COPYRIGHT NOTICEThis software is copyright by Zbigniew Michalewicz. Permission isgranted to copy and use the software for scientific, noncommercial purposes only. The software is provided "as is", i.e., without anywarranties.                              GENERAL REMARKSThe Genocop III system aims at finding a global optimum (minimum ormaximum: this is one of the input parameters) of a function;additional linear and nonlinear constraints (inequalities) canbe specified as well. This is the first version of Genocop III system (version 1.0); a newversion is being developed. The Genocop III system is based on the original Genocop (version 3.0).The current version of Genocop should run without changes on any BSD-UN*Xsystem (preferably on a Sun SPARC machine).                        HOW TO RUN THE GENOCOP III SYSTEMTo run the Genocop III system, there are five simple steps to follow:(1) prepare input file, say, "t100" (for test_case 100),(2) incorporate the objective function in the eval.c file,(3) incorporate nonlinear constraints into the nlinear.c file,(4) type "make",(5) type "genocop t100 100.out" ("t100.out" is the name     of the output file provided by you).A simple example follows. The input file of this example is thetransferred file "t01" you have now in your directory, the typical output is present in the file "t01.out". The function is already incorporated in the file "eval.c". There is also another testcase there (t02) with a typical output (t01.out).In the example we try to maximize a function of 4 variables: X[1]*X[1] + X[2]*X[2] + 2*X[3]*X[3] + X[4]*X[4] - 5*X[1]                - 5*X[2] - 21*X[3] + 7*X[4](NOTE: indexes of variables start from one, not zero).Additional requirements are: * 2 linear inequalities:      #  X[1] - 2*X[3] <= 1, and     #  X[1] + X[4] <= 5.1. * 3 nonlinear inequalities:     #  8 - X[1]*X[1] + X[2]*X[2] - X[3]*X[3] - X[4]*X[4] >= 0,     #  sin(X[2]*X[4]/2) >= -0.1, and     #  2*X[1]*X[2] + X[4] >= 0(note that linear inequalities are given as <= some number, whereas  nonlinear inequalities as >= 0).Also: -1.00   <=  X1   <=     5.00   0.00   <=  X2   <=     4.00  -7.32   <=  X3   <=     1.00  -1.00   <=  X4   <=     1.00 Then the input file "t01" is as follows:___________________________________________________4	2	41.0   0   -2   0    11.0   0    0   1    5.1-1.0	1	 5.0 0.0	2	 4.0-7.32	3	 1.0-1.0	4	 1.070   5004	4	4	4	4	4	40.1016101000.1530___________________________________________________Explanations (line by line) of the input file:4	2	4These three integers have the following meaning (in order):number of variables,number of linear inequalities,number of domains specified.These two lines:1.0     0     -2      0      11.0     0      0      1      5.1represent two inequalities. NOTE, that all inequalities assume thatleft hand side is LESS OR EQUAL to the right hand side. In other words,to represent an inequality:       3.1*X[2] - 4.9*X[4] >= 12.1you have to represent it as:      0.0    -3.1     0.0     4.9    -12.1, i.e.,      -3.1*X[2] + 4.9*X[4] <= -12.1----------------------------------------------------The next four lines of the input file:-1.0	1	 5.0 0.0	2	 4.0-7.32	3	 1.0-1.0	4	 1.0describe domains of variables (the middle - integer - number of each line serves as an index of a variable).The line:70   500indicate the population size (70) and the total number of generations (500).The next line:4	4	4	4	4	4	4provides the frequencies of 7 operators (these are integers; their totalshould not exceed 50% of the population size). You can leave these frequencies as a standard set for all your experiments. The final lines of the input file are:0.1    (the coeficient q for cumulative probability distribution;        higher q values provide stronger selective pressure;        standard value 0.1 is very reasonable for a population        size 70). 0      (1 is for maximization problem, 0 for minimization).1      (0 for a start from a random pupulation, 1 for a start        from a single point, i.e., all individuals in the         initial population are identical). If the system has        difficulties in finding feasible points, it will        prompt you for these (see note below, for parameter TRIES). 6      (a parameter for non-uniform mutation; should stay as 6).10     (a parameter for simple crossover, leave it as it is).1      the number of your test-case; any integer would do. It is       convenient if your eval.c file contains several test cases:       then you can run the system (without recompiling) and any       of the test problems present in eval.c.0.15   Probability of replacement of search vector by a fully feasible       vector.3      Number of non-linear inequalities (specified in nonlinear.c)0      Mode of choosing reference (fully feasible) vector to move to       in the reference population.  0 is random, 1 uses the probability       distribution.EVALUATION FUNCTION:One of the transferred files is "eval.c". For our current example, it is:_____________________________________________________#include "genocop.h"/* COMMENTS */float evaluate(X)VECTOR X;{  switch (test_num)   {    case 1:        return (X[1]*X[1] + X[2]*X[2] + 2*X[3]*X[3] + X[4]*X[4] - 5*X[1]                - 5*X[2] - 21*X[3] + 7*X[4]);    default: printf("Invalid test case in eval.c - test case is %f", test_num);              exit(0);   }  return(0);}_____________________________________________________If the objective function is already present in eval.c file,you can run the system. If not, you have to insert a new case.Also, in the file "nlinear.c", we have :_____________________________________________________#include "genocop.h"int nonlinear(X, ninumber, nenumber, epsilon)    VECTOR          X;    int             ninumber;    int             nenumber;    float           epsilon;{.  .  ..  .  ..  .  ..  .  .    /* initial state of cflag = TRUE */    switch (test_num)    {	      case 1:        g[1] = 8 - X[1]*X[1] + X[2]*X[2] - X[3]*X[3] - X[4]*X[4];        g[2] = sin(X[2]*X[4]/2.0) + 0.1;        g[3] = 2*X[1]*X[2] + X[4];        break;         default:	printf("Non-Linear Constraint Specification error\n");	exit(0);    }.  .  ..  .  ..  .  ..  .  .}_____________________________________________________Now, type 'make' to build the system and then type :% genocop t01 t01.outand (hopefully) you'll get your result.IMPORTANT REMARKS: (1) if you run test case t01 and the system prompts you for a feasible    starting point, provide a point which satisfies all (linear and    nonlinear) constraints. In case t01 it is very easy to find a    feasible solution; for example X[1] = 0.5; X[2] = 3.0; X[3] = 0.0;    X[4] = 0.9 would do.(2) remember about "break" statement when you insert a new test case    in the file nlinear.c.(3) There is a line in the genocop.h file:#define TRIES 100000The variable TRIES defined the number of attempts the Genocop systemtries to find a feasible point in the search space (for initializationprocess, for each individual). If successful, the system will run further. If not, the Genocop will prompt you for an initial point (if startingfrom a single point) or for some number of initial points (you decideon this number) for multiple initial points option.OUTPUT: the output file is self-explanatory. After several controllines, you get the generation number and the current best value(only for generations, where there is an improvement).This is followed by the best solution.FINAL NOTICE: This version is an experimental alpha version.              It is possible that there are some bugs in the system;              please, report them to zbyszek@mosaic.uncc.edu.              I will try to take care of them in the next version.I hope these remarks would be sufficient to experiment with the system.Happy optimizing,Zbigniew Michalewicz************************************************************************ Mail: Department of Computer Science      E-mail: zbyszek@uncc.edu  **       University of North Carolina        Phone:  (704) 547-4873    **       9201 University City  Boulevard     Fax:    (704) 547-3516    **       Charlotte, NC 28223-0001                                      ************************************************************************