Answers.Body: <p>A continous domain can be imagined as a space in which the axes of the coordinate systems are the parameters of the continous domain. If we take 2D Cartesian space as an example, it is a continous domain where there is an infininite amount of possibilities of placing an object in this space. Let's call the position of the object its state. Constraining the space to e.g. a sheet of paper does not change its continuity. There is still an infinte amount of posibilites of placing a dot (or any object) on that sheet of paper or with other words the state space of the dot is still infietly large. </p>
  
  <p>Computational methods are much better in dealing with descretet spaces (mainly because the possiblities to take the next step is limited). In a discrete space the possibilities are limited. If we take the example above and discretize the sheet of paper, e.g. use a grid on the paper and say that we are not interested in the exact location of the point, just in which grid it is in we have succesfully defined a discrete space. </p>
  
  <p>A different example for a problem in descrete domain can be navigation on a map. If we assume that the exact rajectory is not important, then we can make descrete decisions of turning left, right or moving forwards or backwards by one step. Even if add further possibilites (like moving up one step or down) until the number of possibilities in one state is not infinite the domain is descret. </p>
  
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Answers.CreationDate: 2018-12-13T16:27:56.660Z
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Body: <p>According to this website: <a href="http://yarpiz.com/67/ypea104-acor" rel="nofollow noreferrer">http://yarpiz.com/67/ypea104-acor</a> (in the website it is mentioned that it is a project aiming to be a resource of academic and professional scientific source codes and tutorials.):</p>
  
  <blockquote>
    <p>"Originally, the Ant Algorithms are used to solve <strong>discrete and
    combinatorial</strong> optimization problems. Various extensions of Ant Colony
    Optimization (ACO) are proposed to deal with optimization problems,
    defined in <strong>continuous domains</strong>. One of the most useful algorithms of
    this type, is ACOR, the Ant Colony Optimization for Continuous
    Domains, proposed by Socha and Dorigo, in 2008 (<a href="http://www.sciencedirect.com/science/article/pii/S0377221706006333" rel="nofollow noreferrer">here</a>)."</p>
  </blockquote>
  
  <p>What is the difference between continuous domains and discrete combinatorial optimization? I appreciate if you could also mention some examples for each type.</p>
  
Tags: <comparison><swarm-intelligence><combinatorics><ant-colony-optimization>
Title: What is the difference between continuous domains and discrete combinatorial optimization?
UserDisplayName: Questioner
ThreadText: # What is the difference between continuous domains and discrete combinatorial optimization?
  
  (Asked by: username_0 on 2018-12-13)
  
  According to this website: <http://yarpiz.com/67/ypea104-acor> (in the website it is mentioned that it is a project aiming to be a resource of academic and professional scientific source codes and tutorials.):
  
  > "Originally, the Ant Algorithms are used to solve **discrete and
  > combinatorial** optimization problems. Various extensions of Ant Colony
  > Optimization (ACO) are proposed to deal with optimization problems,
  > defined in **continuous domains**. One of the most useful algorithms of
  > this type, is ACOR, the Ant Colony Optimization for Continuous
  > Domains, proposed by Socha and Dorigo, in 2008 ([here](http://www.sciencedirect.com/science/article/pii/S0377221706006333))."
  
  What is the difference between continuous domains and discrete combinatorial optimization? I appreciate if you could also mention some examples for each type.
  
  **Tags:** comparison, swarm-intelligence, combinatorics, ant-colony-optimization
  
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  ## 1 answers
  
  ### Answer by username_1 on 2018-12-13. Score: 1
  
  A continous domain can be imagined as a space in which the axes of the coordinate systems are the parameters of the continous domain. If we take 2D Cartesian space as an example, it is a continous domain where there is an infininite amount of possibilities of placing an object in this space. Let's call the position of the object its state. Constraining the space to e.g. a sheet of paper does not change its continuity. There is still an infinte amount of posibilites of placing a dot (or any object) on that sheet of paper or with other words the state space of the dot is still infietly large.
  
  Computational methods are much better in dealing with descretet spaces (mainly because the possiblities to take the next step is limited). In a discrete space the possibilities are limited. If we take the example above and discretize the sheet of paper, e.g. use a grid on the paper and say that we are not interested in the exact location of the point, just in which grid it is in we have succesfully defined a discrete space.
  
  A different example for a problem in descrete domain can be navigation on a map. If we assume that the exact rajectory is not important, then we can make descrete decisions of turning left, right or moving forwards or backwards by one step. Even if add further possibilites (like moving up one step or down) until the number of possibilities in one state is not infinite the domain is descret.
  
  
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