Theoretical analysis of local search and simple evolutionary algorithms for the generalized travelling salesperson problem

The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which metaheuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a cluster-based approach and a node-based approach, have been proposed by Hu and Raidl (2008) for solving this problem. In this article, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we point out the complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches when initialized on a particular point of the search space, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time. Then we turn our attention to analysing the behaviour of simple evolutionary algorithms that use these approaches. We show that the node-based approach solves the hard instance of the cluster-based approach presented in Corus et al. (2016) in polynomial time. Furthermore, we prove an exponential lower bound on the optimization time of the node-based approach for a class of Euclidean instances.Mojgan Pourhassan, Frank Neuman

The Pickup and Multiple Delivery Problem

This thesis presents my work on the pickup and multiple delivery problem, a real-world vehicle routing and scheduling problem with soft time windows, working time and last-in-first-out constraints, developed in collaboration with Transfaction Ltd., who conduct logistics analysis for several large retailers in the UK. A summary of relevant background literature is presented highlighting where my research fits into and contributes to the broader academic landscape. I present a detailed model of the problem and thoroughly analyse a case-study data set, obtaining distributions used for further research. A new variable neighbourhood descent with memory hyper-heuristic is presented and shown to be an effective technique for solving instances of the real-world problem. I analyse strategies for cooperation and competition amongst haulage companies and quantify their effectiveness. The value of time and timely information for planning pickup and delivery requests is investigated. The insights gained are of real industrial relevance, highlighting how a variety of business decisions can produce significant cost savings

Deep Semantic Learning Machine Initial design and experiments

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced AnalyticsComputer vision is an interdisciplinary scientific field that allows the digital world to interact with the real world. It is one of the fastest-growing and most important areas of data science. Applications are endless, given various tasks that can be solved thanks to the advances in the computer vision field. Examples of types of tasks that can be solved thanks to computer vision models are: image analysis, object detection, image transformation, and image generation. Having that many applications is vital for providing models with the best possible performance. Although many years have passed since backpropagation was invented, it is still the most commonly used approach of training neural networks. A satisfactory performance can be achieved with this approach, but is it the best it can get? A fixed topology of a neural network that needs to be defined before any training begins seems to be a significant limitation as the performance of a network is highly dependent on the topology. Since there are no studies that would precisely guide scientists on selecting a proper network structure, the ability to adjust a topology to a problem seems highly promising. Initial ideas of the evolution of neural networks that involve heuristic search methods have provided encouragingly good results for the various reinforcement learning task. This thesis presents the initial experiments on the usage of a similar approach to solve image classification tasks. The new model called Deep Semantic Learning Machine is introduced with a new mutation method specially designed to solve computer vision problems. Deep Semantic Learning Machine allows a topology to evolve from a small network and adjust to a given problem. The initial results are pretty promising, especially in a training dataset. However, in this thesis Deep Semantic Learning Machine was developed only as proof of a concept and further improvements to the approach can be made

A comparative study of evolutionary approaches to the bi-objective dynamic Travelling Thief Problem

Dynamic evolutionary multi-objective optimization is a thriving research area. Recent contributions span the development of specialized algorithms and the construction of challenging benchmark problems. Here, we continue these research directions through the development and analysis of a new bi-objective problem, the dynamic Travelling Thief Problem (TTP), including three modes of dynamic change: city locations, item profit values, and item availability. The interconnected problem components embedded in the dynamic problem dictate that the effective tracking of good trade-off solutions that satisfy both objectives throughout dynamic events is non-trivial. Consequently, we examine the relative contribution to the non-dominated set from a variety of population seeding strategies, including exact solvers and greedy algorithms for the knapsack and tour components, and random techniques. We introduce this responsive seeding extension within an evolutionary algorithm framework. The efficacy of alternative seeding mechanisms is evaluated across a range of exemplary problem instances using ranking-based and quantitative statistical comparisons, which combines performance measurements taken throughout the optimization. Our detailed experiments show that the different dynamic TTP instances present varying difficulty to the seeding methods tested. We posit the dynamic TTP as a suitable benchmark capable of generating problem instances with different controllable characteristics aligning with many real-world problems

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

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-

New Formulations and Solution Methods for the Dial-a-ride Problem

The classic Dial-A-Ride Problem (DARP) aims at designing the minimum-cost routing solution that accommodates a set of user requests under constraints at the operations planning level. It is a highly constrained combinatorial optimization problem initially designed for providing door-to-door transportation for people with limited mobility (e.g. the elderly or disabled). It consists of routing and scheduling a fleet of capacitated vehicles to service a set of requests with specified pickup and drop-off locations and time windows. With the details of requests obtained either beforehand (static DARP) or en-route (dynamic DARP), dial-a-ride operators strive to deliver efficient and yet high-quality transport services that satisfy each passenger's individual travel needs. The goal of this thesis is threefold: (1) to propose rich DARP formulations where users' preferences are taken into account, in order to improve service quality of Demand-Responsive Transport (DRT) services and promote ridership strategically; (2) to develop novel and efficient solution methods where local search, column generation, metaheuristics and machine learning techniques are integrated to solve large-scale DARPs; and (3) to conduct real-life DARP case studies (using data extracted from NYC Yellow Taxi trip records) to test the practicality of proposed models and solution methods, as well as to emphasise the importance of connecting algorithms with real-world datasets. These aims are achieved and presented in the three core chapters of this thesis. In the first core chapter (Chapter 3), two Mixed Integer Programming (MIP) formulations (link-based and path-based) of DARP are presented, alongside with their objective functions and standard solution methods. This chapter builds the foundation of the thesis by elaborating the base models and algorithms that this thesis is based on, and by running benchmark experiments and reporting numerical results as the base line of the whole thesis. In the second core chapter (Chapter 4), two DARP models (one deterministic, one stochastic) integrated with users' preferences from dial-a-ride service operators' perspective are proposed, facilitating them to optimise their overall profit while maintaining service quality. In these models, users' utility users' preferences are considered within a dial-a-ride problem. A customized local search based heuristic and a matheuristic are developed to solve the proposed Chance-Constrained DARP (CC-DARP). Numerical results are reported for both DARP benchmark instances and a realistic case study based on New York City yellow taxi trip data. This chapter also explores the design of revenue/fleet management and pricing differentiation. The proposed chance-constrained DARP formulation provides a new decision-support tool to inform on revenue and fleet management, including fleet sizing, for DRT systems at a strategic planning level. In the last core chapter (Chapter 5), three hybrid metaheuristic algorithms integrated with Reinforcement Learning (RL) techniques are proposed and implemented, aiming to increase the scale-up capability of existing DARP solution methods. Machine learning techniques and/or a branching scheme are incorporated with various metaheuristic algorithms including VNS and LNS, providing innovative methodologies to solve large-instance DARPs in a more efficient manner. Thompson Sampling (TS) is applied to model dual values of requests under a column generation setting to negate the effect of dual oscillation (i.e. promote faster converging). The performance of proposed algorithms is tested benchmark datasets, and strengths and weaknesses across different algorithms are reported

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance