4 research outputs found
A new genetic algorithm for the asymmetric traveling salesman problem
The asymmetric traveling salesman problem (ATSP) is one of the most important combinatorial optimization problems. It allows us to solve, either directly or through a transformation, many real-world problems. We present in this paper a new competitive genetic algorithm to solve this problem. This algorithm has been checked on a set of 153 benchmark instances with known optimal solution and it outperforms the results obtained with previous ATSP heuristic methods. © 2012 Elsevier Ltd. All rights reserved.This work has been partially supported by the Ministerio de Educacion y Ciencia of Spain (Project No. TIN2008-06441-C02-01).Yuichi Nagata; Soler Fernåndez, D. (2012). A new genetic algorithm for the asymmetric traveling salesman problem. Expert Systems with Applications. 39(10):8947-8953. https://doi.org/10.1016/j.eswa.2012.02.029S89478953391
Optimal ship navigation and algorithms for stochactic obstacle scenes
Tezin basılısı Ä°stanbul Ćehir Ăniversitesi KĂŒtĂŒphanesi'ndedir.This thesis is comprised of two diïŹerent but related sections. In the ïŹrst section, we consider the optimal ship navigation problem wherein the goal is to ïŹnd the shortest path between two given coordinates in the presence of obstacles subject to safety distance and turn-radius constraints. These obstacles can be debris, rock formations, small islands, ice blocks, other ships, or even an entire coastline. We present a graph-theoretic solution on an appropriately-weighted directed graph representation of the navigation area obtained via 8-adjacency integer lattice discretization and utilization of the Aâ algorithm. We explicitly account for the following three conditions as part of the turn-radius constraints: (1) the shipâs left and right turn radii are diïŹerent, (2) shipâs speed reduces while turning, and (3) the ship needs to navigate a certain minimum number of lattice edges along a straight line before making any turns. The last constraint ensures that the navigation area can be discretized at any desired resolution. We illustrate our methodology on an ice navigation example involving a 100,000 DWT merchant ship and present a proof- of-concept by simulating the shipâs path in a full-mission ship handling simulator at Istanbul Technical University.
In the second section, we consider the stochastic obstacle scene problem wherein an agent needs to traverse a spatial arrangement of possible-obstacles, and the status of the obstacles may be disambiguated en route at a cost. The goal is to ïŹnd an algorithm that decides what and where to disambiguate en route so that the expected length of the traversal is minimized. We present a polynomial-time method for a graph-theoretical version of the problem when the associated graph is restricted to parallel avenues with ïŹxed policies within the avenues. We show how previously proposed algorithms for the continuous space version can be adapted to a discrete setting. We propose a gener- alized framework encompassing these algorithms that uses penalty functions to guide the navigation in realtime. Within this framework, we introduce a new algorithm that provides near-optimal results within very short execution times. Our algorithms are illustrated via computational experiments involving synthetic data as well as an actual naval mineïŹeld data set.
Keywords: Graph theory, shortest path, ship navigation, probabilistic path planning, stochastic dynamic programming, Markov decision process, Canadian travelerâs problemContents
Declaration of Authorship ii
Abstract iv
š Oz v
Acknowledgments vii
List of Figures x
List of Tables xi
1 Optimal Ship Navigation with Safety Distance and Realistic Turn Con- straints
1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 1.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 The Optimal Ship Navigation Problem . . . . . . . . . . . . . . . . . . . . 4
1.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4.1 Safety Distance Constraints . . . . . . . . . . . . . . . . . . . . . . 5
