maximinSA_LHS {DiceDesign} | R Documentation |

## Simulated annealing (SA) routine for Latin Hypercube Sample (LHS) optimization via phiP criteria

### Description

The objective is to produce maximin LHS. SA is an efficient algorithm to produce space-filling designs.

### Usage

```
maximinSA_LHS(design, T0=10, c=0.95, it=2000, p=50, profile="GEOM", Imax=100)
```

### Arguments

`design` |
a matrix (or a data.frame) corresponding to the design of experiments |

`T0` |
The initial temperature of the SA algorithm |

`c` |
A constant parameter regulating how the temperature goes down |

`it` |
The number of iterations |

`p` |
power required in phiP criterion |

`profile` |
The temperature down-profile, purely geometric called "GEOM", geometrical according to the Morris algorithm called "GEOM_MORRIS" or purely linear called "LINEAR" |

`Imax` |
A parameter given only if you choose the Morris down-profile. It adjusts the number of iterations without improvement before a new elementary perturbation |

### Details

This function implements a classical routine to produce optimized LHS. It is based on the work of Morris and Mitchell (1995). They have proposed a SA version for LHS optimization according to mindist criterion. Here, it has been adapted to the `phiP`

criterion. It has been shown (Pronzato and Muller, 2012, Damblin et al., 2013) that optimizing phiP is more efficient to produce maximin designs than optimizing mindist. When `p`

tends to infinity, optimizing a design with `phi_p`

is equivalent to optimizing a design with `mindist`

.

### Value

A list containing:

`InitialDesign` |
the starting design |

`T0` |
the initial temperature of the SA algorithm |

`c` |
the constant parameter regulating how the temperature goes down |

`it` |
the number of iterations |

`p` |
power required in phiP criterion |

`profile` |
the temperature down-profile |

`Imax` |
The parameter given in the Morris down-profile |

`design` |
the matrix of the final design (maximin LHS) |

`critValues` |
vector of criterion values along the iterations |

`tempValues` |
vector of temperature values along the iterations |

`probaValues` |
vector of acceptation probability values along the iterations |

### Author(s)

G. Damblin & B. Iooss

### References

Damblin G., Couplet M., and Iooss B. (2013). Numerical studies of space filling designs: optimization of Latin Hypercube Samples and subprojection properties, *Journal of Simulation,* 7:276-289, 2013.

M. Morris and J. Mitchell (1995) Exploratory designs for computationnal experiments. Journal of Statistical Planning and Inference, 43:381-402.

R. Jin, W. Chen and A. Sudjianto (2005) An efficient algorithm for constructing optimal design of computer experiments. Journal of Statistical Planning and Inference, 134:268-287.

Pronzato, L. and Muller, W. (2012). Design of computer experiments: space filling and beyond, *Statistics and Computing,* 22:681-701.

### See Also

Latin Hypercube Sample (`lhsDesign`

),
discrepancy criteria (`discrepancyCriteria`

),
geometric criterion (`mindist`

, `phiP`

),
optimization (`discrepSA_LHS`

, `maximinESE_LHS`

, `discrepESE_LHS`

)

### Examples

```
dimension <- 2
n <- 10
X <- lhsDesign(n ,dimension)$design
Xopt <- maximinSA_LHS(X, T0=10, c=0.99, it=2000)
plot(Xopt$design)
plot(Xopt$critValues, type="l")
plot(Xopt$tempValues, type="l")
## Not run:
Xopt <- maximinSA_LHS(X, T0=10, c=0.99, it=1000, profile="GEOM_MORRIS")
## End(Not run)
```

*DiceDesign*version 1.10 Index]