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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Is there an heuristic for finding out the smallest height you can get when packing items in a tube?

It's sort of similar to bin packing, but instead of the minimum amount of bins,I was interested in just one infinite bin and finding out what's the smallest height you could get when you start packing ...
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46 views

Algorithm for optimal rule-based arrangements?

I am trying to plant a row in a garden. Certain plants are good for some plants and bad for others, and I am trying to find the best order of plants: most adjacent friends and no adjacent foes, as ...
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25 views

What solution to apply for finding the optimal parameters?

For a study, I have a system (black-box) that requires an input in the form of an array with 4 values (input_array) and depending on their values it produces an ...
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22 views

Search algorithm for vehicles moving through a square grid

I started to learn AI and I'm trying to solve the following problem like a search problem and I'm wondering which search algorithm would be the best in this case. Please give me at least some tips, I ...
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35 views

What is an example of meta-heuristic algorithm for solving Mario NP-hard problem?

Applying entertainment with computations is my main motivation in studying Computer Science, however, I'm still a neophyte to this field. While searching across the net, I came across this paper ...
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5 views

Ant Colony Optimization on Maximum Partitioning Graphs with Supply and Demand

I'm still new to the field of Computer Science and I'm having trouble understanding this paper An ant colony optimization algorithm for partitioning graphs with supply and demand. Can I ask for a ...
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1answer
83 views

Algorithm to create dense style crossword puzzles

I am working on creating a program to generate dense American style crossword puzzles of grid sizes between 15x15 - 30x30. The database of words I'm using ranges between 20,000 and 100,000 words of ...
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14 views

Use of Tabu search Algorithm for solving optimization problem

I am trying to solve a maximization problem using the Tabu search algorithm but there is no relevant code available on the internet. Any kind of sample code is highly appreciable. My function is F(...
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1answer
29 views

Proving 2 heuristics are admissible

We have $h_1(n)$ and $h_2(n)$ which are both admissible heuristics. We know that $h_1(n) < h_2(n)$ for every state $n$ in a search problem. Now we are given two heuristics $h_3(n)=\frac{h_1(n)}{1+...
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27 views

Heuristic algorithm for the minimum weighted s-t cut with linear running time

To the best of my knowledge, the best algorithm for the minimum s-t cut in a weighted digraph is the Goldberg push-relabel algorithm with $O(n^{2}\sqrt{m})$ time complexity. I'm interested in solving ...
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1answer
3k views

Nilsson's sequence score for 8-puzzle problem in A* algorithm

I am learning the A* search algorithm on an 8-puzzle problem. I don't have questions about A*, but I have some for the heuristic score - Nilsson's sequence score. Justin Heyes-Jones web pages - A* ...
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1answer
42 views

Partition the indices of 2d array to minimize sum of sub-matrices

Given an $n\times n$ Matrix $M$, and the indices $[{1,2,3,4,...,n}]$ are divided into several intervals : $[1,x_1],[x_1,x_2],...[x_k,n]$, which further extract several squared sub-matrices along the $...
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1k views

the meaning of heuristics in artificial intelligence

I would like to know what 'heuristics' actually means in artificial intelligence. For example, I am reading a paper by Engelbrecht on the convergence analysis of the particles of the algorithm. The ...
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24 views

Least Constraining Value heuristic for graph coloring problem

The graph coloring problem involves assigning colors to vertices in a graph, such that no pair of adjacent vertices have the same color. I was given the problem to use least constraining value ...
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1answer
23 views

Do we understand when metaheuristics are optimal? (gradient descent & simulated annealing in particular)

Gradient descent sometimes works better than simulated annealing and vice versa. Are there conditions under which we can prove that, given perhaps a restriction on the set of allowed algorithms, one ...
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25 views

Is this a valid heuristic for Dots and Boxes to reduce the branching factor of the search tree?

I am implementing an AI based on the MiniMax algorithm that plays the game Dots and Boxes. I would like to reduce the branching factor of the search tree, by introducing a heuristic rule that limits ...
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1answer
2k 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 ...
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17 views

What does the gradient mean in evolutionary algorithm?

I have been reading about evolutionary algorithms and I often find the concept of gradient that is used as "to follow a gradient"...
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33 views

A heuristic for finding an edge cycle cover

I am looking to find a minimum list of cycles in a graph such that their union gives the list of all simple cycles in this graph. In the example below, here are 4 simple undirected cycles: 1-2-3, 2-3-...
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26 views

Rearrange items in order reduce fragmentation and reduce wasted space

I have a segment with some offsets at irregular intervals There are items of various length inside. Items cannot be placed randomly. Instead, their left side must match some offset. Items are free ...
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36 views

Reaching local optimality in simulated annealing

I am currently reading about local search techniques. I understand that local search algorithms tend to get stuck in local optima and therefore usually do not find globally optimal solutions. Thus, ...
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2k views

Why doesn't 2-opt return an optimal solution?

To find a solution for the Traveling Salesman Problem (TSP), one way to go is an algorithm called 2-opt, which is explained below. ...
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1answer
124 views

Greedy Heuristics with an Altered Subset Sum/Partition Problem

Say we have a constant-time function that accepts some integer set. The function outputs True if we can split the integers into two subsets of an equal sum. If we can't partition the integers given, ...
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54 views

How do evaluation functions influence the optimal sequence of moves?

Assume you have a game tree and the features $(f_1, f_2, f_3,\ldots,f_n )$ that describe the state of the game at any node. Also assume that you are using depth-limited minimax and always expand up to ...
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175 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
84 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 ...
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1answer
23 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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59 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 ...
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2answers
321 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 ...
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54 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 (...
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1answer
196 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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2answers
488 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 ...
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1answer
71 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 $$ p = e^{-\dfrac{\Delta \text{length}}{T}}$$ (...
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719 views

Measuring the difficulty of SAT instances

Given an instance of SAT, I would like to be able to estimate how difficult it will be to solve the instance. One way is to run existing solvers, but that kind of defeats the purpose of estimating ...
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1answer
4k views

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 ...
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47 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 ...
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172 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 ...
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280 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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1answer
23 views

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 ...
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1answer
75 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 ...
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123 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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1answer
154 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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31k views

How does an admissible heuristic ensure an optimal solution?

When using A* (or any other best path finding algorithm), we say that the heuristic used should be admissible, that is, it should never overestimate the actual solution path's length (or moves). How ...
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1answer
32 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 ...
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187 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
32 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 ...
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312 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? ...
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1answer
139 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 ...
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132 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 ...
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1answer
49 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 ...