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We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space…

This paper proposes an algorithmic method to heuristically solve the famous Travelling Salesman Problem (TSP) when the salesman's path evolves in continuous state space and discrete time but with otherwise arbitrary (nonlinear) dynamics.…

Recently, deep reinforcement learning (DRL) frameworks have shown potential for solving NP-hard routing problems such as the traveling salesman problem (TSP) without problem-specific expert knowledge. Although DRL can be used to solve…

This paper presents a new method for integrated time-optimal routing and trajectory optimization of multirotor unmanned aerial vehicles (UAVs). Our approach extends the well-known Traveling Salesman Problem by accounting for the limited…

Despite some successful applications of goal-driven navigation, existing deep reinforcement learning (DRL)-based approaches notoriously suffers from poor data efficiency issue. One of the reasons is that the goal information is decoupled…

Large Language Models (LLMs) are deep learning models designed to generate text based on textual input. Although researchers have been developing these models for more complex tasks such as code generation and general reasoning, few efforts…

This paper describes TSP exact solution of polynomial complexity. It is considered properties of proposed method. Effectiveness of proposed solution is illustrated by outcomes of computer modeling.

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…

Path planning is usually solved by addressing either the (high-level) route planning problem (waypoint sequencing to achieve the final goal) or the (low-level) path planning problem (trajectory prediction between two waypoints avoiding…

In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points…

A recently formulated statistical mechanics method is used to study the phase transition occurring in a generalisation of the Traveling Salesman Problem (TSP) known as the centred TSP. The method shows that the problem has clear signs of a…

The Orienteering Problem with Time Windows (OPTW) is a combinatorial optimization problem where the goal is to maximize the total score collected from different visited locations. The application of neural network models to combinatorial…

Power system optimal dispatch with transient security constraints is commonly represented as Transient Security-Constrained Optimal Power Flow (TSC-OPF). Deep Reinforcement Learning (DRL)-based TSC-OPF trains efficient decision-making…

An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such…

Multimodal Large Language Models (MLLMs) have demonstrated proficiency in processing di-verse modalities, including text, images, and audio. These models leverage extensive pre-existing knowledge, enabling them to address complex problems…

Despite the recent advancements in offline reinforcement learning via supervised learning (RvS) and the success of the decision transformer (DT) architecture in various domains, DTs have fallen short in several challenging benchmarks. The…

This study addresses a gap in the utilization of Reinforcement Learning (RL) and Machine Learning (ML) techniques in solving the Stochastic Vehicle Routing Problem (SVRP) that involves the challenging task of optimizing vehicle routes under…

For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today's computation, we employ one…

Route planning for a fleet of vehicles is an important task in applications such as package delivery, surveillance, or transportation, often integrated within larger Intelligent Transportation Systems (ITS). This problem is commonly…

Solving the Traveling Salesman Problem (TSP) is NP-hard yet fundamental for a wide range of real-world applications. Classical exact methods face challenges in scaling, and heuristic methods often require domain-specific parameter…