Ant-Balanced multiple traveling salesmen: ACO-BmTSP

A new algorithm based on the ant colony optimization (ACO) method for the multiple traveling salesman problem (mTSP) is presented and defined as ACO-BmTSP. This paper addresses the problem of solving the mTSP while considering several salesmen and keeping both the total travel cost at the minimum and the tours balanced. Eleven different problems with several variants were analyzed to validate the method. The 20 variants considered three to twenty salesmen regarding 11 to 783 cities. The results were compared with best-known solutions (BKSs) in the literature. Computational experiments showed that a total of eight final results were better than those of the BKSs, and the others were quite promising, showing that with few adaptations, it will be possible to obtain better results than those of the BKSs. Although the ACO metaheuristic does not guarantee that the best solution will be found, it is essential in problems with non-deterministic polynomial time complexity resolution or when used as an initial bound solution in an integer programming formulation. Computational experiments on a wide range of benchmark problems within an acceptable time limit showed that compared with four existing algorithms, the proposed algorithm presented better results for several problems than the other algorithms did.info:eu-repo/semantics/publishedVersio

Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem

Copyright @ 2000 INFORMSThe multisource Weber problem is to locate simultaneously m facilities in the Euclidean plane to minimize the total transportation cost for satisfying the demand of n fixed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms. We compare various heuristics, i.e., alternative location-allocation (Cooper 1964), projection (Bongartz et al. 1994), Tabu search (Brimberg and Mladenovic 1996a), p-Median plus Weber (Hansen ct al. 1996), Genetic search and several versions of Variable Neighbourhood search. Based on empirical tests that are reported, it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that Variable Neighbourhood search gives consistently best results, on average, in moderate computing time.This study was supported by the Department of National Defence (Canada) Academic Research; Office of Naval Research Grant N00014-92-J-1194, Natural Sciences and Engineering Research Council of Canada Grant GPO 105574 and Fonds pour la Formation des Chercheurs et l’Aide a la Recherche Grant 32EQ 1048; and by an International Postdoctoral Fellowship of the Natural Sciences and Engineering Research Council of Canada, Grant OGPOO 39682

A priori optimization

Includes bibliographical references.Partially supported by the National Science Foundation. ECS-8717970Dimitris J. Bertsimas, Patrick Jaillet and Amedeo R. Odoni

Two traveling salesman facility location problems

Includes bibliographical references.Work partially supported by the National Science Foundation. ECS-8717970Dimitris Bertsimas

Task Allocation and Collaborative Localisation in Multi-Robot Systems

To utilise multiple robots, it is fundamental to know what they should do, called task allocation, and to know where the robots are, called localisation. The order that tasks are completed in is often important, and makes task allocation difficult to solve (40 tasks have 1047 different ways of completing them). Algorithms in literature range from fast methods that provide reasonable allocations, to slower methods that can provide optimal allocations. These algorithms work well for systems with identical robots, but do not utilise robot differences for superior allocations when robots are non-identical. They also can not be applied to robots that can use different tools, where they must consider which tools to use for each task. Robot localisation is performed using sensors which are often assumed to always be available. This is not the case in GPS-denied environments such as tunnels, or on long-range missions where replacement sensors are not readily available. A promising method to overcome this is collaborative localisation, where robots observe one another to improve their location estimates. There has been little research on what robot properties make collaborative localisation most effective, or how to tune systems to make it as accurate as possible. Most task allocation algorithms do not consider localisation as part of the allocation process. If task allocation algorithms limited inter-robot distance, collaborative localisation can be performed during task completion. Such an algorithm could equally be used to ensure robots are within communication distance, and to quickly detect when a robot fails. While some algorithms for this exist in literature, they provide a weak guarantee of inter-robot distance, which is undesirable when applied to real robots. The aim of this thesis is to improve upon task allocation algorithms by increasing task allocation speed and efficiency, and supporting robot tool changes. Collaborative localisation parameters are analysed, and a task allocation algorithm that enables collaborative localisation on real robots is developed. This thesis includes a compendium of journal articles written by the author. The four articles forming the main body of the thesis discuss the multi-robot task allocation and localisation research during the author’s candidature. Two appendices are included, representing conference articles written by the author that directly relate to the thesis.Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 201

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.Siirretty Doriast

Problemas de localização-distribuição de serviços semiobnóxios: aproximações e apoio à decisão

