Questions tagged [traveling-salesman]

The Traveling Salesman Problem and variants

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11 views

Do branch - bound and dynamic programming give same solutions for a tsp problem interms of path and cost? , also same number of solutions?

Do branch - bound and dynamic programming give same solutions for a tsp problem interms of path and cost? , also same number of solutions?
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1answer
22 views

Grouping n points into groups of size m with objective to have least traveling distance in each group

Assumptions: There are "n" jobs which are distributed over the city. Company has "k" available workers. Each worker can do "x" jobs per day. "x" is dependent to the worker skills and the distance ...
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1answer
14 views

Performant algorithm to find edges without cross overs

I have a series of graphs with points plotted like this: Like in the image, I need to join these points to create a complete edge. I am currently doing this with nearest-neighbour, but because I don'...
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1answer
50 views

Arranging Colors in a Grid; Two Dimensional TSP?

I am working on an interesting problem, which I believe can be solved algorithmically. I have a 6x8 on which I am attempting to arrange 48 color swatches, such that the transition from each swatch to ...
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2answers
57 views

Can non-metric TSP be approximated within some non-constant value?

It is known that metric TSP can be approximated within some constant value, such as 3/2 through Christofides' algorithm. It is also known that non-metric TSP cannot be approximated within some ...
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Why haven't I solved the Travelling Salesman problem with the following argument using djikstras algorithm?

I claim to have solved the travelling salesman problem as follows. (You will have to be familiar with djikstra's algorithm for this.) 1) I am about to start using djikstra's algorithm on any given ...
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69 views

What is the difference between nearest and cheapest insertion algorithms for a Traveling salesman problem?

I know that in the cheapest insertion algorithm we include the node which is not in the "base group" that has smaller cost given all possible combinations, and for the nearest we include the node with ...
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1answer
26 views

Question about complexity of TSP Optimization problem

Is this statement true? Optimization TSP problems are known to be NP-hard, as we do not have a minimum cost to compare against, and in order to verify a solution is optimal, we need to iterate ...
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2answers
96 views

For what applications of the traveling salesman problem, does visiting each city at most once truely matter?

Traditionally, the traveling salesman problem has you visit a city at least once and at most once. However, if you were an actual traveling salesman, you would want the least cost route to visit each ...
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90 views

TSP Variant — Colored Path

Recently I came up with a traveling-salesman-esque problem. As usual, we have $n$ vertices, and a weighted edge between any two vertices. However, each vertex is associated with a color, which may be ...
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20 views

Comparison of constructive and local-search heuristics for TSP

In my high school class, we are currently looking at evaluating heuristic methods for intractable problems - especially TSP. My question is what is the advantages or disadvantages of using a ...
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1answer
201 views

Hamilton Circuit

The Dirac's theorem states that: "For a Graph G with N vertices, if the degree of each vertex is atleast N/2 then, the Graph has a Hamilton Circuit." Can the same be said if a graph has a Hamilton ...
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96 views

Given n sets of points in the plane find the shortest path which passes from exactly one point from each set

I am trying to find an algorithm for this. You can imagine each set $(S_1, S_2, \ldots, S_n)$ as points with different colour. Also it isn't necessarily $|S_1|=|S_2|=\cdots=|S_n|$. For $n=1$ we ...
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3answers
138 views

How to compute number of possible paths in directed Traveling Salesman problem?

If we have directed modification of TSP, so that some routes are possible in one direction, given directed graph, could you compute number of possible tours? What if we have supercomputer, does it ...
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1answer
28 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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176 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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23 views

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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19 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
40 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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1answer
34 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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2answers
140 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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69 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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42 views

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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367 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
49 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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584 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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1answer
110 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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149 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
418 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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1answer
70 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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17 views

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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40 views

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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269 views

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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42 views

Mathematical modelling on Christofides algorithm

Does a mathematical modelling on Christofides algorithm exist, is it even possible to create one?
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419 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
112 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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1answer
416 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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86 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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64 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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110 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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116 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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139 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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317 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
273 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
177 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 ...