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Multiple-TSP, also abbreviated in the literature as mTSP, is an extension of the Traveling Salesman Problem that lies at the core of many variants of the Vehicle Routing problem of great practical importance. The current paper develops and…
The maximum traveling salesman problem (Max TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. This problem is APX-hard in the general metric case but admits…
Existing neural methods for the Travelling Salesman Problem (TSP) mostly aim at finding a single optimal solution. To discover diverse yet high-quality solutions for Multi-Solution TSP (MSTSP), we propose a novel deep reinforcement learning…
The Traveling Salesman Problem is one of the most studied problems in computational complexity and its approximability has been a long standing open question. Currently, the best known inapproximability threshold known is 220/219 due to…
We study the fair capacitated vehicle routing problem, in which a fleet of vehicles must serve a set of customers such that the difference between the longest and shortest route, the range, is minimized. A key challenge is that the range…
The 2-Opt heuristic is one of the simplest algorithms for finding good solutions to the metric Traveling Salesman Problem. It is the key ingredient to the well-known Lin-Kernighan algorithm and often used in practice. So far, only upper and…
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…
Safety is extremely important for urban flights of autonomous Unmanned Aerial Vehicles (UAVs). Risk-aware path planning is one of the most effective methods to guarantee the safety of UAVs. This type of planning can be represented as a…
The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it…
This paper implements a new way of solving a problem called the traveling salesman problem (TSP) using quantum genetic algorithm (QGA). We compared how well this new approach works to the traditional method known as a classical genetic…
We present a black-box reduction from the path version of the Traveling Salesman Problem (Path TSP) to the classical tour version (TSP). More precisely, we show that given an $\alpha$-approximation algorithm for TSP, then, for any $\epsilon…
The Multi-Traveling Salesman Problem (MTSP) is a commonly used mathematical model for multi-agent task allocation. However, as the number of agents and task targets increases, existing optimization-based methods often incur prohibitive…
We study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to…
This study investigates the problem of traveling salesman problem with circular neighborhood (TSPCN). Instead of cities there are circles and each point on circle can be a potential visiting node. The problem is to find the minimum length…
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the $(1,2)$-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on…
Aerial vehicles have recently attracted significant attention in a variety of commercial and civilian applications due to their high mobility, flexible deployment and cost-effectiveness. To leverage these promising features, the aerial…
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…
This paper studies energy-efficient unmanned aerial vehicle (UAV)-enabled wireless communications, where the UAV acts as a flying base station (BS) to serve the ground users (GUs) within some predetermined latency constraints, e.g.,…
The Generalized Traveling Salesman Problem (GTSP) is one of the NP-hard combinatorial optimization problems. A variant of GTSP is E-GTSP where E, meaning equality, has the constraint: exactly one node from a cluster of a graph partition is…
The Flying Sidekick Traveling Salesman Problem (FSTSP) considers a delivery system composed by a truck and a drone. The drone launches from the truck with a single package to deliver to a customer. Each drone must return to the truck to…