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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.
Quantum computing (QC) is expected to solve incredibly difficult problems, including finding optimal solutions to combinatorial optimization problems. However, to date, QC alone is still far to demonstrate this capability except on…
The Steiner Traveling Salesman Problem (STSP) is a variant of the Traveling Salesman Problem (TSP) that is particularly suitable when dealing with sparse networks, such as road networks. The standard integer programming formulation of the…
Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a…
Yatsenko gives a polynomial-time algorithm for solving the traveling salesman problem. We examine the correctness of the algorithm and its construction. We also comment on Yatsenko's evaluation of the algorithm.
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…
In this case study, the renowned Travelling Salesmen problem has been studied. Travelling Salesman problem is a most demanding computational problem in Computer Science. The Travelling Salesmen problem has been solved by two different ways…
Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems,…
Many real-world optimization problems have multiple interacting components. Each of these can be NP-hard and they can be in conflict with each other, i.e., the optimal solution for one component does not necessarily represent an optimal…
Neural solvers have shown significant potential in solving the Traveling Salesman Problem (TSP), yet current approaches face significant challenges. Supervised learning (SL)-based solvers require large amounts of high-quality labeled data,…
The Travelling Salesman and its variations are some of the most well known NP hard optimisation problems. This paper looks to use both centralised and decentralised implementations of Evolutionary Algorithms (EA) to solve a dynamic variant…
We introduce Limited Rollout Beam Search (LRBS), a beam search strategy for deep reinforcement learning (DRL) based combinatorial optimization improvement heuristics. Utilizing pre-trained models on the Euclidean Traveling Salesperson…
Discrete version of state transition algorithm is proposed in order to solve the traveling salesman problem. Three special operators for discrete optimization problem named swap, shift and symmetry transformations are presented. Convergence…
Several important optimization problems in the area of vehicle routing can be seen as a variant of the classical Traveling Salesperson Problem (TSP). In the area of evolutionary computation, the traveling thief problem (TTP) has gained…
Using an enhanced Self-Organizing Map method, we provided suboptimal solutions to the Traveling Salesman Problem. Besides, we employed hyperparameter tuning to identify the most critical features in the algorithm. All improvements in the…
Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based…
The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. Currently, there is no algorithm that can find an optimal…
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For…
Robotic systems often require a team of robots to collectively visit multiple targets while optimizing competing objectives, such as total travel cost and makespan. This setting can be formulated as the Multi-Objective Multiple Traveling…
In order to deal with the high development time of exact and approximation algorithms for NP-hard combinatorial optimisation problems and the high running time of exact solvers, deep learning techniques have been used in recent years as an…