The Permutation FlowShop Problem
Problem Description
Program Descriptions
 pfsp.m
This MATLAB program gives the best found permutation via the CE method.Usage:
Call the program from MATLAB, with the following syntax:
[ pi , t ] = pfsp( N , rho , alpha , traj , n , m , t , z )
Example: [ perm , cost ] = pfsp( 100 , 0.1 , 0.8 , 2 , 10 , 2 , t , 10 )
where t is a 10 x 2 matrix of costs.Inputs: N  Number of samples to generate each round rho  fraction of best samples to take alpha  smoothing parameter traj  0, node transitions, x(1)=1 1, node transitions, x(1) random 2, node placement (default) n  number of jobs m  number of machines t  t(i,j) is the cost of job i on machine j z  number of succesive rhoth quantiles the same before stop Outputs: pi  the output permutation t  the cost (in time) matrix used  gpfsp.m
This program is used internally to generate tours via node transitions.  gpfsp2.m
This program is used internally to generate tours via node placement, using the first row of the P matrix to generate the first position.  gpfsp3.m
This program is used internally to generate tours via node placement, using a random row of the P matrix to generate the first position.  fpfsp.m
This MATLAB program gives the best found permutation via the CE method, using ``fast'' trajectory generation, as mentioned in Remark 4.12, and described in Algorithms 4.11.3 and 4.11.4, as well as Section 4.11.2 in [1].Usage:
Call the program from MATLAB, with the following syntax:
[ pi , t ] = fpfsp( N , rho , alpha , traj , n , m , t , z )
Example: [ perm , cost ] = fpfsp( 200 , 0.05 , 0.75 , 3 , 12 , 1 , t , 10 )
where t is a 12 x 3 matrix of costs.Inputs: N  Number of samples to generate each round rho  fraction of best samples to take alpha  smoothing parameter traj  0, alias technique (default) uses x% = 70% 1, composition method n  number of jobs m  number of machines t  t(i,j) is the cost of job i on machine j z  number of succesive rhoth quantiles the same before stop Outputs: pi  the output permutation t  the cost (in time) matrix used  fgpfsp.m
This program is used internally to generate tours via the alias speedup.  fgpfsp2.m
This program is used internally to generate tours via the composition speedup.  spfsp.m
This program is used internally to evaluate the performance of these algorithms.
Bibliography

D. P. Kroese and R. Y. Rubinstein.
The CrossEntropy Method: A Unified Approach to Combinatorial Optimization, MonteCarlo Simulation and Machine Learning.
Springer, 2004.