# Questions tagged [heuristics]

Questions about algorithmic strategies that quickly solve a problem well most of the time, but give no guarantees.

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### 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 ...
33 views

### What is meant by a preemptive algorithm?

The definition on Google says 'serving or intended to pre-empt or forestall something, especially to prevent attack by disabling the enemy.' So, how does this relate to an algorithm, especially the ...
16 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 ...
52 views

### Matching of two weighted graphs allowing one-to-many mapping

I am looking for a heuristic for a graph matching problem as follows. Given two graphs: $A$ (consisting of nodes $a_i$) and $B$ (consisting of nodes $b_i$). Typically the size of $B$ is larger than ...
66 views

### A* without heuristic more efficient than Dijkstra

I am using the module networkx to operate on graphs made from OpenStreetMap. I wanted to compare the shortest path algorithm to ...
48 views

### Can data be compressed through this hash function technique?

I'd like to know if this data compression scheme would work or not, and why: Suppose we have a file. If we treat the bits that make up the file as the binary representation of a number n, we have n (...
47 views

### How do you prove a heuristic is admissible?

How does one prove that a suggested heuristic is admissible? Is this even possible? For Example: Let's say I have the game Free Cell. Rules: https://en.wikipedia.org/wiki/FreeCell How can I ...
45 views

### Why is the usual simulated annealing algorithm using a Boltzmann probability?

I've coded a personal version for the simulated annealing problem, and I was wondering why, (other than by analogy to the physics), the probability is $$p = e^{-\dfrac{\Delta \text{length}}{T}}$$ (...
35 views

### What kind of standard deviation must be used in optimization algorithms?

I would like to ask about the standard deviation of objective function value. There are two types of standard deviations: Population standard deviation Sample standard deviation In metaheuristic ...
167 views

### Morphing Hypercubes, Token Sliding and Odd Permutations

A month ago, I asked the following question math.exchange (https://math.stackexchange.com/questions/3127874/morphing-hypercubes-and-odd-permutations), but for completeness, I will include the details ...
157 views

### How can an A* algorithm visit all nodes?

Is it possible to find the shortest path and visit all the nodes in a graph by A* algorithm? If yes, how?
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### Term for an A*-like pathfinding strategy where only the heuristic goal distance matters

I am trying to find a proper term for the A*-like best-first pathfinding strategy where the node to expand next is the one with the least estimated distance from the goal, regardless of its distance ...
50 views

### Ant Colony optimisation for finding subsets with ~0 sum

I have a set A = [x1, x2...xn] where xi in R (real). I need to find all non intersecting subsets with subset sum ~0 (approximately equal to zero). Since the set can have non zero real numbers, I have ...
66 views

### Does an optimal path imply the heuristic is admissible?

If we are given an A$^*$ path search with some heuristic $h$ that yields an optimal path, without knowing that the heuristic is admissible beforehand, would this imply that $h$ is admissible?
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### 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 ...
28 views

### Longest simple walk below a certain weight

Given a directed graph G and a starting vertex $v$ and a cutoff weight $w$, I want to find a simple walk with net weight < $w$ that visits as many nodes as possible. Currently, I have a recursive ...
129 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 ...
23 views

### Defining Local Search stopping criteria

When performing a local search, for example, a 2-node exchange in a metaheuristic (like GRASP), what is the usual stopping criteria for that procedure? Some bibliography says that the local search ...
31 views

### MAC-AC3 algorithm puts arcs in queue

I am studying Csp and I don't understand the line no 1.1 . Does queue contains all arcs or not?Explain with me 4-queens please. ...
130 views

### How MAC-3(maintaining arc consistency-3) algorithm works?

I am studying CSP problems in artificial intelligence. I don't understand the MAC-3 algorithm especially line number 10. Could you tell me with step by step? ...
128 views

### Optimal partitioning of n-tuples

Motivation Recently I was trying to optimize some API calls and reduced the problem to optimization of a cumulative number of identifiers across all the requests. I put some considerable effort into ...
63 views

### Choosing heuristic for A* algorithm where cost is less than absolute distance

Looking for information on choosing a heuristic for instances where the cost of traversing an edge can be less than one. For example, say movement is allowed in the cardinal directions. Should all ...
22 views

### Relevance of the ZeroSum game to Heuristic search?

A question was posed to me as to the relevance of the ZeroSum game to Heuristic search algorithms. I know that the zero sun game is a theory in which one persons gain is exactly balanced to another ...
46 views

