CAN I USER A MIXED INTEGER GA FOR THIS??

I have 5 objects and each object has 3 sets of variables. The values of the variables within each object are integers. Ex:

Object 1: [Var1; Var2; Var3]

Object 1: [1,3,8,12,15;15,52,25,14,14;25,43,15,0,74]

...

Object 5:[11,12,13,14,0;41,0,0,41,1;85,69,56,0,75]

The numerical values of the variables of each object must be added to a total number, i.e., (Object1, Var1+ Object2, Var1….), (Object 1, Var2+Object 2, Var2+….)

I have a target value for the sum of each of the values of variables which is an integer and is constant. Target_Sumvar1, Target_Sumvar2, Target_Sumvar3

What I need to do is to find the optimal combination of VALUES for each variable within each object that when ADDED, minimizes the error with respect to their respective target variables.

1. Can I use the mixed integer genetic algorithm for this problem? If not, what would be the recommended approach?

2. How can I express the objective function for this problem?

Thank you.

[Walter Roberson]

You seem to indicate that object1 contains a list of values. As you do not indicate otherwise, we must guess that might be floating point.

You indicate that the target sum is integer. Your example values in object1 and object5 are all integers but you do not specify that, so we need to guess that they might be floating point.

When you speak about optimal combination of values, it is not clear how you are combining them. For example is the task to calculate that you want to use 7 * object5(1,1) + 2 * object5(1,2) - 11 * object5(1,3) and so on up to object5(3,5), and that these integer multipliers [7 2 -11 etc] are to be the used for all of the objects? Or is the task to select one value from each column of the object independently of all of the other objects? Or something else?

Is the task to find indices into the objects such that accessing the objects at the indices and summing the results gives as close as possible to the target? Is the task a Binary Knapsack Problem?

I spoke of floating point earlier even though you do not list any floating point values because you asked about mixed-integer programming. If you had not mentioned mixed-integer programming I would have thought you wanted to find only constrained integer values, perhaps indices.

[italogomu]

- All the values in every object 1 to 5 are integers

-The task is to:

1. Select one SET of values from each object (see attached pdf)

2. Add the values of each set from all objects as shown in the attached file

3. Select the combination of sets that when added, minimizes the difference with respect to the target matrix

4. Display optimal combination i.e., obtect1_Set4, Object_2_Set5,Object3_Set3

The “try them all approach” that I’m showing in the attached file is not suitable because I will not be able to generate the entire range of possibilities with the memory I have. That’s what I thought the use of a genetic algorithm might be applicable in this case.

Questions

1. Is a GA optimization the best way to solve this problem? Or is there a better approach?

2. How can I frame the optimization function in this case?