<p>Ok, I have found how to do this by reading <a href="http://rads.stackoverflow.com/amzn/click/1904602827" rel="nofollow">Introduction to Mathematical Optimization: From Linear Programming to Metaheuristics</a>. Chapters 7 and 10 clearly explain the possibilities, essentially the penalty method and the use of Lagrange multipliers coupled with Kuhn-Tucker conditions if necessary.</p>

CC BY-SA 3.0
2011-06-23T15:06:43.057Z
2011-06-23T15:18:33.437Z
2011-06-23T15:18:33.437Z
Massimo Cafaro
<p>Is there an algorithm to transform an arbitrary <a href="http://en.wikipedia.org/wiki/Linear_programming#Integer_unknowns" rel="nofollow">Mixed Integer Programming</a> problem into the corresponding formulation for <a href="http://en.wikipedia.org/wiki/Particle_swarm_optimization" rel="nofollow">Particle Swarm Optimization</a>? I have found some information related to the use of penalty functions to avoid violation of constraints, but not a well defined procedure to convert the objective function and each of the constraints as required for a PSO solution. </p>

CC BY-SA 3.0
2011-06-21T21:21:30.463Z
Note that MIP is a problem formulation and PSO is a heuristic. So what you mean is that you're asking how to solve an MIP using PSO.
Suresh Venkat
CC BY-SA 3.0
2011-06-22T11:06:06.240Z
Suresh, I am not asking how to solve the MIP problem using PSO: I know how PSO works and I have already implemented in C and MPI parallel versions of PSO to solve other problems. What I am asking for is how to translate the MIP problem in the corresponding PSO function whose fitness must be optimized.
Massimo Cafaro
<ds.algorithms><reference-request><optimization><linear-programming>
Algorithm to transform an arbitrary MIP problem into the corresponding formulation for PSO
Massimo Cafaro
# Algorithm to transform an arbitrary MIP problem into the corresponding formulation for PSO

(Asked by: username_0 on 2011-06-14)

Is there an algorithm to transform an arbitrary [Mixed Integer Programming](http://en.wikipedia.org/wiki/Linear_programming#Integer_unknowns) problem into the corresponding formulation for [Particle Swarm Optimization](http://en.wikipedia.org/wiki/Particle_swarm_optimization)? I have found some information related to the use of penalty functions to avoid violation of constraints, but not a well defined procedure to convert the objective function and each of the constraints as required for a PSO solution.

**Tags:** ds.algorithms, reference-request, optimization, linear-programming
> **Comments:**
> **username_1**: Note that MIP is a problem formulation and PSO is a heuristic. So what you mean is that you're asking how to solve an MIP using PSO.  
> **username_0**: Suresh, I am not asking how to solve the MIP problem using PSO: I know how PSO works and I have already implemented in C and MPI parallel versions of PSO to solve other problems. What I am asking for is how to translate the MIP problem in the corresponding PSO function whose fitness must be optimized.  

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## 1 answers

### Answer by username_0 on 2011-06-23. Score: 2

Ok, I have found how to do this by reading [Introduction to Mathematical Optimization: From Linear Programming to Metaheuristics](http://rads.stackoverflow.com/amzn/click/1904602827). Chapters 7 and 10 clearly explain the possibilities, essentially the penalty method and the use of Lagrange multipliers coupled with Kuhn-Tucker conditions if necessary.


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