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

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3
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1answer
22 views

Search problem when the effects of actions are not deterministic

The standard search problem studied in AI contains: An initial state $A$; A final (goal) state $Z$; A set of actions that can change the state; each action takes as input a certain state and returns ...
-1
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0answers
13 views

Heuristic value of the goal state of an admissible heuristic

If the heuristic value of the goal state of an admissible heuristic is not 0 and say it is a very huge negative value(assume that the edge weights can be negative) like -infinity(still it will be an ...
1
vote
0answers
22 views

Does the vehicle routing problem and variations have approximation ratios or a PTAS?

This is a somewhat big question since there are many variations on the VRP. The most studied seems to be the capacitated version, the CVRP, but variations considering time windows, backhaul/linehaul, ...
0
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1answer
25 views

Heuristic function

Is there any way to prove that an admissible heuristic may not be consistent? Most proof I came across are through examples .Is there a generalized proof?
3
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1answer
79 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 ...
3
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0answers
42 views

Testing whether an analytic function vanishes identically

I have an application that basically reduces to testing whether a given function vanishes identically. The function is given symbolically, using unary and binary operators on complex numbers. For ...
1
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0answers
32 views

TSP heuristics for limited distance information [closed]

this is my first question on ComputerScience beta. :) I've posted a similiar question on Mathoverflow and a friendly user advised me to post my question on this site. Problem: I'm looking for ...
3
votes
1answer
54 views

What makes a metaheuristic meta?

According to Wikipedia: ...metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a lower-level procedure or heuristic (partial search algorithm) that may ...
2
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0answers
40 views

Heuristic for weighted maximum independent set in graph with ~$2 \times 10^5$ nodes and $|E| \propto |V|$

I want to find a near-optimal solution for a maximum weight independent set. i.e given a graph $G = (V,E)$ I want to find a set $S = \{v_1,v_2,\dots,v_n\}$ of nodes in $V$ such that the sum of their ...
2
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2answers
346 views

Why is 'Manhattan distance' a better heuristic for 15 puzzle than 'number of tiles misplaced'?

Consider two heuristics $h_1$ and $h_2$ defined for the 15 puzzle problem as: $h_1(n)$ = number of misplaced tiles $h_2(n)$ = total Manhatten distance Could anyone tell why $h_2$ is a better ...
3
votes
1answer
98 views

How can I fill bookcases with shelves of books using the least number of bookcases?

Sorry for layman's term question, my background in computer science is weak. What I have is a list of shelves with books of varying height. Each shelf stores a value that describes how many shelves ...
0
votes
1answer
82 views

Heuristic for sokoban puzzle problem

I am trying to write IDA* for Sokoban puzzle problem (http://en.wikipedia.org/wiki/Sokoban) but It seems that my heuristic is not so good for making the algorithm fast. My heuristic is to consider ...
0
votes
1answer
78 views

Given two heuristic values how do I tell which one is admissible?

I am given 2 list of admissible values for a graph, and the graph with the real cost to each of the nodes. Am I correct in thinking the way to see which one is admissible is add up all the values of ...
0
votes
2answers
72 views

Why is it the lower the h(n) cost the more nodes need to be expanded in A*?

Why is it the lower the h(n) cost the more nodes need to be expanded in A*? As found here - http://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html If h(n) is always lower than (or ...
2
votes
1answer
58 views

Global relabeling heuristic: Push-relabel maxflow

I have a correct, working implementation of the preflow-push-relabel maxflow algorithm [2]. I am trying to implement the global relabeling update heuristic [3], but have run into some issues. I have ...
2
votes
2answers
115 views

Heuristic for Tournament Scheduling

I am holding a bi-yearly tournament in my city, for which I want to write a program that gives me (nearly-)optimal pairings, and waiting time. The setup is as follows: ...
3
votes
1answer
68 views

Unsplittable flow in capacitated networks

I have an undirected network with capacitated links/edges. Between some nodes unsplittable traffic has to be routed. All demands and capacities are known, but it is uncertain if all flows can be ...
0
votes
1answer
49 views

Why do heuristic functions only approximate the real value of the cost?

