Questions tagged [traveling-salesman]

The Traveling Salesman Problem and variants

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can i calculate time of finding optimum of travel salesman problem with super computer and can i know that is limit of cities to now computers?

i want to know the real limit of our computational power that we have now what is the limit of cities that i can reach with optimum sol. i believe that first computer is 10^19 process in second and ...
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23 views

Dubins TSP NP-hardness proof detail

In Le Ny et al.'s paper On the Dubins Traveling Salesman Problem (https://tinyurl.com/y59f7d8x) the authors prove, among other works, that the Dubins Traveling Salesman Problem (DTSP) is NP-hard. I ...
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26 views

Travelling Salesman: Big O Complexity when starting city is fixed

We are studying the Travelling Salesman problem in my high school class, and I am wondering what the Big O complexity of the TSP is when you MUST start and end at the same city. For example, given 4 ...
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Number of Solutions for Brute Force Algorithm of Travelling Salesperson Problem

We are learning about the travelling salesperson problem in my high school class and we are discussing how computers could solve for the problem, even though the problem is intractable, using a brute ...
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16 views

TSP with knapsack combo

My problem statement is that my agent has to visit multiple pickup points once to collect orders, say Item A, Item B, Item C...... etc. We are using TSP for that. Now say Item A are stored in 3 ...
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1answer
27 views

Dubins TSP crossing trajectory theorem

In the Dubins TSP (DTSP for short), one needs to visit a set of given points in the plane, and return to the starting point, minimizing the distance of such a trajectory. The difference with the ...
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1answer
32 views

Why isn't the search space size of TSP $(n-1)!$ instead of $n!$?

I'm just learning about the travelling salesman problem, and I've been playing around with it. I'm not sure if what I've found is just a special case or not. My professor says the search space size is ...
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31 views

Approximation algorithm to visit all nodes in an undirected, weighted, complete graph, with shortest sum of edge weights

I'm looking for an algorithm that gives a smallest value of 'travel cost' within the following constraints: a complete, connected, weighted graph, vertices are defined in 3d euclidean space, ...
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35 views

What is the graphic TSP?

I'm not sure if I understand the following definition of the (well-known apparently) Graphic TSP, also known as graph-TSP : ...graph-TSP, that is, the traveling salesman problem where distances ...
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62 views

League and Divisions problem (np-hard)

There is a League. And there are Divisions, that are the disjoint subsets of this League. There are n teams (unique locations are given, let's assume it's x and y for simplicity reasons). Every team ...
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Traveling Salesman Problem with profit and time limit as ILP formulation

How to formulate the following problem? The salesman gains a profit $p_{i}$ when visiting a city i, trip between city i and city j costs $c_{ij}$ and takes $t_{ij}$ time. The trip must not exceed a ...
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Delivering to two or more locations in one go while respecting deadlines?

Assume that I have a business where people can place product orders. Each order must be delivered within a time limit, say $x$ minutes. I need 15 minutes to make each product. However, multiple ...
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364 views

Linear Path Optimization with Two Dependent Variables

Alright, so this is a fairly interesting problem I have but also slightly difficult to explain so I will try my best. There are two runners on a line that goes from $x=0$ to $x=100$. The two runners ...
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1answer
39 views

A problem to maximize the number of edges in a cycle while minimizing the total weight

I encountered the problem below and the only solution I came up with is branch and bound like that is used in TSP and I don’t think the bound I used is good enough. Are there any better idea on this? ...
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484 views

Is there an efficient solution to the travelling salesman problem with binary edge weights?

Is there a way to solve TSP in polynomial time if there are only two kinds of weights, 0 and 1?
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5k views

If I can solve Sudoku, can I solve the Travelling Salesman Problem (TSP)? If so, how?

