Distributed Services with Foreseen and Unforeseen Tasks: The Mobile Re-allocation Problem

In this paper we deal with a common problem found in the operations of security and preventive/corrective maintenance services: that of routing a number of mobile resources to serve foreseen and unforeseen tasks during a shift. We define the (Mobile Re-Allocation Problem) MRAP as the problem of devising a routing strategy to maximize the expected weighted number of tasks served on time. For obtaining a solution to the MRAP, we propose to solve successively a multi-objective optimization problem called the stochastic Team Orienteering Problem with Multiple Time Windows (s-TOP-MTW) so as to consider information about known tasks and the arrival process of new unforeseen tasks. Solving successively the s-TOP-MTW we find that considering information about the arrival process of new unforeseen tasks may aid in maximizing the expected proportion of tasks accomplished on time.location;reliability;routing;distributed services

Approximation Algorithms for Capacitated Assignment with Budget Constraints and Applications in Transportation Systems

In this article, we propose algorithms to address two critical transportation system problems: the Generalized Real-Time Line Planning Problem (GRLPP) and the Generalized Budgeted Multi-Visit Team Orienteering Problem (GBMTOP). The GRLPP aims to optimize high-capacity line plans for multimodal transportation networks to enhance connectivity between passengers and lines. The GBMTOP focuses on finding optimal routes for a team of heterogeneous vehicles within budget constraints to maximize the reward collected. We present two randomized approximation algorithms for the generalized budgeted multi-assignment problem (GBMAP), which arises when items need to be assigned to bins subject to capacity constraints, budget constraints, and other feasibility constraints. Each item can be assigned to at most a specified number of bins, and the goal is to maximize the total reward. GBMAP serves as the foundation for solving GRLPP and GBMTOP. In addition to these two algorithms, our contributions include the application of our framework to GRLPP and GBMTOP, along with corresponding models, numerical experiments, and improvements on prior work

Towards the solution of variants of Vehicle Routing Problem

Some of the problems that are used extensively in -real life are NP complete problems. There is no any algorithm which can give the optimal solution to NP complete problems in the polynomial time in the worst case. So researchers are applying their best efforts to design the approximation algorithms for these NP complete problems. Approximation algorithm gives the solution of a particular problem, which is close to the optimal solution of that problem. In this paper, a study on variants of vehicle routing problem is being done along with the difference in the approximation ratios of different approximation algorithms as being given by researchers and it is found that Researchers are continuously applying their best efforts to design new approximation algorithms which have better approximation ratio as compared to the previously existing algorithms

Distributed Services with Foreseen and Unforeseen Tasks: The Mobile Re-allocation Problem

In this paper we deal with a common problem found in the operations of security and preventive/corrective maintenance services: that of routing a number of mobile resources to serve foreseen and unforeseen tasks during a shift. We define the (Mobile Re-Allocation Problem) MRAP as the problem of devising a routing strategy to maximize the expected weighted number of tasks served on time. For obtaining a solution to the MRAP, we propose to solve successively a multi-objective optimization problem called the stochastic Team Orienteering Problem with Multiple Time Windows (s-TOP-MTW) so as to consider information about known tasks and the arrival process of new unforeseen tasks. Solving successively the s-TOP-MTW we find that considering information about the arrival process of new unforeseen tasks may aid in maximizing the expected proportion of tasks accomplished on time

Robust UAV Mission Planning

Unmanned Areal Vehicles (UAVs) can provide significant contributions to information gathering in military missions. UAVs can be used to capture both full motion video and still imagery of specific target locations within the area of interest. In order to improve the effectiveness of a reconnaissance mission, it is important to visit the largest number of interesting target locations possible, taking into consideration operational constraints related to fuel usage between target locations, weather conditions and endurance of the UAV. We model this planning problem as the well-known orienteering problem, which is a generalization of the traveling salesman problem. Given the uncertainty in the military operational environment, robust planning solutions are required. As such, our model takes into account uncertainty in the fuel usage between targets (for instance due to weather conditions) as well as uncertainty in the importance of visiting specific target locations. We report results using different uncertainty sets that specify the degree of uncertainty against which any feasible solution will be protected. We also compare the probability that a solution is feasible for the robust solution on one hand and the solution found with average fuel usage and expected value of information on the other. In doing so, we show how the sustainability of a UAV mission can be significantly improved

