usually people use pn-search or pn^2 Or df-pn to answer if there is a win solution.
then they use alpha-beta pruning on the min-max game tree with a good evaluation function
they can reach a depth of 15 ply or even more
now there is a Monte Carlo method which is successful in dealing with Go.
Is the same tech can be used in Gomoku ? any examples (source code or paper)
Is there any paper describe a good way to build a well tuned evaluation function.
or Is there any other state-of-the-art or useful tech to deal with Gomoku ?
Is pn search necessary in dealing with Gomoku?
Is there any different VCT engine (src better) ?
To the best of my knowledge, proof number search, dependency based search (also referred as threat space search), and searching algorithms based on alpha-beta framework are mainly used in top Gomoku programs. There also exist some Gomoku programs using Monte Carlo Tree Search, however, the current result is not that good. The article on http://www.aiexp.info/gomoku-renju-resources-an-overview.html summarizes the reading materials, protocols and source code for Gomoku AI.
As for evaluation function, up to now, although there are some papers describing how to build a well tuned evaluation function for Gomoku, none of them really works to achieve the state of the art.
Pn-search is not necessary in dealing with Gomoku. In fact, the state-of-the-art Gomoku engine Yixin does not use pn-search.
Renjusolver is the best VCT engine. Except for renjusolver, there are many other Gomoku engines which have relative good performance on solving VCT and can be downloaded at http://gomocup.org/download/. Currently, pela is the best open source engine on solving VCT.
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I'm working on project where I need to minimize functions by several variables like func(input_parameters, variable_parameters) -> min(variable_parameters).
I use optimizing functions from SciPy, so minimization process is a grey box: I can see the code on GitHub and read about used algorithms, but I'd like to think that it's okay and aim to testing of my own project.
Though, particular libraries shouldn't matter in this question.
At the moment I use few approaches:
Create simple examples and find global/local minima by hand and create test that performs optimization and compares its solution with the right one
If method needs gradients, compare analytically calculated gradients with their numerical approximation in tests
For iterative algorithms built upon ones provided by SciPy check that sequence of function values is monotonically nonincreasing in tests
Is there a book or an article about testing of mathematical optimization procedures?
P. S. I'm not talking about Test functions for optimization
, I'm asking about approaches used to test optimization procedure to find bugs faster.
I find the hypothesis library really useful for testing optimisation algorithms in development.
You can set it up to generate random test cases (functions, linear programs, etc) according to some specification. The idea is that you pass these to your algorithm and test for known invariants. For example you could have it throw random problems or subproblems at your algorithm and check that (for example):
Gradient descent methods produce a series of nonincreasing objectives
Local search finds a solution with no better neighbours
Heuristics maintain feasibility
There's a useful PyCon talk here explaining the idea of property based testing. It focuses more on testing APIs than algorithms, but I think the ideas transfer. I've found this approach does a pretty good job finding cases of unexpected behaviour as I'm writing a new algorithm.
I have got a job scheduling problem. We are given start time, time to
complete the order, deadline.
It is given that start time + time to
complete <= deadline.
I have also been given the loss that will occur if I am not able to
complete the job before the deadline. I have to design an algorithm to minimize the loss.
I have tried changing the standard algorithm of dynamic programming for maximizing the profit in job scheduling but to no success.
What algorithm can I use to solve the question?
Dynamic Programming isn't the right approach based on what you're aiming to optimize. You can find the optimized schedule by using a greedy approach.
Here's a thorough guide with sample code for your desire language (C++), in the guide it assumes each jobs takes only 1 unit of time, which you can easily modify by using time_to_complete instead.
Your problem is similar to the knapsack one. Using a greedy approach is convenient if you aren't actually looking for the best possible solution, but just a "good enough" one.
The big pro of the greedy approach is that the cost is rather lower than other "more thorough" approaches but, if you need the best solution to your problem, I would say that backtracking is the way to go.
Since the deadline can be violated, the problems looks like a Total Weighted Tardiness Scheduling Problem. There are many flavors of it, but most problems under this umbrella are computationally hard, therefore Dynamic Programming (DP) would not be my first choice. In my experience, DP also poses difficulties during modeling and implementation. Same comment for mathematical programming "as-is". Some approaches that can be implemented more quickly are:
constraint programming: very small learning curve, and there are many libraries out there, included very good open source ones (most have C++ API). Bonus: constraint programming can demonstrate optimality.
ad hoc heuristics: (1) start with a constructive algorithm (like the greedy approach suggested by Ling Zhong and Flavio Giobergia), then (2) use some local search approach to improve if and finally (3) embed the approach into a metaheuristic scheme. This way you can build on top of the previous step, and learn a lot about the problem. Note: in general, heuristics cannot demonstrate optimality
special mention: local solver, a hybrid approach between the two above: it lets you model the problem using a formalism similar to constraint programming and then it solves it using heuristics. It is very easy to learn, it usually lets you get started quickly and, in my tests, it provides remarkably good results.
