The Orienteering Problem under Uncertainty Stochastic Programming and Robust Optimization compared

The Orienteering Problem (OP) is a generalization of the well-known traveling salesman problem and has many interesting applications in logistics, tourism and defense. To reflect real-life situations, we focus on an uncertain variant of the OP. Two main approaches that deal with optimization under uncertainty are stochastic programming and robust optimization. We will explore the potentialities and bottlenecks of these two approaches applied to the uncertain OP. We will compare the known robust approach for the uncertain OP (the robust orienteering problem) to the new stochastic programming counterpart (the two-stage orienteering problem). The application of both approaches will be explored in terms of their suitability in practice

Optimisation of the T-square sampling method to estimate population sizes.

Population size and density estimates are needed to plan resource requirements and plan health related interventions. Sampling frames are not always available necessitating surveys using non-standard household sampling methods. These surveys are time-consuming, difficult to validate, and their implementation could be optimised. Here, we discuss an example of an optimisation procedure for rapid population estimation using T-Square sampling which has been used recently to estimate population sizes in emergencies. A two-stage process was proposed to optimise the T-Square method wherein the first stage optimises the sample size and the second stage optimises the pathway connecting the sampling points. The proposed procedure yields an optimal solution if the distribution of households is described by a spatially homogeneous Poisson process and can be sub-optimal otherwise. This research provides the first step in exploring how optimisation techniques could be applied to survey designs thereby providing more timely and accurate information for planning interventions

Application of genetic algorithms to the travelling salesperson problem.

Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1996.Genetic Algorithms (GAs) can be easily applied to many different problems since they make few assumptions about the application domain and perform relatively well. They can also be modified with some success for handling a particular problem. The travelling salesperson problem (TSP) is a famous NP-hard problem in combinatorial optimization. As a result it has no known polynomial time solution. The aim of this dissertation will be to investigate the application of a number of GAs to the TSP. These results will be compared with those of traditional solutions to the TSP and with the results of other applications of the GA to the TSP

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

A Systematic Review of Approximability Results for Traveling Salesman Problems leveraging the TSP-T3CO Definition Scheme

The traveling salesman (or salesperson) problem, short TSP, is a problem of strong interest to many researchers from mathematics, economics, and computer science. Manifold TSP variants occur in nearly every scientific field and application domain: engineering, physics, biology, life sciences, and manufacturing just to name a few. Several thousand papers are published on theoretical research or application-oriented results each year. This paper provides the first systematic survey on the best currently known approximability and inapproximability results for well-known TSP variants such as the "standard" TSP, Path TSP, Bottleneck TSP, Maximum Scatter TSP, Generalized TSP, Clustered TSP, Traveling Purchaser Problem, Profitable Tour Problem, Quota TSP, Prize-Collecting TSP, Orienteering Problem, Time-dependent TSP, TSP with Time Windows, and the Orienteering Problem with Time Windows. The foundation of our survey is the definition scheme T3CO, which we propose as a uniform, easy-to-use and extensible means for the formal and precise definition of TSP variants. Applying T3CO to formally define the variant studied by a paper reveals subtle differences within the same named variant and also brings out the differences between the variants more clearly. We achieve the first comprehensive, concise, and compact representation of approximability results by using T3CO definitions. This makes it easier to understand the approximability landscape and the assumptions under which certain results hold. Open gaps become more evident and results can be compared more easily

An efficient evolutionary algorithm for the orienteering problem

This paper deals with the Orienteering Problem, which is a routing problem. In the Orienteering Problem, each node has a profit assigned and the goal is to find the route that maximizes the total collected profit subject to a limitation on the total route distance. To solve this problem, we propose an evolutionary algorithm, whose key characteristic is to maintain unfeasible solutions during the search. Furthermore, it includes a novel solution codification for the Orienteering Problem, a novel heuristic for node inclusion in the route, an adaptation of the Edge Recombination crossover developed for the Travelling Salesperson Problem, specific operators to recover the feasibility of solutions when required, and the use of the Lin-Kernighan heuristic to improve the route lengths. We compare our algorithm with three state-of-the-art algorithms for the problem on 344 benchmark instances, with up to 7397 nodes. The results show a competitive behavior of our approach in instances of low-medium dimensionality, and outstanding results in the large dimensionality instances reaching new best known solutions with lower computational time than the state-of-the-art algorithms.MTM2015-65317-P, TIN2016-78365-R, IT-609-13, IT-928-16, UFI BETS 201

Practical Route Planning Algorithm

Routing algorithms are traditionally considered to apply thesum of profits gathered at visited locations as an objectivefunction since the Traveling Salesman Problem. This heritagedisregards many practical considerations, hence the result ofthese models meet with user’s needs rarely.Thus considering the importance of this theoretical and modelingproblem, a novel objective function will be presented inthis paper as an extension of the one inherited from the TSPthat is more aligned with user preferences and aims to maximizethe tourist’s satisfaction. We also propose a heuristicalgorithm to solve the Team Orienteering Problem with relativelylow computation time in case of high number of verticeson the graph and multiple tour days. Based on the key performanceindicators and user feedback the algorithm is suitableto be implemented in a GIS application considering that even a3-day tour is designed less than 4 seconds