As stated in the title I'm wondering why do heuristic functions only approximate the real value of the cost? I understand it can never overestimate, but can it ensure the cost is accurate?
3
votes
1answer
44 views

What algorithm is suitable for very small scale, time dependent optimization?

I have a time-dependent (dynamic) optimization problem: $$ f_t : [0;1]^2 \mapsto \mathbb{R}^+; t \in [1, \dots, n] $$ $f_t$ is to be maximized. That is for each $t$ I would like to find a relatively ...
4
votes
2answers
1k views

Why is the A* search heuristic optimal even if it underestimates costs?

A* search finds optimal solution to problems as long as the heuristic is admissible which means it never overestimates the cost of the path to the from any given node (and consistent but let us focus ...
1
vote
1answer
42 views

Is there a way to predict rendering times? [closed]

In purpose of load balancing I need to approximatively predict rendering time my graphics software (in the specific case it's Autodesk Maya) needs to render a task given an input file (.ma/.mb) and ...
1
vote
0answers
143 views

Improving MSE as fitness function for a genetic algorithm

I am implementing an autoencoder neural network in matlab, the weights of which are being optimised by a genetic algorithm. At the moment I am working on the first layer, trying to get an improved ...
0
votes
1answer
244 views

Longest Path A*, Admissible Heuristics, and Optimalness

Im working on a modified A Star algorithm, that instead of attempting to find the shortest path, it tries to find the longest past, or in my specific case, the highest weighted path. I have some ...
1
vote
2answers
356 views

Ant colony optimization for continuous functions

I am trying to do optimization of a voice activity detection function, which is a function with continuous parameters. This is easily accomplished with genetic algorithms, simulated annealing, and ...
1
vote
1answer
262 views

Can heuristic methods and machine learning approaches be considered alternate methods to solve NP-Complete problems?

I was watching the videos from Skiena's Computational Biology Lectures, which is also available at youtube. In those videos, the professor made a statement that, most of the problems posed to computer ...
0
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1answer
27 views

Quickly pruning edges below average weight for a membership-based weighting

I have points represented as sparse high-dimensional binary vectors, or put another way, I have a list of groups that each point belongs to. For two points, the edge weight between them is $\sum_i ...
4
votes
1answer
90 views

How to perform local search on simple paths?

I have a local search problem. The set of valid solutions are all the simple paths (i.e. without repeated nodes) from a node $S$ to a node $T$ in a directed graph. The question is: given a current ...
8
votes
1answer
130 views

Maximum Stacking Height Problem

Has the following problem been studied before? If yes, what approaches/algorithms were developed to solve it? Problem ("Maximum Stacking Height Problem") Given $n$ polygons, find their ...
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0answers
37 views
2
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0answers
197 views

Trying to understand the Gilmore-Lawler lower bound

For a class project we're developing a software that solves a common optimisation problem. After some research we've found out that our problem is called QAP (Quadratic Asssignment Problem) and the ...
1
vote
0answers
51 views

Mutation and crossover operations in discrete differential evolutionary operations?

I need to use discrete differential evolutionary algorithm for assigning discrete values from set size $L$ to vectors of size $D$ where $L$ could be smaller, equal or larger than $D$. Elements of ...
2
votes
1answer
175 views

Genetic algorithm fitness function [closed]

I'm trying to write some little code (POC for the selection/mutation operators) that uses a genetic algorithm to solve a global maximum for a function. ...
4
votes
2answers
1k views

What is the no free lunch theorem?

I've been reading about the No Free Lunch Theorem, but I can't quite understand what it is about. I've heard this theorem described elsewhere as the claim that "no general purpose universal optimiser ...
-1
votes
1answer
434 views

Where is the recursion, in the minimax-decision algorithm?