How to implement 3d kDTree build and search algorithm in c or c++? I am wondering if we have a working code to follow
I'd like to recommend you a two good presentations to start with:
"Introduction to k-d trees"
"Lecture 6: Kd-trees and range trees".
Both give all (basic ideas behind kd-trees, short visual examples and code snippets) you need to start writing your own implementation.
Update-19-10-2021: Resources are now longer public. Thanks to #Hari for posting new links down below in the comments.
I found the publications of Vlastimil Havran very useful. His Ph.d Thesis gives a nice introduction to kd-trees and traversal algorithms. Further articles are about several improvements, e.g. how to construct kd-tree in O(nlogn). There are also a lot of implementations in different graphic libs. You should just google for it.
For an example of a 3D kd-tree implementation in C, take a look at kd3. It is not general purpose library and requires the input data to be in a specific form, but the ideas and approach should be transferable.
Disclosure: I am the author of kd3.
Disclaimer: It was written as proof-of-concept code for an existing application and is therefore not as generic nor as well-tested as it should be. Bug reports/fixes are welcome.
I am newbie for integer linear programming.
I plan to use a integer linear programming solver to solve my combinatorial optimization problem.
I am more familiar with C++/object oriented programming on an IDE.
Now I am using NetBeans with Cygwin to write my applications most of time.
May I ask if there is an easy use ILP solver for me?
Or it depends on the problem I want to solve ? I am trying to do some resources mapping optimization. Please let me know if any further information is required.
Thank you very much, Cassie.
If what you want is linear mixed integer programming, then I would point to Coin-OR (and specifically to the module CBC). It's Free software (as speech)
You can either use it with a specific language, or use C++.
Use C++ if you data requires lots of preprocessing, or if you want to put your hands into the solver (choosing pivot points, column generation, adding cuts and so on...).
Use the integrated language if you want to use the solver as a black box (you're just interested in the result and the problem is easy or classic enough to be solved without tweaking).
But in the tags you mention genetic algorithms and graphs algorithms. Maybe you should start by better defing your problem...
For graphs I like a lot Boost::Graph
I have used lp_solve ( http://lpsolve.sourceforge.net/5.5/ ) on a couple of occasions with success. It is mature, feature rich and is extremely well documented with lots of good advice if your linear programming skills are rusty. The integer linear programming is not a just an add on but is strongly emphasized with this package.
Just noticed that you say you are a 'newbie' at this. Well, then I strongly recommend this package since the documentation is full of examples and gentle tutorials. Other packages I have tried tend to assume a lot of the user.
For large problems, you might look at AMPL, which is an optimization interpreter with many backend solvers available. It runs as a separate process; C++ would be used to write out the input data.
Then you could try various state-of-the-art solvers.
Look into GLPK. Comes with a few examples, and works with a subset of AMPL, although IMHO works best when you stick to C/C++ for model setup. Copes with pretty big models too.
Linear Programming from Wikipedia covers a few different algorithms that you could do some digging into to see which may work best for you. Does that help or were you wanting something more specific?
i am trying to implement discrete curve evolution algorithm in c++ do any one help me with psudo code or c code or
some simple steps of your understanding
Discrete Curve Evolution is an algorithm to compute an everywhere convex curve from one that is concave. It moves concave sections of the curve outward along their normal in discrete steps until all concavities are eliminated. It is not a genetic algorithm, the term evolution refers to 'evolving' the position of the curve over time.
Having searched on this for quite some time the best source on the internet is here:
https://cis.temple.edu/~latecki/Software/Evo.zip
This is matlab code so it's not quite what you are looking for but you have three good options:
Port it to C++ (usually not to hard with matlab as long as it doesn't use matrix prims.)
Wrap the matlab code so you can call it from C (matlab provides libraries to do this)
Compile it to an executable and call that from C (matlab also allows this)
Option 2 would require anyone that want's to run it to have a copy of the matlab dynamic library on their computer which may be undesirable. I'm guessing option 3 would require this too, but I only have experience with options 1 and 2. Porting matlab to c++ is usually not that bad; it depends on how much the code utilizes matrix primitives and matrix operations which are easy to use in matlab and hard to use in C++ (because they aren't built-in). Still, I'd recommend giving it the old college try!
If you're just looking for DCE, check out the file evolution.m. That's the function that implements DCE. The full skeleton pruning algorithm this comes from can only be described simply at a high level. The individual steps and parts are QUITE complicated and DCE is only a small piece of that.
Hope this helps! I will be working with this code myself so if I do end up using it in C++ in some way that might help you I will let you know.
I'm not exactly sure what you mean by Discrete Curve evolutionary algorithm, but if you mean a Symbolic regression algorithm, you can start by reading about symbolic regression (or genetic programming in general):
http://en.wikipedia.org/wiki/Symbolic_Regression
There's also some nice existing programs. The Eureqa one has an open API:
http://code.google.com/p/eureqa-api/