Spatial coverage in routing and path planning problems

Routing and path planning problems that involve spatial coverage have received increasing attention in recent years in different application areas. Spatial coverage refers to the possibility of considering nodes that are not directly served by a vehicle as visited for the purpose of the objective function or constraints. Despite similarities between the underlying problems, solution approaches have been developed in different disciplines independently, leading to different terminologies and solution techniques. This paper proposes a unified view of the approaches: Based on a formal introduction of the concept of spatial coverage in vehicle routing, it presents a classification scheme for core problem features and summarizes problem variants and solution concepts developed in the domains of operations research and robotics. The connections between these related problem classes offer insights into common underlying structures and open possibilities for developing new applications and algorithms

A GRASP-Based Approach for Planning UAV-Assisted Search and Rescue Missions

Search and Rescue (SAR) missions aim to search and provide first aid to persons in distress or danger. Due to the urgency of these situations, it is important to possess a system able to take fast action and effectively and efficiently utilise the available resources to conduct the mission. In addition, the potential complexity of the search such as the ruggedness of terrain or large size of the search region should be considered. Such issues can be tackled by using Unmanned Aerial Vehicles (UAVs) equipped with optical sensors. This can ensure the efficiency in terms of speed, coverage and flexibility required to conduct this type of time-sensitive missions. This paper centres on designing a fast solution approach for planning UAV-assisted SAR missions. The challenge is to cover an area where targets (people in distress after a hurricane or earthquake, lost vessels in sea, missing persons in mountainous area, etc.) can be potentially found with a variable likelihood. The search area is modelled using a scoring map to support the choice of the search sub-areas, where the scores represent the likelihood of finding a target. The goal of this paper is to propose a heuristic approach to automate the search process using scarce heterogeneous resources in the most efficient manner

Determining reliable solutions for the team orienteering problem with probabilistic delays

In the team orienteering problem, a fixed fleet of vehicles departs from an origin depot towards a destination, and each vehicle has to visit nodes along its route in order to collect rewards. Typically, the maximum distance that each vehicle can cover is limited. Alternatively, there is a threshold for the maximum time a vehicle can employ before reaching its destination. Due to this driving range constraint, not all potential nodes offering rewards can be visited. Hence, the typical goal is to maximize the total reward collected without exceeding the vehicle’s capacity. The TOP can be used to model operations related to fleets of unmanned aerial vehicles, road electric vehicles with limited driving range, or ride-sharing operations in which the vehicle has to reach its destination on or before a certain deadline. However, in some realistic scenarios, travel times are better modeled as random variables, which introduce additional challenges into the problem. This paper analyzes a stochastic version of the team orienteering problem in which random delays are considered. Being a stochastic environment, we are interested in generating solutions with a high expected reward that, at the same time, are highly reliable (i.e., offer a high probability of not suffering any route delay larger than a user-defined threshold). In order to tackle this stochastic optimization problem, which contains a probabilistic constraint on the random delays, we propose an extended simheuristic algorithm that also employs concepts from reliability analysis.This work has been partially funded by the Spanish Ministry of Science (PID2019-111100RB-C21-C22/AEI/10.13039/501100011033), the Barcelona City Council and Fundació “la Caixa” under the framework of the Barcelona Science Plan 2020–2023 (grant 21S09355-001), and the Generalitat Valenciana (PROMETEO/2021/065).Peer ReviewedPostprint (published version

Models and algorithms for multi-agent search problems

The problem of searching for objects of interest occurs in important applications ranging from rescue, security, transportation, to medicine. With the increasing use of autonomous vehicles as search platforms, there is a need for fast algorithms that can generate search plans for multiple agents in response to new information. In this dissertation, we develop new techniques for automated generation of search plans for different classes of search problems. First, we study the problem of searching for a stationary object in a discrete search space with multiple agents where each agent can access only a subset of the search space. In these problems, agents can fail to detect an object when inspecting a location. We show that when the probabilities of detection only depend on the locations, this problem can be reformulated as a minimum cost network optimization problem, and develop a fast specialized algorithm for the solution. We prove that our algorithm finds the optimal solution in finite time, and has worst-case computation performance that is faster than general minimum cost flow algorithms. We then generalize it to the case where the probabilities of detection depend on the agents and the locations, and propose a greedy algorithm that is 1/2-approximate. Second, we study the problem of searching for a moving object in a discrete search space with multiple agents where each agent can access only a subset of a discrete search space at any time and agents can fail to detect objects when searching a location at a given time. We provide necessary conditions for an optimal search plan, extending prior results in search theory. For the case where the probabilities of detection depend on the locations and the time periods, we develop a forward-backward iterative algorithm based on coordinate descent techniques to obtain solutions. To avoid local optimum, we derive a convex relaxation of the dynamic search problem and show this can be solved optimally using coordinate descent techniques. The solutions of the relaxed problem are used to provide random starting conditions for the iterative algorithm. We also address the problem where the probabilities of detection depend on the agents as well as the locations and the time periods, and show that a greedy-style algorithm is 1/2-approximate. Third, we study problems when multiple objects of interest being searched are physically scattered among locations on a graph and the agents are subject to motion constraints captured by the graph edges as well as budget constraints. We model such problem as an orienteering problem, when searching with a single agent, or a team orienteering problem, when searching with multiple agents. We develop novel real-time efficient algorithms for both problems. Fourth, we investigate classes of continuous-region multi-agent adaptive search problems as stochastic control problems with imperfect information. We allow the agent measurement errors to be either correlated or independent across agents. The structure of these problems, with objectives related to information entropy, allows for a complete characterization of the optimal strategies and the optimal cost. We derive a lower bound on the performance of the minimum mean-square error estimator, and provide upper bounds on the estimation error for special cases. For agents with independent errors, we show that the optimal sensing strategies can be obtained in terms of the solution of decoupled scalar convex optimization problems, followed by a joint region selection procedure. We further consider search of multiple objects and provide an explicit construction for adaptively determining the sensing actions

