Search Results (7)

In practical missions, quadrotor drones frequently face the challenge of navigating through multiple predetermined waypoints in cluttered environments where the sequence of the waypoints is not specified. This study presents a comprehensive multi-waypoint motion planning framework for quadrotor drones, comprising multi-waypoint trajectory planning and waypoint sequencing. To generate a trajectory that follows a specified sequence of waypoints, we integrate uniform B-spline curves with a bidirectional A* search to produce a safe, kinodynamically feasible initial trajectory. Subsequently, we model the optimization problem as a quadratically constrained quadratic program (QCQP) to enhance the trackability of the trajectory. Throughout this process, a replanning strategy is designed to ensure the traversal of multiple waypoints. To accurately determine the shortest flight time waypoint sequence, the fast marching (FM) method is utilized to efficiently establish the cost matrix between waypoints, ensuring consistency with the constraints and objectives of the planning method. Ant colony optimization (ACO) is then employed to solve this variant of the traveling salesman problem (TSP), yielding the sequence with the lowest temporal cost. The framework’s performance was validated in various complex simulated environments, demonstrating its efficacy as a robust solution for autonomous quadrotor drone navigation. Full article

Delivery drones have been attracting attention as a means of solving recent logistics issues, and many companies are focusing on their practical applications. Many research studies on delivery drones have been active for several decades. Among them, extended routing problems for drones have been proposed based on the Traveling Salesman Problem (TSP), which is used, for example, in truck vehicle routing problems. In parcel delivery by drones, additional constraints such as battery capacity, payload, and weather conditions need to be considered. This study addresses the routing problem for delivery drones. Most existing studies assume that the drone’s flight speed is constant regardless of the load. On the other hand, some studies assume that the flight speed varies with the load. This routing problem is called the Flight Speed-Aware Traveling Salesman Problem (FSTSP). The complexity of the drone flight speed function in this problem makes it difficult to solve the routing problem using general-purpose mathematical optimization solvers. In this study, the routing problem is reduced to an integer programming problem by using linear and quadratic approximations of the flight speed function. This enables us to solve the problem using general-purpose mathematical optimization solvers. In experiments, we compared the existing and proposed methods in terms of solving time and total flight time. The experimental results show that the proposed method with multiple threads has a shorter solving time than the state-of-the-art method when the number of customers is 17 or more. In terms of total flight time, the proposed methods deteriorate by an average of 0.4% for integer quadratic programming and an average of 1.9% for integer cubic programming compared to state-of-the-art methods. These experimental results show that the quadratic and cubic approximations of the problem have almost no degradation of the solution. Full article

Traveling salesman, linear ordering, quadratic assignment, and flow shop scheduling are typical examples of permutation-based combinatorial optimization problems with real-life applications. These problems naturally represent solutions as an ordered permutation of objects. However, as the number of objects increases, finding optimal permutations is extremely difficult when using exact optimization methods. In those circumstances, approximate algorithms such as metaheuristics are a plausible way of finding acceptable solutions within a reasonable computational time. In this paper, we present a technique for clustering and discriminating ordered permutations with potential applications in developing neural network-guided metaheuristics to solve this class of problems. In this endeavor, we developed two different techniques to convert ordered permutations to binary-vectors and considered Adaptive Resonate Theory (ART) neural networks for clustering the resulting binary vectors. The proposed binary conversion techniques and two neural networks (ART-1 and Improved ART-1) are examined under various performance indicators. Numerical examples show that one of the binary conversion methods provides better results than the other, and Improved ART-1 is superior to ART-1. Additionally, we apply the proposed clustering and discriminating technique to develop a neural-network-guided Genetic Algorithm (GA) to solve a flow-shop scheduling problem. The investigation shows that the neural network-guided GA outperforms pure GA. Full article

An algorithm for automatically planning trajectories designed for painting large objects is proposed in this paper to eliminate the difficulty of painting large objects and ensure their surface quality. The algorithm was divided into three phases, comprising the target point acquisition phase, the trajectory planning phase, and the UR5 robot inverse solution acquisition phase. In the target point acquisition phase, the standard triangle language (STL) file, algorithm of principal component analyses (PCA), and k-dimensional tree (k-d tree) were employed to obtain the point cloud model of the car roof to be painted. Simultaneously, the point cloud data were compressed as per the requirements of the painting process. In the trajectory planning phase, combined with the maximum operating space of the UR5 robot, the painting trajectory of the target points was converted into multiple traveling salesman problem (TSP) models, and each TSP model was created with a genetic algorithm (GA). In the last phase, in conformity with the singularities of the UR5 robot’s motion space, the painting trajectory was divided into a recommended area trajectory and a non-recommended area trajectory and created by the analytical method and sequential quadratic programming (SQP). Finally, the proposed algorithm for painting large objects was deployed in a simulation experiment. Simulation results showed that the accuracy of the algorithm could meet the requirements of painting technology, and it has promising engineering practicability. Full article

This paper studies the Hamiltonian cycle problem (HCP) and the traveling salesman problem (TSP) on D-Wave quantum systems. Motivated by the fact that most libraries present their benchmark instances in terms of adjacency matrices, we develop a novel matrix formulation for the HCP and TSP Hamiltonians, which enables the seamless and automatic integration of benchmark instances in quantum platforms. We also present a thorough mathematical analysis of the precise number of constraints required to express the HCP and TSP Hamiltonians. This analysis explains quantitatively why, almost always, running incomplete graph instances requires more qubits than complete instances. It turns out that QUBO models for incomplete graphs require more quadratic constraints than complete graphs, a fact that has been corroborated by a series of experiments. Moreover, we introduce a technique for the min-max normalization for the coefficients of the TSP Hamiltonian to address the problem of invalid solutions produced by the quantum annealer, a trend often observed. Our extensive experimental tests have demonstrated that the D-Wave Advantage_system4.1 is more efficient than the Advantage_system1.1, both in terms of qubit utilization and the quality of solutions. Finally, we experimentally establish that the D-Wave hybrid solvers always provide valid solutions, without violating the given constraints, even for arbitrarily big problems up to 120 nodes. Full article

We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of necessary variables. After, we will present a detailed study of the constraints subject to the new TSP model and benchmark it with MTZ and native formulations. Finally, we will test whether the correctness of the formulation by entering it into a QUBO problem solver. The solver chosen is a D-Wave_2000Q6 quantum computer simulator due to the connection between Quantum Annealing and QUBO formulations. Full article

One fundamental problem of bioinformatics is the computational recognition of DNA and RNA binding sites. Given a set of short DNA or RNA sequences of equal length such as transcription factor binding sites or RNA splice sites, the task is to learn a pattern from this set that allows the recognition of similar sites in another set of DNA or RNA sequences. Permuted Markov (PM) models and permuted variable length Markov (PVLM) models are two powerful models for this task, but the problem of finding an optimal PM model or PVLM model is NP-hard. While the problem of finding an optimal PM model or PVLM model of order one is equivalent to the traveling salesman problem (TSP), the problem of finding an optimal PM model or PVLM model of order two is equivalent to the quadratic TSP (QTSP). Several exact algorithms exist for solving the QTSP, but it is unclear if these algorithms are capable of solving QTSP instances resulting from RNA splice sites of at least 150 base pairs in a reasonable time frame. Here, we investigate the performance of three exact algorithms for solving the QTSP for ten datasets of splice acceptor sites and splice donor sites of five different species and find that one of these algorithms is capable of solving QTSP instances of up to 200 base pairs with a running time of less than two days. Full article