1.4.2 Lattice Discretization . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.3 Ship-Turn Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.4 The Aâ Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.5 Smoothing the Optimal Path . . . . . . . . . . . . . . . . . . . . . 13
1.5 Ice Navigation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.6 Simulator Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.7 Summary, Conclusions, and Future Research . . . . . . . . . . . . . . . . 18
2 Algorithms for Stochastic Obstacle Scenes 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 The Stochastic Obstacle Scene Problem: Continuous vs. Discrete Settings 23
2.2.1 Deciding Where to Disambiguate: Single Disk Case . . . . . . . . 23
2.2.2 Deciding Where to Disambiguate: Two Disks Case . . . . . . . . . 25
2.2.3 Discretization of the Continuous Setting: An Example . . . . . . . 27
2.3 DeïŹnition of the Stochastic Obstacle Scene Problem . . . . . . . . . . . . 27
2.3.1 Continuous SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.2 Discrete SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.3 Discretized SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 A Polynomial Algorithm for Discrete SOSP on Parallel Graphs . . . . . . 29
2.5 Discrete Adaptation of the Simulated Risk Disambiguation Algorithm . . 30
2.5.1 Adaptation to Discrete SOSP . . . . . . . . . . . . . . . . . . . . . 30
2.5.2 Adaptation to Discretized SOSP . . . . . . . . . . . . . . . . . . . 32
2.6 Discrete Adaptation of the Reset Disambiguation Algorithm . . . . . . . . 33
2.7 Generalizing SRA and RDA: Penalty-Based Algorithms and DTA . . . . . 34
2.7.1 Illustration of the Algorithms . . . . . . . . . . . . . . . . . . . . . 36
2.8 Computational Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.8.1 Environment A (The COBRA Data) Experiments . . . . . . . . . 40
2.8.2 Environment B Experiments . . . . . . . . . . . . . . . . . . . . . 41
2.8.3 Environment C Experiments . . . . . . . . . . . . . . . . . . . . . 43
2.9 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A Impact of Cost Change in Parallel Graphs 47
Bibliograph
Optimisation de tournées de véhicules en viabilité hivernale
RĂSUMĂ : Cette thĂšse dĂ©veloppe des outils mathĂ©matiques et informatiques pour amĂ©liorer les opĂ©rations de viabilitĂ© hivernale. En particulier, la confection des tournĂ©es de dĂ©neigement est traitĂ©e comme un problĂšme de tournĂ©es sur les arcs avec plusieurs contraintes. Une mĂ©taheuristique
est dâabord dĂ©veloppĂ©e pour la confection de ces tournĂ©es. Par la suite, des modifications majeures sont apportĂ©es Ă cet algorithme pour tenir compte des caractĂ©ristiques
spĂ©cifiques aux problĂšmes de tournĂ©es sur les arcs (arc routing problem) (ARP) sur des rĂ©seaux routiers rĂ©els. Finalement, un second problĂšme combinant les tournĂ©es de dĂ©neigement et dâĂ©pandage avec la mise en commun de certains vĂ©hicules pour les opĂ©rations est traitĂ©. La solution dĂ©veloppĂ©e permet de tirer parti des caractĂ©ristiques de chaque vĂ©hicule. Tout au long de la thĂšse, un accent particulier est portĂ© sur lâutilisation des donnĂ©es rĂ©elles ainsi que sur le dĂ©veloppement de mĂ©thodes pour faciliter lâimportation et lâexportation de
ces donnĂ©es. Les travaux entourant cette thĂšse dĂ©butent avec la confection de tournĂ©es de dĂ©neigement pour une ville au QuĂ©bec, soit Dolbeau-Mistassini (DM). De nombreux problĂšmes ont Ă©tĂ© rencontrĂ©s avec lâutilisation dâune mĂ©thode tirĂ©e de la littĂ©rature. Parmi ceux-ci, on compte :
â de nombreux demi-tours difficiles Ă exĂ©cuter par les vĂ©hicules ; â le faible respect des prioritĂ©s accordĂ©es aux rues Ă lâĂ©chelle du rĂ©seau ; â de nombreux vĂ©hicules parcourent de longues distances pour se rendre dans les coins reculĂ©s du rĂ©seau ; â le dĂ©sĂ©quilibre des tĂąches de travail en raison des diffĂ©rentes vitesses dâopĂ©ration des