### How to perform local search to find maximal induced subgraphs?

I'm looking for efficient ways to perform local search to find maximal induced subgraphs that satisfy certain properties : a tree, a forest or a bipartite subgraph for example. What I mean by local ...
16 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. ...
83 views

### Heuristics vs meta-heuristics vs hyper-heuristics?

The wikipedia page on meta-heuristics states that they are "heuristics designed to find, generate, or select a heuristic". The wikipedia page on hyper-heuristics states that they are "heuristic ...
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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.
215 views

### 8 puzzle admissible heuristic where tiles are in correct position

For the 8 puzzle problem, it has been proved that if h(n) = number of tiles on wrong place. h(n) is an admissible heuristic as every tile which is in wrong place must be moved out at least once. But ...
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### How many states are examined in the most wins heuristic for tic-tac-toe (9-grid)?

I'm new to AI, and have a hard time to understanding how to count the total states are examined in the most wins heuristic for tic-tac-toe two plys deeper(9-grid)? Need help
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### How to prove if a heuristic function is admissible or not

Can somebody tell me how to solve this problem?
284 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 ...
269 views

### A* Search Algorithm Implementation with Priority Queue

I've got a question regarding the A* search algorithm's implementation. According to Wikipedia, one has to use a priority queue for retrieving the next node with the lowest f value, is it possible to ...
79 views

### Does domination rule apply for inadmissible heuristics?

Let's say $h_1(n) \geq h_2(n)$ so that dominance is established even if $h_1$ and $h_2$ are both inadmissible/non-optimal heuristics -in whichever given search space. Is $h_1$ still faster/better ...
50 views

### Optimization Problem when calculating fitness is expensive

I need to solve an optimization problem, maximizing fitness in a set of around 1 million solutions. Calculating the fitness of any solution is very time consuming, taking around 5 minutes. Therefore, ...
573 views

### Aren’t most constraining variable and least constraining value the exact opposite?

So aren’t MCV and LCV the exact opposite?MCV tries to choose the variable with the most constraints on remaining variables but LCV is opposite: it tries to rule out as least values for other variables ...
32 views

### Steps to create a heuristic for solving a problem

I am completely new to AI and doing self-learning to acquire this knowledge. I went through the different available search algorithm like BFS, DFS and A* but something that I can't understand is a ...
31 views

### What is the peak in fitness landscape

I have just started reading about fitness landscapes and I couldn't understand what the peak means. What does the peak mean?
146 views

### SAT Solving + Turing Machines

I have a couple of questions based on how SAT solvers work. I understand that SAT solvers may employ any/all of the following techniques: Randomness Heuristics Backtracking SAT is just one example ...
22 views

### Justification behind this heuristic in SMA*+

I'm reading the paper Enhanced Simplified Memory-bounded A Star (SMA*+). In short, the authors propose a limited-memory version of A* where we cull nodes if we are out of memory, to re-expand them ...
177 views

### Consistent heuristic and A*

The following graph has consistent heuristic. An A* algorithm will alter its first guess ACD to the correct shortest path ABD... if it has consistent heuristic, doesnt it mean, that AB should be ...
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 ...
78 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 ...
96 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 ...
255 views

### What is the best heuristic function for evaluating the state in game of sprouts?

We are developing game of sprouts bot using min-max algorithm. We need a good heuristic function for evaluating the state of the game/player. Can someone please suggest?
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### How does the nearest insertion heuristic for TSP work?

In my theoretical computer science class and we were covering "Heuristics". In it we covered "Greedy Heuristics" for the "Vertex Cover Problem", "Interval Scheduling" and the "Traveling Salesperson ...
40 views

### Defining preferred paths makes $A^*$ heuristic lose admissibility

In a geographical graph, where each edge's cost is equal to the physical distance between its nodes, one can be tempted to manipulate the cost of some of the edges, to make it a bit lower, in order to ...
89 views

### Greedy Heuristic for the Traveling Salesperson Problem

We're studying Heuristic in my Theoretical CS class, more specifically Greedy-Algorithms for the Traveling Salesperson Problem. The first one is the "next neighbor heuristic", where you start at any ...
271 views

### If $h(s)$ is an admissible heuristic, is $\sqrt{h(s)}$ admissible?

I was thinking yes because $0 \leq \sqrt{h(s)} < h(s)$ but I'm not entirely sure.