Let us say there is a program such that if you give a partially filled Sudoku of any size it gives you corresponding completed Sudoku. Can you treat this program as a black box and use this to solve ...
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66 views

Overall time complexity of Heuristical Algorithm for travelling salesman problem [TSP]

I am trying to figure out the time complexity of a heuristical algorithm used to solve the Travelling Salesman Problem in a more efficient way than by brute force, ($\theta(n!)$ or similar) The ...
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110 views

Travelling Salesman problem using Guided Local Search

I am doing Week_4 of https://www.coursera.org/learn/discrete-optimization/ stuck in solving TSP. As there are a lot of methods to solve this problem, I am currently coding Guided Local Search as ...
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1answer
158 views

2-opt vs 3-opt comparison

I have a question regarding performance of 2-opt and 3-opt algorithms. I tried implementing the 3-opt and 2-opt algorithms and most of the time 3-opt outperforms the 2-opt algorithm around 5%. ...
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64 views

Is TSP a more detailed form of the “Set Inclusion” question?

Background Set Inclusion GIVEN: set of cards, some with blue backs, and each with a positive, integer face value. QUESTION: Are there any [blue-backed cards] with a [face value <= L]? 2 ...
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2k views

Which of the following statements are true for the given special cases of the Traveling Salesman Problem?

I'm taking the Algorithms: Design and Analysis II class, one of the questions asks: Which of the following statements is true? Consider a TSP instance in which every edge cost is either 1 ...
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Can Heuristic repair algorithm be applied to TSP?

Can Heuristic repair algorithm (or it's modification) be applied to Traveling Sales Person problem ? My gut feeling is that it can. But I have no idea - what cost(s)/conflicts should be minimized. ...
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can someone provide a good resource for understanding 2 opt heuristic?

I have looked into wikipedia and this MIT slide. A step by step iteration of the algorithm with a clear example would be appreciated.
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Solve this integer program (problem: Travelling salesman problem)

How do one solve the following integer program? $$ \begin{align*} \text{minimize} \quad &\sum_{(i,j) \in E} d_{ij} x_{ij} \\ \text{subject to} \quad & \sum_{j \in V} x_{ij} = 2 \;\; \forall i ...
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Clarify the steps: what happened in this mathematical modelling of TSP?

Source: http://examples.gurobi.com/traveling-salesman-problem I don't get this part: (look at the source) $$\sum_{i,j\in\{1,2,3\},i\neq j} x_{ij}=3>2=|\{1,2,3\}|-1$$ I get that $x_{ij}$ is ...
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Mathematical modelling on Christofides algorithm

Does a mathematical modelling on Christofides algorithm exist, is it even possible to create one?
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266 views

Nearest Insertion Traveling Salesman Heuristic: is it faster to insert nearest nodes first?

I am trying to implement the nearest insertion TSP heuristic. However, I am wondering if it matters which node I insert into the subgraph first. For example, should I start with one node; calculate ...
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2answers
88 views

How to Solve TSP Given Length of Path?

I am trying to devise an algorithm in which given the length of a path that satisfies the constraints of the Traveling Salesman Problem, I can find the path. Currently, my only solution is to find a ...
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231 views

Christofides algorithm (by hand)

I am following this algorithm example: https://en.wikipedia.org/wiki/Christofides_algorithm#example The graph: [![enter image description here][1]][1] ...
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60 views

Do you >have< to define the upper and lower bound? (context: traveling salesman)

Do one have to define the upper and lower bound to be able to solve the tsp, or is that just an unnecessary intermediate step? And if so, why would one define those bounds? (context: the traveling ...
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44 views

Grid Based DP: How do we tweak the Travelling Salesman Problem to work with Grids

The question is: There is a n x n grid (Maze) which has either 0, 1 or 2. 0 means a path exists, 1 means the cell is blocked and 2 means there exists gold in that cell. Task is to start from 0,...
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82 views

Shortest route through ordered points

My algorithm-fu is really weak and I do not know how to express following problem in terms of any other problem known to me: Given a small rectilinear grid and coordinates of four cells in this grid (...
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103 views

Is there a solution for this maze problem in polynomial time?

Suppose you have a maze represented by a graph where each vertex represents a room and edges represent paths between rooms and each edge has a weight denoting the time it takes to go that way. Now ...
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136 views

Does there exist a travelling salesmen generating algorithm?