Algorithms for Large Orienteering Problems

In this thesis, we have developed algorithms to solve large-scale Orienteering Problems. The Orienteering Problem is a combinatorial optimization problem were given a weighted complete graph with vertex profits and a maximum distance constraint, the goal is to find the simple cycle which maximizes the sum of the profits of the visited vertices. To solve the Orienteering Problem, we have developed an evolutionary algorithm and an Branch-and-Cut algorithm. One of the key characteristics of the evolutionary algorithm is to work with unfeasible solutions. From the point of view of genetic operators, the main contribution has been the development of the Edge Recombination Crossover for the Orienteering Problem, which in a wider context it is also valid for any cycle problem. Another contribution has been the developed local search to handle large problems. The Branch-and-Cut algorithm includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. At the same time, we have generalized for cycle problems the support graph shrinking techniques and procedures to speed up the exact separation algorithms for subcycle elimination constraints. The experiments carried out in large-sized instances, up to 7393 nodes, show that both algorithms achieve outstanding results, both in terms of the quality of solutions and in terms of the execution time.BERC.2014-2017 SEV-2013-0323 PID2019-104933GB-I00 MTM2015-65317-

Algorithms for large orienteering problems

185 p.Tesi lan honetan, tamaina handiko Orientazio Problemak ebazteko algoritmoak garatu ditugu. Orientazio Problema optimizazio konbinatorioko problema bat da: herri multzo bat eta hauen arteko distantzia emanik, herri bakoitzak bere saria duelarik, eta ibilbidearen distantzia osoaren murrizketa bat ezarririk, problemaren helburua sarien batura maximizatzen duen ibilbidea aurkitzean datza. Orientazio Problema ebazteko, algoritmo ebolutibo bat eta Branch-and-Cut algoritmo bat garatu ditugu. Algoritmo ebolutiboaren ezaugarri nagusienetako bat, soluzio ez bideragarriekin lan egitea da. Eragile genetikoen ikuspuntutik algoritmo honen ekarpen nagusia Orientazio Problemarentzako proposatutako Ertzen Birkonbinazio Gurutzaketa da. Beste ekarpen bat problema handiak ebazteko aproposa den bilaketa lokala da. Branch-and-Cut algoritmoak berriz, ziklo problementzako banantze algoritmoetan, banantze begiztan, aldagaien baloratzean, eta problemaren goi eta behe-mugen kalkuluan ditu ekarpen nagusiak. Aldi berean, ziklo problementzako algoritmo zehatzaren parte diren euskarri grafoen sinplifikazio teknika eta azpizikloak identifikatzeko separazio algoritmoak aztertu ditugu. Tamaina handiko problemekin, 7393 herrirainokoak, egindako esperimentuek erakusten dute bi algoritmoek primerako emaitzak lortzen dituztela, bai soluzioen kalitatearen aldetik eta bai algoritmoen azkartasunaren aldetik ere.En esta tesis, hemos desarrollado algoritmos para resolver instancias de gran tamaño para el Problema de Orientación. El Problema de Orientación es un problema de optimización combinatoria en el cual, dado un grafo, con distancias asociadas en las aristas y premios en los vértices, y la restricción de longitud máxima de la ruta, el objetivo es maximizar la suma de recompensas de las ciudades visitadas.Para resolver el Problema de Orientación, hemos desarrollado un algoritmo evolutivo y un algoritmo Branch-and-Cut. La principal característica del algoritmo evolutivo es el uso de soluciones infactibles durante de la búsqueda. Desde el punto de vista de los operadores genéticos, la contribución más notable es el desarrollo del Cruce de Recombinación de Aristas para el Problema de Orientación. Otra contribución ha sido el desarrollo de una búsqueda local que permite abarcar problemas de gran tamaño. El algoritmo Branch-and-Cut incluye contribuciones en los algoritmos de separación para problemas de ciclos, en el bucle de separación, en la estimación de precios de las variables, y en el cálculo de las cotas inferiores y superiores del problema. Al mismo tiempo, generalizamos para problemas de ciclos, la contracción de grafos soporte y procedimientos para acelerar la separación exacta de las restricciones de eliminación de subciclos. Los experimentos llevados a cabo en problemas de gran tamaño, problemas de hasta 7393 nodos, muestran que ambos algoritmos obtienen resultados excelentes, en términos de la calidad de la solución y en términos del tiempo de ejecución.-In this thesis, we have developed algorithms to solve large-scale Orienteering Problems. The Orienteering Problem is a combinatorial optimization problem were given a weighted complete graph with vertex profits and a maximum distance constraint, the goal is to find the simple cycle which maximizes the sum of the profits of the visited vertices. To solve the Orienteering Problem, we have developed an evolutionary algorithm and a Branch-and-Cut algorithm. One of the key characteristics of the evolutionary algorithm is to work with unfeasible solutions. From the point of view of genetic operators, the main contribution has been the development of the Edge Recombination Crossover for the Orienteering Problem, which in a wider context it is also valid for any cycle problem. Another contribution has been the developed local search to handle large problems. The Branch-and-Cut algorithm includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. At the same time, we have generalized for cycle problems the support graph shrinking techniques and procedures to speed up the exact separation algorithms for subcycle elimination constraints. The experiments carried out in large-sized instances, up to 7393 nodes, show that both algorithms achieve outstanding results, both in terms of the quality of solutions and in terms of the execution time.bcam:basque center for applied mathematic