Determining Reliable Solutions for the Team Orienteering Problem with Probabilistic Delays

[EN] In the team orienteering problem, a fixed fleet of vehicles departs from an origin depot towards a destination, and each vehicle has to visit nodes along its route in order to collect rewards. Typically, the maximum distance that each vehicle can cover is limited. Alternatively, there is a threshold for the maximum time a vehicle can employ before reaching its destination. Due to this driving range constraint, not all potential nodes offering rewards can be visited. Hence, the typical goal is to maximize the total reward collected without exceeding the vehicle's capacity. The TOP can be used to model operations related to fleets of unmanned aerial vehicles, road electric vehicles with limited driving range, or ride-sharing operations in which the vehicle has to reach its destination on or before a certain deadline. However, in some realistic scenarios, travel times are better modeled as random variables, which introduce additional challenges into the problem. This paper analyzes a stochastic version of the team orienteering problem in which random delays are considered. Being a stochastic environment, we are interested in generating solutions with a high expected reward that, at the same time, are highly reliable (i.e., offer a high probability of not suffering any route delay larger than a user-defined threshold). In order to tackle this stochastic optimization problem, which contains a probabilistic constraint on the random delays, we propose an extended simheuristic algorithm that also employs concepts from reliability analysis.This work has been partially funded by the Spanish Ministry of Science (PID2019-111100RBC21-C22/AEI/10.13039/501100011033), the Barcelona City Council and Fundacio "la Caixa" under the framework of the Barcelona Science Plan 2020-2023 (grant 21S09355-001), and the Generalitat Valenciana (PROMETEO/2021/065).Herrera, EM.; Panadero, J.; Carracedo-Garnateo, P.; Juan-Pérez, ÁA.; Pérez Bernabeu, E. (2022). Determining Reliable Solutions for the Team Orienteering Problem with Probabilistic Delays. Mathematics. 10(20). https://doi.org/10.3390/math10203788102

On Solving Close Enough Orienteering Problem with Overlapped Neighborhoods

The Close Enough Traveling Salesman Problem (CETSP) is a well-known variant of the classic Traveling Salesman Problem whereby the agent may complete its mission at any point within a target neighborhood. Heuristics based on overlapped neighborhoods, known as Steiner Zones (SZ), have gained attention in addressing CETSPs. While SZs offer effective approximations to the original graph, their inherent overlap imposes constraints on the search space, potentially conflicting with global optimization objectives. Here we present the Close Enough Orienteering Problem with Non-uniform Neighborhoods (CEOP-N), which extends CETSP by introducing variable prize attributes and non-uniform cost considerations for prize collection. To tackle CEOP-N, we develop a new approach featuring a Randomized Steiner Zone Discretization (RSZD) scheme coupled with a hybrid algorithm based on Particle Swarm Optimization (PSO) and Ant Colony System (ACS) - CRaSZe-AntS. The RSZD scheme identifies sub-regions for PSO exploration, and ACS determines the discrete visiting sequence. We evaluate the RSZD's discretization performance on CEOP instances derived from established CETSP instances, and compare CRaSZe-AntS against the most relevant state-of-the-art heuristic focused on single-neighborhood optimization for CEOP. We also compare the performance of the interior search within SZs and the boundary search on individual neighborhoods in the context of CEOP-N. Our results show CRaSZe-AntS can yield comparable solution quality with significantly reduced computation time compared to the single-neighborhood strategy, where we observe an averaged 140.44% increase in prize collection and 55.18% reduction of execution time. CRaSZe-AntS is thus highly effective in solving emerging CEOP-N, examples of which include truck-and-drone delivery scenarios.Comment: 26 pages, 10 figure