The below is from an article titled: Minimax: Recursive Implementation To be a recursive function, you need to call yourself. What part of this pseudo code is calling itself? How does ...
1
vote
1answer
56 views

How do I compute this non terminal positions evaluation, for tic-tac-toe?

Looking at this solution on page 3 but having trouble understanding the evaluation function specifically. For non terminal positions, we use a linear evaluation function defined as Eval ...
3
votes
2answers
366 views

A heuristic for finding a maximum disjoint set

Background I need to find a largest set of non-overlapping axis-parallel squares, out of a given collection of candidate squares. This problem is NP-complete. Many papers suggest approximation ...
2
votes
1answer
169 views

Solving AlienTiles with an A* heuristic

Hello I am trying to solve the AlienTiles problem described at alientiles.com using the A* algorithm but I cannot find any good heuristic function so far. In AlienTiles you have a board with $N ...
2
votes
1answer
355 views

Creating admissible heuristics from functions?

I'm having trouble figuring out how to create admissible heuristics from cost functions. For example, if I was trying to create an admissible heuristic from a cost function that takes in starting ...
3
votes
2answers
3k views

How does the 3-opt algorithm for TSP work?

I understand that the 3-Opt Heuristic for solving the Traveling Salesman problem involves removing three edges from a graph and adding three more to recomplete the tour. However, I've seen many papers ...
1
vote
1answer
98 views

Local search: Problem with neighborhood definition

I have question on understanding the following neighborhood relation within a local-search approximation scheme. Let $M$ be a legal matching on any bipartite graph. Let $U_k$ be the neighborhood ...
1
vote
1answer
109 views

Algorithm to use for a TSP variant

What type of algorithm would you suggest me to use for this problem? I want to implement an algorithm that minimize the total distance in a graph (TSP) but for only X nodes. Also, we can go as many ...
1
vote
2answers
221 views

Heuristics & Constrain Satisfaction Problem Differences

I'm currently taking an Algorithms course, and we are covering Backtracking, CSP, and heuristics. However, I'm getting confused on exactly the differences between these terms and their applications. ...
1
vote
2answers
4k 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 i.e. it should never overestimate the actual solution path (moves). Can someone tell me how ...
0
votes
2answers
549 views

When does the nearest neighbor heuristic fail for the Traveling Salesperson?

Can you provide an example of NN algorithm failure on the Euclidean traveling salesman problem? I was trying to construct a specific example of this for my friends and was failing.
4
votes
2answers
5k views

Trying to improve minimax heuristic function for connect four game in JS

I have made a connect four game in JS and currently have a functioning minimax algorithm. The problem I'm having is that it is very, very easy to beat, even with a large depth. This is leading me to ...
5
votes
1answer
568 views

Classification of job shop scheduling problems

I'm writing a program (using genetic algorithms) that finds sort-of-optimal scheduling plan for a factory. The factory has several types of machines (say, ...
6
votes
1answer
257 views

When to use SAT vs Constraint Satisfaction?

If I have a hard problem, one standard approach is to express it as a SAT instance and try running a SAT solver on it. Another standard approach is to express it as a constraint satisfaction problem, ...
4
votes
1answer
212 views

How approximate are “approximate” nearest neighbor (ANN) search algorithms?

Starting to use nanoflann to do some point cloud nearest neighbor searching and it got me thinking about just how "approximate" ANN methods are. If I have a (more or less) randomly distributed point ...
10
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2answers
3k views

Initial temperature in simulated annealing algorithm

I've done some testing of different initial temperatures in my simulating annealing algorithm and noticed the starting temperature has an affect on the performance of the algorithm. Is there any way ...
2
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0answers
283 views

Time complexity 2-opt method

I'm doing a practice test for a course on routing problems. There's a question asking to infere the time complexity of the 2-opt method. I can see that the complexity per iteration is in $O(n^2)$ ...