vĂ©hicules ; â le fait que la mĂ©thode ne tient pas compte des ruelles qui peuvent ĂȘtre traitĂ©es dans une direction ou dans lâautre en un seul passage. Ă la suite de nombreux ajustements manuels pour corriger les tournĂ©es obtenues, force a Ă©tĂ© de constater que des amĂ©liorations pouvaient ĂȘtre apportĂ©es Ă ce type de mĂ©thode. Les travaux concernant la premiĂšre contribution de cette thĂšse ont donc portĂ© sur le dĂ©veloppement dâune mĂ©thode de crĂ©ation de tournĂ©es de dĂ©neigement. En raison du grand nombre de variables et de contraintes considĂ©rĂ©es dans le problĂšme, le choix sâest portĂ© sur une mĂ©thode heuristique. Ce type de mĂ©thode offre un bon Ă©quilibre entre le temps de traitement et la qualitĂ© des solutions obtenues. Plus prĂ©cisĂ©ment, le choix sâest arrĂȘtĂ© sur une mĂ©taheuristique de type algorithme de recherche Ă voisinage adaptatif large (adaptive large
neighborhood search) (ALNS), en raison du succĂšs remportĂ© rĂ©cemment par ce type de mĂ©thode. Le premier article a permis de constater que lâalgorithme dĂ©veloppĂ© permet de crĂ©er des tournĂ©es pour les vĂ©hicules de dĂ©neigement. Les contraintes suivantes sont respectĂ©es : Ă©quilibrage des tournĂ©es, couverture partielle du rĂ©seau, vitesses hĂ©tĂ©rogĂšnes, restrictions de virages, restrictions rue/vĂ©hicule et hiĂ©rarchie du rĂ©seau. Pour la deuxiĂšme contribution de thĂšse, le problĂšme a dâabord Ă©tĂ© formalisĂ© par lâintermĂ©diaire dâun programme linĂ©aire en nombres entiers (mixed integer programming) (MIP). Le problĂšme a Ă©tĂ© formulĂ© comme un problĂšme des k-postiers ruraux avec objectif minmax (min-max k-vehicles rural postman problem) (MM K-RPP) avec hiĂ©rarchies, pĂ©nalitĂ©s sur virages, vitesses dâopĂ©ration hĂ©tĂ©rogĂšnes et tournĂ©es ouvertes sur un graphe mixte. Tel quâanticipĂ©, la rĂ©solution devient rapidement impossible Ă traiter avec un solveur commercial
en utilisant seulement 20 segments de rue. Il a Ă©tĂ© dĂ©cidĂ© de poursuivre lâapprofondissement de lâalgorithme dĂ©veloppĂ© en premiĂšre partie. Cette dĂ©cision a Ă©tĂ© prise notamment en raison du trĂšs long temps de traitement qui rĂ©duit lâutilitĂ© du premier algorithme. Cette dĂ©cision repose aussi sur le fait que visuellement, on constate que les tournĂ©es obtenues peuvent ĂȘtre amĂ©liorĂ©es. Dans cette optique, une collaboration a Ă©tĂ© initiĂ©e avec messieurs Fabien LehuĂ©dĂ© et Olivier PĂ©ton du laboratoire des sciences du numĂ©rique de Nantes (LS2N) Ă IMT Atlantique. Leur expertise avec la mĂ©thode ALNS a effectivement permis dâamĂ©liorer grandement les rĂ©sultats obtenus. Parmi les amĂ©liorations apportĂ©es, on note une transformation du rĂ©seau permettant de tenir compte des pĂ©nalitĂ©s sur virages lors du calcul des plus courts chemins. Cette transformation
permet Ă©galement de mieux prendre en compte les ruelles qui requiĂšrent un seul passage dans une direction ou dans lâautre. De plus, la possibilitĂ© dâappliquer plusieurs fois un opĂ©rateur de destruction avant de passer Ă la construction est ajoutĂ©e. Cette contribution a Ă©galement
Ă©tĂ© lâoccasion de dĂ©velopper et tester de nouveaux opĂ©rateurs de voisinage, dĂ©velopper une mĂ©thode de groupement des arcs et revoir et simplifier le code de la mĂ©taheuristique. Lâalgorithme a Ă©tĂ© appliquĂ© Ă la premiĂšre Ă©tude de cas ainsi quâa deux nouvelles Ă©tudes de cas, Baie-Comeau (BC) et Plateau-Mont-Royal (PMR). Des tests ont Ă©galement Ă©tĂ© exĂ©cutĂ©s en comparant les nouvelles tournĂ©es obtenues Ă des tournĂ©es conçues quelques annĂ©es plus tĂŽt
ainsi quâaux rĂ©sultats obtenus par un solveur commercial. Les rĂ©sultats obtenus dĂ©montrent que la mĂ©thodologie amĂ©liore les tournĂ©es conçues prĂ©cĂ©demment. Il est aussi possible de conclure que la mĂ©thode de groupage des arcs amĂ©liore la qualitĂ© des solutions obtenues et lâefficacitĂ© des nouveaux opĂ©rateurs dĂ©veloppĂ©s varie selon le rĂ©seau utilisĂ©. Pour la troisiĂšme contribution, nous sommes revenus sur le cas dâĂ©tude initial tel que dĂ©crit par les intervenants de la premiĂšre Ă©tude de cas. Il a Ă©tĂ© dit que les charges de travail doivent ĂȘtre Ă©quilibrĂ©es, mais que certains vĂ©hicules doivent Ă©galement Ă©pandre des fondants ou des abrasifs en plus de dĂ©neiger. Pour tenir compte de cette contrainte, certaines tournĂ©es avaient dĂ©libĂ©rĂ©ment Ă©tĂ© gardĂ©es plus courtes dans les premiĂšres solutions. Pour le troisiĂšme article, il a Ă©tĂ© dĂ©cidĂ© de traiter cette problĂ©matique de front. Ce quâil faut savoir est que
