Introduction
The molecular conformation corresponding to the global minimum of the energy of N atoms interacting via the Lennard-Jones potential is used as a test case here.
The function to be minimized is given by:
Parameters
The user can pass through init() procedure the following 5 parameters:
1. natoms. The amount of atoms in potential. The default value is 10
2. potentialepsilon. The value of in the potential equation. The default value is 1
3. potentialsigma. The value of in the potential equation. The default value is 1
4. tolminiters. The maximum number of iters for Tolmin procedure. The default value is 2001
5. outputfile. The file where the discovered minimum will be written. The default value is potential.txt. If the value exists then outpufile will be renamed to outputfile-N, where N is the first integer number for which the file outputfile-N does not exist. The program stores in outputfile the following information
(a) Number of atoms (integer number)
(b) Position of atoms (3 double precision values in every row)
(c) The discovered minimum (double precision number)
Experimental results
In the following table the results from the application of the proposed method to the potential problem are listed. The method was executed 30 times and averages were taken. The column NATOMS denotes number of atoms, the column C2 denotes average results of success for two clients, the column C4 denotes average results for success for 4 clients and the column C8 stands for the average success results for 8 clients.
| Natoms | C2 | C4 | C8 |
|---|---|---|---|
| 5 | 100% | 100% | 100% |
| 6 | 100% | 100% | 100% |
| 7 | 80% | 100% | 100% |
| 8 | 60% | 80% | 100% |
| 9 | 70% | 100% | 100% |
| 10 | 40% | 80% | 90% |
| 12 | 100% | 100% | 100% |
| 15 | 10% | 20% | 50% |
| 20 | 70% | 80% | 100% |
| 25 | 40% | 40% | 70% |