Crowdsensing-driven route optimisation algorithms for smart urban mobility

Urban rörlighet anses ofta vara en av de främsta möjliggörarna för en hållbar statsutveckling. Idag skulle det dock kräva ett betydande skifte mot renare och effektivare stadstransporter vilket skulle stödja ökad social och ekonomisk koncentration av resurser i städerna. En viktig prioritet för städer runt om i världen är att stödja medborgarnas rörlighet inom stadsmiljöer medan samtidigt minska trafikstockningar, olyckor och föroreningar. Att utveckla en effektivare och grönare (eller med ett ord; smartare) stadsrörlighet är en av de svåraste problemen att bemöta för stora metropoler. I denna avhandling närmar vi oss problemet från det snabba utvecklingsperspektivet av ITlandskapet i städer vilket möjliggör byggandet av rörlighetslösningar utan stora stora investeringar eller sofistikerad sensortenkik. I synnerhet föreslår vi utnyttjandet av den mobila rörlighetsavkännings, eng. Mobile Crowdsensing (MCS), paradigmen i vilken befolkningen exploaterar sin mobilkommunikation och/eller mobilasensorer med syftet att frivilligt samla, distribuera, lokalt processera och analysera geospecifik information. Rörlighetavkänningssdata (t.ex. händelser, trafikintensitet, buller och luftföroreningar etc.) inhämtad från frivilliga i befolkningen kan ge värdefull information om aktuella rörelsesförhållanden i stad vilka, med adekvata databehandlingsalgoriter, kan användas för att planera människors rörelseflöden inom stadsmiljön. Såtillvida kombineras i denna avhandling två mycket lovande smarta rörlighetsmöjliggörare, eng. Smart Mobility Enablers, nämligen MCS och rese/ruttplanering. Vi kan därmed till viss utsträckning sammanföra forskningsutmaningar från dessa två delar. Vi väljer att separera våra forskningsmål i två delar, dvs forskningssteg: (1) arkitektoniska utmaningar vid design av MCS-system och (2) algoritmiska utmaningar för tillämpningar av MCS-driven ruttplanering. Vi ämnar att visa en logisk forskningsprogression över tiden, med avstamp i mänskligt dirigerade rörelseavkänningssystem som MCS och ett avslut i automatiserade ruttoptimeringsalgoritmer skräddarsydda för specifika MCS-applikationer. Även om vi förlitar oss på heuristiska lösningar och algoritmer för NP-svåra ruttproblem förlitar vi oss på äkta applikationer med syftet att visa på fördelarna med algoritm- och infrastrukturförslagen.La movilidad urbana es considerada una de las principales desencadenantes de un desarrollo urbano sostenible. Sin embargo, hoy en día se requiere una transición hacia un transporte urbano más limpio y más eficiente que soporte una concentración de recursos sociales y económicos cada vez mayor en las ciudades. Una de las principales prioridades para las ciudades de todo el mundo es facilitar la movilidad de los ciudadanos dentro de los entornos urbanos, al mismo tiempo que se reduce la congestión, los accidentes y la contaminación. Sin embargo, desarrollar una movilidad urbana más eficiente y más verde (o en una palabra, más inteligente) es uno de los temas más difíciles de afrontar para las grandes áreas metropolitanas. En esta tesis, abordamos este problema desde la perspectiva de un panorama TIC en rápida evolución que nos permite construir movilidad sin la necesidad de grandes inversiones ni sofisticadas tecnologías de sensores. En particular, proponemos aprovechar el paradigma Mobile Crowdsensing (MCS) en el que los ciudadanos utilizan sus teléfonos móviles y dispositivos, para nosotros recopilar, procesar y analizar localmente información georreferenciada, distribuida voluntariamente. Los datos de movilidad recopilados de ciudadanos que voluntariamente quieren compartirlos (por ejemplo, eventos, intensidad del tráfico, ruido y contaminación del aire, etc.) pueden proporcionar información valiosa sobre las condiciones de movilidad actuales en la ciudad, que con el algoritmo de procesamiento de datos adecuado, pueden utilizarse para enrutar y gestionar el flujo de gente en entornos urbanos. Por lo tanto, en esta tesis combinamos dos prometedoras fuentes de movilidad inteligente: MCS y la planificación de viajes/rutas, uniendo en cierta medida los distintos desafíos de investigación. Hemos dividido nuestros objetivos de investigación en dos etapas: (1) Desafíos arquitectónicos en el diseño de sistemas MCS y (2) Desafíos algorítmicos en la planificación de rutas aprovechando la información del MCS. Nuestro objetivo es demostrar una progresión lógica de la investigación a lo largo del tiempo, comenzando desde los fundamentos de los sistemas de detección centrados en personas, como el MCS, hasta los algoritmos de optimización de rutas diseñados específicamente para la aplicación de estos. Si bien nos centramos en algoritmos y heurísticas para resolver problemas de enrutamiento de clase NP-hard, utilizamos ejemplos de aplicaciones en el mundo real para mostrar las ventajas de los algoritmos e infraestructuras propuestas