Doutoramento em Gestão IndustrialA presente tese resulta de um trabalho de investigação cujo objectivo se centrou no problema de localização-distribuição (PLD) que pretende abordar, de forma integrada, duas actividades logísticas intimamente relacionadas: a localização de equipamentos e a distribuição de produtos. O PLD, nomeadamente a sua modelação matemática, tem sido estudado na literatura, dando origem a diversas aproximações que resultam de diferentes cenários reais. Importa portanto agrupar as diferentes variantes por forma a facilitar e potenciar a sua investigação. Após fazer uma revisão e propor uma taxonomia dos modelos de localização-distribuição, este trabalho foca-se na resolução de alguns modelos considerados como mais representativos. É feita assim a análise de dois dos PLDs mais básicos (os problema capacitados com procura nos nós e nos arcos), sendo apresentadas, para ambos, propostas de resolução. Posteriormente, é abordada a localização-distribuição de serviços semiobnóxios. Este tipo de serviços, ainda que seja necessário e indispensável para o público em geral, dada a sua natureza, exerce um efeito desagradável sobre as comunidades contíguas. Assim, aos critérios tipicamente utilizados na tomada de decisão sobre a localização destes serviços (habitualmente a minimização de custo) é necessário adicionar preocupações que reflectem a manutenção da qualidade de vida das regiões que sofrem o impacto do resultado da referida decisão. A abordagem da localização-distribuição de serviços semiobnóxios requer portanto uma análise multi-objectivo. Esta análise pode ser feita com recurso a dois métodos distintos: não interactivos e interactivos. Ambos são abordados nesta tese, com novas propostas, sendo o método interactivo proposto aplicável a outros problemas de programação inteira mista multi-objectivo. Por último, é desenvolvida uma ferramenta de apoio à decisão para os problemas abordados nesta tese, sendo apresentada a metodologia adoptada e as suas principais funcionalidades. A ferramenta desenvolvida tem grandes preocupações com a interface de utilizador, visto ser direccionada para decisores que tipicamente não têm conhecimentos sobre os modelos matemáticos subjacentes a este tipo de problemas.This thesis main objective is to address the location-routing problem (LRP) which intends to tackle, using an integrated approach, two highly related logistics activities: the location of facilities and the distribution of materials. The LRP, namely its mathematical formulation, has been studied in the literature, and several approaches have emerged, corresponding to different real-world scenarios. Therefore, it is important to identify and group the different LRP variants, in order to segment current research and foster future studies. After presenting a review and a taxonomy of location-routing models, the following research focuses on solving some of its variants. Thus, a study of two of the most basic LRPs (capacitated problems with demand either on the nodes or on the arcs) is performed, and new approaches are presented. Afterwards, the location-routing of semi-obnoxious facilities is addressed. These are facilities that, although providing useful and indispensible services, given their nature, bring about an undesirable effect to adjacent communities. Consequently, to the usual objectives when considering their location (cost minimization), new ones must be added that are able to reflect concerns regarding the quality of life of the communities impacted by the outcome of these decisions. The location-routing of semi-obnoxious facilities therefore requires to be analysed using multi-objective approaches, which can be of two types: noninteractive or interactive. Both are discussed and new methods proposed in this thesis; the proposed interactive method is suitable to other multi-objective mixed integer programming problems. Finally, a newly developed decision-support tool to address the LRP is presented (being the adopted methodology discussed, and its main functionalities shown). This tool has great concerns regarding the user interface, as it is directed at decision makers who typically don’t have specific knowledge of the underlying models of this type of problems

A MODELING FRAMEWORK ON DISTANCE PREDICTING FUNCTIONS FOR LOCATION MODELS IN CONTINUOUS SPACE

Continuous location models are the oldest models in locations analysis dealing with the geometrical representations of reality, and they are based on the continuity of location area. The classical model in this area is the Weber problem. Distances in the Weber problem are often taken to be Euclidean distances, but almost all kinds of the distance functions can be employed. In this survey, we examine an important class of distance predicting functions (DPFs) in location problems all of practical relevance. This paper provides a review on recent efforts and development in modeling travel distances based on the coordinates they use and their applicability in certain practical settings. Very little has been done to include special cases of the class of metrics and its classification in location models and such merit further attention. The new metrics are discussed in the well-known Weber problem, its multi-facility case and distance approximation problems. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions. Research issues which we believe to be worthwhile exploring in the future are also highlighted

Distribution network design on the battlefield

Cataloged from PDF version of article.Ammunition, whether it be an arrow in the middle ages, a lead bullet in the 1800s, or a laser guided smart bomb today, has been the most prominent factor in determining the outcome of combat. Failing to supply the required amount of ammunition properly may lead to defeat. Our main objective in this study is to provide a decision support tool that can help plan ammunition distribution on the battlefield. We demonstrate through an extensive literature review that the existing models are not capable of handling the specifics of the problem in this study. To this end, we propose a novel three-layer commodity-flow location routing formulation that distributes multiple products, respects hard time windows, allows demand points to be supplied by more than one vehicle or depot, and locates facilities at two different layers. We derive several valid inequalities to speed up the solution time of our model, illustrate the performance of the model in several realistically sized scenarios, and report encouraging results. Finally, we introduce a dynamic model that designs the distribution system in consecutive time periods for the entire combat duration. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 58: 188–209, 201