certains vĂ©hicules sont Ă©quipĂ©s pour lâĂ©pandage et le dĂ©neigement alors que dâautres sont Ă©quipĂ©s pour le dĂ©neigement seulement. Lorsque les premiers traitent un segment de rue, ils exĂ©cutent les deux opĂ©rations simultanĂ©ment. Lorsque les deuxiĂšmes traitent un segment de
rue, il faut planifier un second passage par les premiers vĂ©hicules pour quâils puissent Ă©pandre des fondants ou des abrasifs. Lâalgorithme dĂ©veloppĂ© prĂ©cĂ©demment a donc Ă©tĂ© modifiĂ© dans cette optique. En plus, la considĂ©ration des contraintes de restrictions rue/vĂ©hicule a Ă©tĂ© ajoutĂ©e dans lâalgorithme. Les rĂ©sultats dĂ©montrent que lâalgorithme permet effectivement de concevoir des tournĂ©es qui
respectent les contraintes de la nouvelle Ă©tude de cas. Cet outil permet donc de tirer profit de lâinteraction entre les divers types de vĂ©hicules. La contribution souligne Ă©galement lâutilitĂ© dâun tel outil pour supporter lâanalyse des besoins justifiant lâachat de nouveaux vĂ©hicules.
En parallĂšle aux dĂ©veloppements algorithmiques, des mĂ©thodes dâimportation et dâexportation des donnĂ©es provenant des cas dâĂ©tude rĂ©els sont aussi dĂ©veloppĂ©es. DĂšs le dĂ©part, il a Ă©tĂ© choisi dâutiliser des fichiers de type Shapefile comme source de donnĂ©es en raison de sa grande disponibilitĂ© et de la compatibilitĂ© avec les systĂšme dâinformation gĂ©ographique (SIG). Une mĂ©thode pour passer du rĂ©seau gĂ©ographique vers un rĂ©seau mathĂ©matique a donc Ă©tĂ© amĂ©liorĂ©e au cours des travaux. Alors quâau dĂ©but des travaux de la thĂšse, il fallait passer par un chiffrier Microsoft ExcelTM pour ensuite importer les donnĂ©es dans le code, Ă la fin, une mĂ©thode automatisĂ©e permet lâimportation directe Ă partir des fichiers Shapefiles vers le code de la mĂ©taheuristique. Quant aux rĂ©sultats obtenus, ils furent obtenus dans les premiĂšres Ă©tapes sous forment de reprĂ©sentations gĂ©ographiques dans un SIG ainsi que des feuilles dâinstructions indiquant les Ă©tapes, coin de rue par coin de rue, aux opĂ©rateurs de vĂ©hicules. De ce cĂŽtĂ©, les dĂ©veloppements ont permis dâobtenir des fichiers de type KML. Ce type de fichier est compatible avec plusieurs logiciels et applications, dont Google EarthviewTM et
des applications de guidage routier sur des appareils mobiles.----------ABSTRACT : In this thesis, we develop mathematical and computerized tools to improve winter viability operations. More precisely, the snow routing design problem is treated as an problĂšme de tournĂ©e sur les arcs (arc routing problem) (ARP). In a first effort to solve the problem, a metaheuristic procedure is designed. Then, some major modifications are made to the algorithm to improve the consideration of specific characteristics of real road networks. Finally, a second problem combining the routing of the snowplow and the spreading vehicles are addressed. The objective is to fully take advantage of the characteristics of the different type of vehicles. In parallel with the algorithmic development, this thesis also develops some methodologies to facilitate the importation and exportation of the real world data. Works concerning this thesis were initiated with a mandate to design snowplow routes for a city in the province of QuĂ©bec, namely DM. The problem was addressed by using a methodology found in the literature, however, several difficulties were encountered. Among others: â the routes contained several U-turns which are difficult to perform by the snow plowing
vehicles; â little consideration of the priorities at the network level; â several vehicles have to travel to some remote streets in the same sector of the city where we would expect only one vehicle to go; â unbalanced sectors due to the different speeds of operation of the vehicles;
â no consideration for back alleys that needs to be serviced only once in either direction. In respond to these problems, several manual modifications of the routes were undertaken to make them feasible. It was found that the methodology fails to solve the problem as it is encountered.
