little impact on the algorithm\u27s ability to find an optimal solution but it did create a better initial solution and allowed the algorithm to produce a relatively good solution early in the search. Also, the analysis showed that a directed approach to crossover operations was effective and produced superior solutions. Finally, the analysis showed that a directed approach toward mutation did not have a large impact on the overall functionality of the algorithm and may be inferior to an arbitrary approach to mutation

GIS and Location Theory Based Bioenergy Systems Planning

This research is concerned with bioenergy systems planning and optimization modelling in the context of locating biomass power plants and allocating available biomass feedstock to the active plants. Bioenergy, a promising renewable energy resource, has potentially significant benefits to climate change, global warming, and alternative energy supplies. As modern bioenergy applications in power production have the ability to generate cleaner electricity and reduce Green House Gas (GHG) emissions compared with traditional fossil fuels, many researchers have proposed various approaches to obtain competitive power generation prices from biomass in different ways. However, the highly dispersed geographical distribution of biomass is a big challenge for regional bioenergy systems planning. This thesis introduces an integrated methodology combining Geographic Information Systems (GIS) and discrete location theories for biomass availability assessment, biomass power plant candidate selection, and location-allocation of power plants and biomass supplies. Firstly, a well known discrete location model – the p-Median Problem (PMP) model is employed to minimize the weighted transportation costs of delivering all collectable biomass to active power plants. Then, a p-Uncapacitated Facility Location Problem (p-UFLP) model for minimizing the Levelized Unit Costs of Energy (LUCE) is proposed and genetic algorithms (GAs) for solving these optimization problems are investigated. To find the most suitable sites for constructing biomass power plants, the Analytic Hierarchy Process (AHP) and GIS based suitability analysis are employed subject to economical, societal, public health, and environmental constraints and factors. These methods and models are aimed at evaluating available biomass, optimally locating biomass power plants and distributing all agricultural biomass to the active power plants. The significance of this dissertation is that a fully comprehensive approach mixed with the applications of GIS, spatial analysis techniques, an AHP method and discrete location theories has been developed to address regional bioenergy systems planning, involving agricultural biomass potential estimation, power plants siting, and facility locations and supplies allocation scenarios. With the availability of the spatial and statistical data, these models are capable of evaluating and identifying electric power generation from renewable bioenergy on the regional scale optimally. It thus provides the essential information to decision makers in bioenergy planning and renewable bioenergy management. An application sited in the Region of Waterloo, Ontario Canada is presented to demonstrate the analysis and modelling process