Orienteering Problem: A survey of recent variants, solution approaches and applications

National Research Foundation (NRF) Singapore under International Research Centres in Singapore Funding Initiativ

Optimizing transportation systems and logistics network configurations : From biased-randomized algorithms to fuzzy simheuristics

242 páginasTransportation and logistics (T&L) are currently highly relevant functions in any competitive industry. Locating facilities or distributing goods to hundreds or thousands of customers are activities with a high degree of complexity, regardless of whether facilities and customers are placed all over the globe or in the same city. A countless number of alternative strategic, tactical, and operational decisions can be made in T&L systems; hence, reaching an optimal solution –e.g., a solution with the minimum cost or the maximum profit– is a really difficult challenge, even by the most powerful existing computers. Approximate methods, such as heuristics, metaheuristics, and simheuristics, are then proposed to solve T&L problems. They do not guarantee optimal results, but they yield good solutions in short computational times. These characteristics become even more important when considering uncertainty conditions, since they increase T&L problems’ complexity. Modeling uncertainty implies to introduce complex mathematical formulas and procedures, however, the model realism increases and, therefore, also its reliability to represent real world situations. Stochastic approaches, which require the use of probability distributions, are one of the most employed approaches to model uncertain parameters. Alternatively, if the real world does not provide enough information to reliably estimate a probability distribution, then fuzzy logic approaches become an alternative to model uncertainty. Hence, the main objective of this thesis is to design hybrid algorithms that combine fuzzy and stochastic simulation with approximate and exact methods to solve T&L problems considering operational, tactical, and strategic decision levels. This thesis is organized following a layered structure, in which each introduced layer enriches the previous one.El transporte y la logística (T&L) son actualmente funciones de gran relevancia en cual quier industria competitiva. La localización de instalaciones o la distribución de mercancías a cientos o miles de clientes son actividades con un alto grado de complejidad, indepen dientemente de si las instalaciones y los clientes se encuentran en todo el mundo o en la misma ciudad. En los sistemas de T&L se pueden tomar un sinnúmero de decisiones al ternativas estratégicas, tácticas y operativas; por lo tanto, llegar a una solución óptima –por ejemplo, una solución con el mínimo costo o la máxima utilidad– es un desafío realmente di fícil, incluso para las computadoras más potentes que existen hoy en día. Así pues, métodos aproximados, tales como heurísticas, metaheurísticas y simheurísticas, son propuestos para resolver problemas de T&L. Estos métodos no garantizan resultados óptimos, pero ofrecen buenas soluciones en tiempos computacionales cortos. Estas características se vuelven aún más importantes cuando se consideran condiciones de incertidumbre, ya que estas aumen tan la complejidad de los problemas de T&L. Modelar la incertidumbre implica introducir fórmulas y procedimientos matemáticos complejos, sin embargo, el realismo del modelo aumenta y, por lo tanto, también su confiabilidad para representar situaciones del mundo real. Los enfoques estocásticos, que requieren el uso de distribuciones de probabilidad, son uno de los enfoques más empleados para modelar parámetros inciertos. Alternativamente, si el mundo real no proporciona suficiente información para estimar de manera confiable una distribución de probabilidad, los enfoques que hacen uso de lógica difusa se convier ten en una alternativa para modelar la incertidumbre. Así pues, el objetivo principal de esta tesis es diseñar algoritmos híbridos que combinen simulación difusa y estocástica con métodos aproximados y exactos para resolver problemas de T&L considerando niveles de decisión operativos, tácticos y estratégicos. Esta tesis se organiza siguiendo una estructura por capas, en la que cada capa introducida enriquece a la anterior. Por lo tanto, en primer lugar se exponen heurísticas y metaheurísticas sesgadas-aleatorizadas para resolver proble mas de T&L que solo incluyen parámetros determinísticos. Posteriormente, la simulación Monte Carlo se agrega a estos enfoques para modelar parámetros estocásticos. Por último, se emplean simheurísticas difusas para abordar simultáneamente la incertidumbre difusa y estocástica. Una serie de experimentos numéricos es diseñada para probar los algoritmos propuestos, utilizando instancias de referencia, instancias nuevas e instancias del mundo real. Los resultados obtenidos demuestran la eficiencia de los algoritmos diseñados, tanto en costo como en tiempo, así como su confiabilidad para resolver problemas realistas que incluyen incertidumbre y múltiples restricciones y condiciones que enriquecen todos los problemas abordados.Doctorado en Logística y Gestión de Cadenas de SuministrosDoctor en Logística y Gestión de Cadenas de Suministro