I'm curious if somebody has already figured this out. Is there an efficient algorithm that will generate (in $\mathbb{R}^2$) a sequence of points in such a way that the solution to the travelling ...
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234 views

Minimum weight Hamiltonian path on a weighted (0 and 1) tournament graph

Suppose we have a weighted tournament graph. (A directed graph in which every pair of distinct vertices is connected by a single directed edge.) The weights are constrained to be 0 and 1. I know ...
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1answer
152 views

Why does Travelling Salesman Problem pose the restriction that each vertex can only be visited once?

According to the wiki page of TSP as a graph problem, It is a minimization problem starting and finishing at a specified vertex after having visited each other vertex exactly once Then what if a ...
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1answer
141 views

Reducing closed TSP to open with fixed starting vertex

I have implemented a branch and bound algoritm for finding a Hamiltonian cycle in my software, but I actually need to find a shortest route from fixed vertex through all verticies ending at any of ...
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Partial TSP in Euclidian plane

I'm interested in the following variant of Travelling Salesman Problem sometimes called Partial TSP. I'm particulary interested in the euclidian version : Input : A set $\{x_1,\dots,x_n\}\subset \...
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In the Traveling Salesperson Problem, is the shortest tour the same regardless of the start/return city? How do you prove it?

This is the form of the problem where you start at a city, visit every other city, and return to the start city. Since you "return" to every city in the completed cycle, it seems intuitive that the ...
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18 views

How to get initial flow for TSP with missing edges

I need to solve a version of the traveling salesman problem with missing edges. I've decided to use simulated annealing. How do I generate a valid initial path effectively? I would use a greedy ...
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73 views

Comparison of time-dependent traveling salesman heuristics

I'm looking into implementing a heuristic for the time-dependent traveling traveling salesman problem (TDTSP) that completes in a certain amount of time. There are a wide range of possible ways to ...
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327 views

if traveling salesman problem is decidable in polynomial time, can an actual solution be proposed in polynomial time?

I'm asking because it seems that P problems refer to decision problems rather than actually propose a solution.
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89 views

Improvement Heuristics for Asymmetric TSP

i have been solving the Time-Dependent Traveling Salesman Problem using an Ant Colony Optimization. Upon reading the ACO papers, there are several reminders which state that ACO performs best with ...
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131 views

Is Euclidean TSP strongly NP-hard

Is Euclidean TSP strongly NP-hard? What I mean is if it is NP-hard with weights specified in unary? Can someone provide a reference?
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168 views

Travelling salesman problem with small edge weights

Are there any advantages in finding the shortest tour for the problem if edge weights are much smaller than the number of vertices? Let's say the maximum edge weight is $n$, and the number of ...
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1answer
566 views

Using 2-opt Heuristic in a Genetic Algorithm for TSP

I read few papers while trying to find some better approachs to solve the TSP (Traveling salesman problem) as close to the optimal solution as possible. I implemented a Improved Greedy Crossover (...
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147 views

How to find the best parameters of a Genetic Algorithm applied to the TSP problem?

I have an assignement where I need to use a Genetic Algorithm to solve the TSP (Traveling Salesman Problem). I alrerady implemented a solution in C# but the problem is we're asked to use some kind of ...
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28 views

TSP when cost depends only on location in sequence

I want to change the original TSP problem as follows: the cost to visit a city is not related to the previous city that it visited just now, but only on its position in the sequence. Is the problem of ...
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1answer
233 views

Traveling salesman problem with disconnected cities / infinite length edge

I am looking to solve a variant of the traveling salesman problem with a certain set of constraints: the graph is not complete, i.e. some nodes are not connected to each other the weight of an edge ...
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334 views

What if the travelling salesman travelled by plane?

It seems intuitive to solve a 2D dot-to-dot travelling salesman problem by eye using a greedy strategy. However we can only solve the TSP by eye if the graph is topographically accurate e.g. if A to B ...