414 research outputs found
Tour recommendation for groups
Consider a group of people who are visiting a major touristic city, such as NY, Paris, or Rome. It is reasonable to assume that each member of the group has his or her own interests or preferences about places to visit, which in general may differ from those of other members. Still, people almost always want to hang out together and so the following question naturally arises: What is the best tour that the group could perform together in the city? This problem underpins several challenges, ranging from understanding people’s expected attitudes towards potential points of interest, to modeling and providing good and viable solutions. Formulating this problem is challenging because of multiple competing objectives. For example, making the entire group as happy as possible in general conflicts with the objective that no member becomes disappointed. In this paper, we address the algorithmic implications of the above problem, by providing various formulations that take into account the overall group as well as the individual satisfaction and the length of the tour. We then study the computational complexity of these formulations, we provide effective and efficient practical algorithms, and, finally, we evaluate them on datasets constructed from real city data
An evolutionary algorithm for online, resource constrained, multi-vehicle sensing mission planning
Mobile robotic platforms are an indispensable tool for various scientific and
industrial applications. Robots are used to undertake missions whose execution
is constrained by various factors, such as the allocated time or their
remaining energy. Existing solutions for resource constrained multi-robot
sensing mission planning provide optimal plans at a prohibitive computational
complexity for online application [1],[2],[3]. A heuristic approach exists for
an online, resource constrained sensing mission planning for a single vehicle
[4]. This work proposes a Genetic Algorithm (GA) based heuristic for the
Correlated Team Orienteering Problem (CTOP) that is used for planning sensing
and monitoring missions for robotic teams that operate under resource
constraints. The heuristic is compared against optimal Mixed Integer Quadratic
Programming (MIQP) solutions. Results show that the quality of the heuristic
solution is at the worst case equal to the 5% optimal solution. The heuristic
solution proves to be at least 300 times more time efficient in the worst
tested case. The GA heuristic execution required in the worst case less than a
second making it suitable for online execution.Comment: 8 pages, 5 figures, accepted for publication in Robotics and
Automation Letters (RA-L
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
The Vehicle Routing Problem with Service Level Constraints
We consider a vehicle routing problem which seeks to minimize cost subject to
service level constraints on several groups of deliveries. This problem
captures some essential challenges faced by a logistics provider which operates
transportation services for a limited number of partners and should respect
contractual obligations on service levels. The problem also generalizes several
important classes of vehicle routing problems with profits. To solve it, we
propose a compact mathematical formulation, a branch-and-price algorithm, and a
hybrid genetic algorithm with population management, which relies on
problem-tailored solution representation, crossover and local search operators,
as well as an adaptive penalization mechanism establishing a good balance
between service levels and costs. Our computational experiments show that the
proposed heuristic returns very high-quality solutions for this difficult
problem, matches all optimal solutions found for small and medium-scale
benchmark instances, and improves upon existing algorithms for two important
special cases: the vehicle routing problem with private fleet and common
carrier, and the capacitated profitable tour problem. The branch-and-price
algorithm also produces new optimal solutions for all three problems
The Team Orienteering Problem: Formulations and Branch-Cut and Price
The Team Orienteering Problem is a routing problem on a graph with durations associated to the arcs and profits assigned to visiting the vertices. A fixed number of identical vehicles, with a limited total duration for their routes, is given. The total profit gathered by all routes is to be maximized.
We devise an extended formulation where edges are indexed by the time they are placed in the route. A new class of inequalities, min cut, and the triangle clique cuts of Pessoa et. al., 2007 are added. The resulting formulation is solved by column generation. Branching is done following the work of Boussier et al. 2007, to which the branch-cut-and-price algorithm here proposed is compared. A few new upper bounds were obtained. Overall the presented approach has shown to be very competitive
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
A multi-criteria decision support system for a routing problem in waste collection
Autor proofThis work presents a decision support system for route planning of vehicles performing waste collection for recycling. We propose a prototype system that includes three modules: route optimization, waste generation prediction, and multiple-criteria decision analysis (MCDA). In this work we focus on the application of MCDA in route optimization. The structure and functioning of the DSS is also presented.
We modelled the waste collection procedure as a routing problem, more specifically as a team orienteering problem with capacity constraints and time windows. To solve the route optimization problem we developed a cellular genetic algorithm. For the MCDA module, we employed three methods: SMART, ValueFn and Analytic Hierarchy Process (AHP).
The decision support system was tested with real-world data from a waste management company that collects recyclables, and the capabilities of the system are discussed.FCT Fundação para a Ciência e Tecnologia, Project Scope: PEst-OE/EEI/UI0319/2
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
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
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