# Problems that have been solved using CCM

## Combinatorial problems as temporary target

Although the aim of CCM is to solve
real-world problems, it cannot be
achieved in a short period. Our first goal has been solving
combinatorial problems,
such as the *N* queens problem,
graph or map coloring problem,
integer programming problems,
and so on. Combinatorial problems are classified to NP-complete or
NP-hard problems, which is not believed to be solved by algorithms
whose time complexity is in a polynomial order.

## Constraint satisfaction and optimization problems

Combinatorial problems such as the *N* queens or coloring problems
are called constraint satisfaction problems (CSP),
and those such as the integer programming problems or
traveling salesperson problems are called
optimization problems. CSP are problems to find a solution that satisfy
all the constraints specified, and optimization problems are to find a
solution, in which the objective function takes the optimal value.
There are complex problems that are combination of a CSP and optimization
problem. Real world problems are often formalized as constraint
satisfaction and/or optimization problems.

Y. Kanada
(yasusi @ kanadas.com)
Created: 11/21/95, Modified: 5/6/2002.