best combination for lowest possible dose and lowest possible material cost

Hello,

I have been trying to get the best possible combination of low dose and low material cost.

The dose and cost seem to be correct, but the ratios i get are wrong. It gives me the maximum values, so i suppose the values are not being held correctly. What are your thoughts and how could i fix this?

Thank you in advance!

 mixDoseRate = zeros(1,9261);
        mixCost = zeros(1,9261);
        proportions = zeros(9261,3);

        % Initialize index for cells
        index = 1;
        for p1 = 0:0.05:1
            for p2 = 0:0.05:1
                for p3 = 0:0.05:1

                    % Calculate the mixed dose rate
                    mixDoseRate(index) = InDoseRate(i) * exp(-((selectedSource.(materials{1}) * density.(materials{1}) * ceil(thickness(1,i)) * p1) + (selectedSource.(materials{2}) * density.(materials{2}) * ceil(thickness(2,i)) * p2) + (selectedSource.(materials{3}) * density.(materials{3}) * ceil(thickness(3,i)) * p3)));
                    mixvolume = areaEditField{i}.Value*1e6*(thickness(1,i)*p1 + thickness(2,i)*p2 + thickness(3,i)*p3);
                    mixCost(index) = (PriceEditField.(materials{1}).Value * density.(materials{1}) + PriceEditField.(materials{2}).Value * density.(materials{2}) + PriceEditField.(materials{3}).Value * density.(materials{3})) * mixvolume;
                    proportions(index,:) = [p1, p2, p3];
                        
                    % Increment index
                    index = index + 1;
                    if index > 9261
                        break;
                    end
                end
            end
        end
        for index = 2:9261
            if (mixDoseRate(index) <= mixDoseRate(index-1)) && (mixCost(index) <= mixCost(index-1))
                bestDoseRate = mixDoseRate(index);
                bestCost = mixCost(index);
                Proportions = proportions(index,:);
            else
                continue;
            end
        end

        tableData{4, 2*i} = sprintf('%.2e uSv/h', bestDoseRate);
        tableData{4, 2*i+1} = sprintf('€ %.2e', bestCost);
        tableData{5, 2*i} = sprintf('%.2f, %.2f, %.2f', Proportions(1), Proportions(2), Proportions(3));

Answer 1

[Torsten]

You mean

bestDoseRate = Inf;
bestCost = Inf;
for index = 2:9261
   if (mixDoseRate(index) <= bestDoseRate && mixCost(index) <= bestCost)
     bestDoseRate = mixDoseRate(index);
     bestCost = mixCost(index);
     Proportions = proportions(index,:);
   end
end

?

Does it really make sense to minimize Dose and Cost this way ?

My guess is that low dose means high cost - so you have two conflicting aims in your optimization.

Take a look at

https://en.wikipedia.org/wiki/Multi-objective_optimization

on how to handle such a situation mathematically.

There are also MATLAB tools for such cases:

https://uk.mathworks.com/help/gads/paretosearch.html

https://uk.mathworks.com/help/gads/gamultiobj.html

[ALEXANDROS]

Hi,

Thank you for your fast reply.

It might seem kind of strange, i agree. But i have already calculated the thickness and cost for each material required to minimize the dose rate at an acceptale value. At this point i want to find the best material combination iterrating through the percentages of each thickness from 0 to 1 with step 0.05 while also keeping the cost as low as possible.

And yes, you could preallocate the values of the variables as you have added, but i believe since there is an array of the values, it is not needed. I might be wrong though.

I will check out the tools you mention in your reply and see where i can take it.

[Torsten]

It's not the "preallocation", but the comparison that makes the difference:

if (mixDoseRate(index) <= bestDoseRate && mixCost(index) <= bestCost)

instead of

if (mixDoseRate(index) <= mixDoseRate(index-1)) && (mixCost(index) <= mixCost(index-1))