how to select values from matrix?

I have 10 cores C1,C2,C3,C4,C5,C6,C7,C8,C9,C10,, each core have their own testing time,, I represent the testing time of each core by matrix A where each row corresponds to core no.

A = [ 428,220,155,116,103,90,77,64,64,63,51,51,51,51,50,38;
15292,7719,4067,3175,2655,2070,1774,1624,1405,1257,1182,1107,1034,960,886,813;
5058,2582,2507,2507,2507,2507,2507,2507,2507,2507,2507,2507,2507,2507,2507,2507;
26602,13354,11129,6782,5829,5829,5829,5829,5829,5829,5829,5829,5829,5829,5829,5829;
191874,95992,64070,48106,38481,32167,27613,24163,21518,19757,17624,16194,14983,14873,14873,12192;  
185794,93014,62248,46741,37364,31241,28199,23488,20906,19034,19034,18799,18799,18564,18564,11978;  
65686,32891,21959,16493,13243,11027,9695,8342,7383,6717,6431,6431,6431,6431,6431,4219;  
22427,11262,8721,5680,4605,4605,4605,4605,4605,4605,4605,4605,4605,4605,4605,4605;
26351,13182,8802,6597,5310,4440,3798,3305,2964,2820,2418,2226,2118,2118,2118,1659;  
120188,60128,40137,30132,24701,21182,17663,15100,14144,14144,11033,10625,10625,10625,10625,7586 ]  ;

And also I have represent all the core by matrix Z

Z=[6,10,5,4;7,8,3,0;1,2,9,0];

each element in matrix Z correspond to the no of rows of matrix A. I have generate a temporary matrix temp which always produce random number and summation of each element in a must not be greater than 16. the code is

highest_num=14;
n=randperm(14);
c=combnk(n,3);
t=1;
for i=1:((highest_num*(highest_num-1)*(highest_num-2))/(3*2*1))
    sum=0;
    for j=1:3

          sum=sum+c(i,j);
      end
      if(sum==16)
          m=1;
          for k=1:3
              if(m<4)
              temp(t,k)=c(i,m);
              m=m+1;
              end
          end
          t=t+1;
      end
  end

suppose temp matrix is

temp =[ 9  6  1 ; 9  2  5 ;  9  4  3 ; 6  2  8 ; 6  7  3 ; 1  2  13 ; 1  8  7 ; 1  12  3 ;1  5  10 ; 1  4  11 ; 2  4  10 ; 2  3  11 ; 8  5  3 ; 5  4  7]

I have to pick values from matrix A according to mapping between matrix Z and matrix temp,, I want to say that the 1st element of 1st row and 1st column of temp is 9 and the 1st element of 1st row and 1st column of Z is 6 so i have to pick the value of row no 6 and colum no 9 from matrix A afterthat the element of 2nd row and 1st column of Z is 7 so i have pick value of row no 7 and col no 9 from matrix A, afterthat the element of 3rd row and 1st column of Z is 1 so i have pick value of row no 1 and col no 9 from matrix A,, then i have to do summation of of these trhee values,,likewise I have to pick values from A for 2nd column and 3rd column of Z and temp and calculate the summation of 2nd column and 3rd column.. the total_testingTime is the maximum among three summation.

Now i have apply simulated annealing for selecting the best total_testingTime so the above technique has to be done until temperature>1 the initial temperature = 100 and the cooling_rate = 5

so can u please me suggest me to perform this code in matlab

Answer 1

[Prateekshya]

Hello Mitali,

To implement the described process in MATLAB, you will need to follow these steps:

• Initialize Parameters: Define your initial temperature, cooling rate, and any other necessary parameters.
• Simulated Annealing Loop: Use a while loop to perform the simulated annealing process until the temperature drops below a threshold.
• Generate Random Permutations: Use the randperm and combnk functions to generate combinations. For more information on combnk and nchoosek, please go through: https://www.mathworks.com/help/stats/combnk.html. For randperm please follow: https://www.mathworks.com/help/matlab/ref/randperm.html.
• Mapping and Summation: For each valid permutation, map the values from temp to Z and then to A to calculate the total testing time.
• Update Best Solution: Check if the current solution is better than the best found so far and update accordingly.
• Cooling Schedule: Reduce the temperature using the cooling rate.

Here is a sample MATLAB code to get you started:

% Initialize parameters
initial_temperature = 100;
cooling_rate = 5;
temperature = initial_temperature;
highest_num = 14;

% Define matrices A and Z
A = [...];  % Your matrix A
    Z = [6, 10, 5, 4; 7, 8, 3, 0; 1, 2, 9, 0];
    
    % Initialize best total testing time
    best_total_testingTime = Inf;
    
    % Simulated annealing loop
    while temperature > 1
    % Generate random permutations
    n = randperm(highest_num);
    c = combnk(n, 3);
    
    % Initialize temporary matrix
    temp = [];
    t = 1;
    
    % Select combinations that sum to 16
    for i = 1:size(c, 1)
        if sum(c(i, :)) == 16
            temp(t, :) = c(i, :);
            t = t + 1;
        end
    end
    
    % Iterate over each column of Z
    for col = 1:size(Z, 2)
        if Z(1, col) == 0, continue; end  % Skip if Z element is zero
        
        % Calculate total testing time for this column
        total_testingTime = 0;
        for row = 1:size(temp, 1)
            for z_row = 1:size(Z, 1)
                if Z(z_row, col) == 0, continue; end  % Skip if Z element is zero
                
                % Map temp to Z and then to A
                core_number = Z(z_row, col);
                temp_value = temp(row, z_row);
                total_testingTime = total_testingTime + A(core_number, temp_value);
            end
        end
        
        % Update best total testing time
        if total_testingTime < best_total_testingTime
            best_total_testingTime = total_testingTime;
        end
    end
    
    % Cool down
    temperature = temperature - cooling_rate;
    end
    
    % Display the best total testing time found
    disp(['Best Total Testing Time: ', num2str(best_total_testingTime)]);

I hope this helps!