Therefore, works concerning the first contribution of this thesis focused on the development of a methodology to design snowplow routing. Due to numerous variables and constraints, it was decided to develop a metaheuristic algorithm. This type of methodology offers a good balance between runtime and the quality of the solution obtained. In particular, an ALNS is selected because of its recent success cited in the literature. Thus, the first article concludes that the algorithm can design snowplow routing. The following constraints are considered: workload balance, partial area coverage, heterogeneous vehicle speeds, road/vehicle dependencies, network hierarchies and turn restrictions. In the second contribution of this thesis, the problem was modeled as a mixed integer program. It is formulated as a min-max k-rural postmen problem with hierarchies, turn penalties, open tours and heterogeneous speed on a mixed graph. As expected, the formulation
is intractable even for a number of arcs as low as 20. It was then decided to pursue the development of the ALNS algorithm. This decision was taken considering the long runtime of the first algorithm and the fact that the routes obtained can be visually improved. A collaboration with Fabien Lehuédé and Olivier Péton from the Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique was undertaken. Their expertise with ALNS greatly helped to improve the results obtained. Among other improvements brought to the algorithm, one can cite the transformation of
the graph which allows to better take into account turn penalties during the computation of the shortest paths. This transformation also allows to better take into account the back alleys which only need one service in either direction. This contribution also allowed to develop and test new neighborhood operators and an arc grouping methodology. Both of these innovations improve the quality of the solutions obtained. However the efficiency of
the new operators varies with the network. For the third contribution, we took back the case study as it was described by the collaborator in DM. It was said that the workload needs to be balanced among the vehicles. However
some vehicles must also perform winter spreading in addition to plowing. For the first set of routes produced, some of the routes were deliberately left with a lower workload to allow them to perform winter spreading. For the third article, it was decided to consider the spreading
and the plowing directly during the construction and the improvement steps. Thus this problem was tackled more directly in the third article. It must be noted that some vehicles are equipped to perform both winter spreading and snow plowing and some others can only perform plowing. When the former service a street, they can perform both plowing and spreading at the same time. When the latter service a street, a second passage is required to spread salt or abrasives. The algorithm developed for the second contribution was then adapted for this new problem. Moreover, the street/vehicle restriction constraints were also added. The result shows that the algorithm can produce a set of routes respecting the constraints of the new problem. It can take advantage of the interaction between the various types of vehicles. The article also shows that such tool can be beneficial in analyzing the requirements for new vehicles. In parallel with the development of the algorithms, data importation and exportation techniques
from real road networks are also developed. It was chosen to use Shapefiles because of its good relative availability and because of its compatibility with Geographic Information
System (GIS). A method to transfer from a geographical to a mathematical network is improved during the thesis. At the beginning, a Microsoft ExcelTM datasheet is used to transfer the data from the GIS to the metaheuristic. At the end, it is possible to fetch the data directly from the Shapefiles to the metaheuristic. As for the results obtained, at the beginning, they were provided in the form of a Shapefile for visualization and indications on sheets of paper for the operators. At the end, the results can be exported to the KML format. This type of file is compatible with several software such as Google EarthviewTM and application Global Positioning System (GPS) applications on mobile devices