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One of the important problems in multiprocessor systems is Task Graph Scheduling. Task Graph Scheduling is an NP-Hard problem. Both learning automata and genetic algorithms are search tools which are used for solving many NP-Hard problems.…

Computational Complexity · Computer Science 2011-06-13 Vahid Majid Nezhad , Habib Motee Gader , Evgueni Efimov

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-27 Rabab Alkhalifa , Fatima Alkhomayes , Boushra Almazroua , Dana Alhaidan , Maryam Alothman , Jumana Almuhaidib

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

Data Structures and Algorithms · Computer Science 2022-05-31 Amey Gohil , Manan Tayal , Tezan Sahu , Vyankatesh Sawalpurkar

The asymptotic behavior of the optimal TSP tour length is well known from the classical Beardwood--Halton--Hammersley theorem. We extend this result to the Traveling Salesman Problem with Drone (TSPD), a cooperative routing problem in which…

Optimization and Control · Mathematics 2026-03-03 Jae Hyeok Lee , Taekang Hwang , Changhyun Kwon

The vehicle routing problem with drones (VRP-D) is to determine the optimal routes of trucks and drones such that the total operational cost is minimized in a scenario where the trucks work in tandem with the drones to deliver parcels to…

Computers and Society · Computer Science 2024-04-16 Navid Imran , Myounggyu Won

The emergence of truck-drone collaborative systems in last-mile logistics has positioned the Traveling Salesman Problem with Drones (TSP-D) as a pivotal extension of classical routing optimization, where synchronized vehicle coordination…

Machine Learning · Computer Science 2025-11-10 Taihelong Zeng , Yun Lin , Yuhe Shi , Yan Li , Zhiqing Wei , Xuanru Ji

In this paper we consider a problem related to deliveries assisted by an unmanned aerial vehicle, so-called drone. In particular we consider the Flying Sidekick Traveling Salesman Problem, where a truck and a drone cooperate to delivery…

Optimization and Control · Mathematics 2022-10-31 Mauro Dell'Amico , Roberto Montemanni , Stefano Novellani

In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the…

Methodology · Statistics 2013-09-25 Adriano Zanin Zambom , Julian A. A. Collazos , Ronaldo Dias

The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization task with numerous practical applications. Classic heuristic solvers can attain near-optimal performance for small problem instances, but become…

Machine Learning · Computer Science 2025-08-13 Michael Li , Eric Bae , Christopher Haberland , Natasha Jaques

In a near future drones are likely to become a viable way of distributing parcels in a urban environment. In this paper we consider the parallel drone scheduling traveling salesman problem, where a set of customers requiring a delivery is…

Optimization and Control · Mathematics 2022-10-31 Mauro Dell'Amico , Roberto Montemanni , Stefano Novellani

The travelling salesman problem (TSP) of space trajectory design is complicated by its complex structure design space. The graph based tree search and stochastic seeding combinatorial approaches are commonly employed to tackle the…

Optimization and Control · Mathematics 2021-09-07 Liqiang Hou , Shufan Wu , Zhongcheng Mu , Meilin Liu

In this paper we schedule the travel path of a set of drones across a graph where the nodes need to be visited multiple times at pre-defined points in time. This is an extension of the well-known multiple traveling salesman problem. The…

Artificial Intelligence · Computer Science 2021-01-06 Emmanouil Rigas , Panayiotis Kolios , Georgios Ellinas

In this paper, we revisit the application of Genetic Algorithm (GA) to the Traveling Salesperson Problem (TSP) and introduce a family of novel crossover operators that outperform the previous state of the art. The novel crossover operators…

Neural and Evolutionary Computing · Computer Science 2024-01-10 Martin Uray , Stefan Wintersteller , Stefan Huber

In this work, a novel idea is presented for combinatorial optimization problems, a hybrid network, which results in a superior outcome. We applied this method to graph pointer networks [1], expanding its capabilities to a higher level. We…

We study last-mile delivery problems where trucks and drones collaborate to deliver goods to final customers. In particular, we focus on problem settings where either a single truck or a fleet with several homogeneous trucks work in…

Optimization and Control · Mathematics 2023-07-10 Roberto Montemanni , Mauro Dell'Amico , Andrea Corsini

We propose an efficient branch-and-cut algorithm to exactly solve the parallel drone scheduling traveling salesman problem. Our algorithm can find optimal solutions for all but two existing instances with up to 229 customers in a reasonable…

Data Structures and Algorithms · Computer Science 2021-11-23 Minh Anh Nguyen , Hai Long Luong , Minh Hoàng Hà , Ha-Bang Ban

In (Zhu et al., 2022), it proposes an electric vehicle traveling salesman problem with drone while assuming that the electric vehicle (EV) is a battery-electric vehicle whose energy could be refreshed in a battery swap station in minutes.…

Optimization and Control · Mathematics 2022-05-30 Tengkuo Zhu , Stephen D. Boyles , Avinash Unnikrishnan

Evolutionary algorithms have been shown to obtain good solutions for complex optimization problems in static and dynamic environments. It is important to understand the behaviour of evolutionary algorithms for complex optimization problems…

Neural and Evolutionary Computing · Computer Science 2023-05-31 Jakob Bossek , Aneta Neumann , Frank Neumann

Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition…

Optimization and Control · Mathematics 2015-09-22 Xiaolin Tang , Chunhua Yang , Xiaojun Zhou , Weihua Gui

In this paper, a novel knowledge-based genetic algorithm for path planning of a mobile robot in unstructured complex environments is proposed, where five problem-specific operators are developed for efficient robot path planning. The…

Robotics · Computer Science 2022-09-07 Yanrong Hu , Simon X. Yang