Related papers: The Computational Complexity of the Traveling Sale…
Given an undirected graph $G=(V, E)$ with a weight function $c\in R^E$, and a positive integer $K$, the Kth Traveling Salesman Problem (KthTSP) is to find $K$ Hamilton cycles $H_1, H_2, , ..., H_K$ such that, for any Hamilton cycle $H\not…
The travelling salesman problem is a well-known example of computationally-hard combinatorial problem for classical machines. Here, we propose a novel variational quantum algorithm to solve it. The method is based on the preparation of two…
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…
Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking…
We propose a learning algorithm for solving the traveling salesman problem based on a simple strategy of trial and adaptation: i) A tour is selected by choosing cities probabilistically according to the ``synaptic'' strengths between…
In this note, we polynomially reduce an instance of the partition problem to a dynamic lot sizing problem, and show that solving the latter problem solves the former problem. By solving the dynamic program formulation of the dynamic lot…
This article describes counter example prepared in order to prove that linear formulation of TSP problem proposed in [arXiv:0803.4354] is incorrect (it applies also to QAP problem formulation in [arXiv:0802.4307]). Article refers not only…
The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time $O(2^n n^2)$, with no improvement in the last sixty years. We break this barrier for the first time by…
The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques…
We propose a simple and exact method for the Traveling Salesman Problem with Time Windows and Makespan objective (\TSPTW-M) that solves all instances of the classical benchmark with $50$ or more customers in less than ten seconds each.…
We present a self-learning approach that combines deep reinforcement learning and Monte Carlo tree search to solve the traveling salesman problem. The proposed approach has two advantages. First, it adopts deep reinforcement learning to…
This paper presents the differences between two NP problems. It focuses in the Euclidian 2 Dimension Travelling Salesman Problems and General Assign Problems. The main results are the triangle reduction to verify the solution in polynomial…
It is shown that graph-theoretic problem CLIQUE can't be solved in polynomial time by any deterministic TM. This upgrades the well-known partial result that claims only monotone unsolvability thereof, and eventually implies P $\neq$ NP as…
Routing problems are a common optimization problem in industrial applications, which occur on a large scale in supply chain planning. Due to classical limitations for solving NP-hard problems, quantum computing hopes to improve upon speed…
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…
We present a framework for efficiently solving Approximate Traveling Salesman Problem (Approximate TSP) for Quantum Computing Models. Existing representations of TSP introduce extra states which do not correspond to any permutation. We…
Previously the author has demonstrated that a representative polynomial search partition is required to solve a NP-complete problem in deterministic polynomial time. It has also been demonstrated that finding such a partition can only be…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
The traveling salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We characterize the optimal cycle for every convex and increasing…
In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost $c_{ij}$ of traveling from city $i$ to city $j$, which is the same in either direction for the Symmetric TSP. The objective…