I need a name for this optimization code. Also who can help me plot a pareto front with this code or at specify which objective function i can use for the pareto.

clc

faces = load("buildings.dat");

rays = load("SunRays.dat");

% to get the optimum number of panels on facades

[ntotal,wtotal,htotal] = CountPanels(faces);

% to get the optimum numbr of panel width &heights per facades

n = zeros(44,1); % 44 facades in total and 1 dimension

w = zeros(44,1);

h = zeros(44,1);

for i = 1: 44

[n(i,1),w(i,1),h(i,1)] = CountPanels(faces(i,:));

end

% Getting the efficiency of solar panels for time period 1(1.8hrs)

for i = 1:44

for j = 1: n(i,1)

eff1(i,j) = panelEfficiency(i,j,faces,rays(1,:));

end

end

%Getting the efficiency of solar panels for time period 1(2.2hrs)

for i = 1:44

for j = 1: n(i,1)

eff2(i,j) = panelEfficiency(i,j,faces,rays(2,:));

end

end

% Getting the efficiency of solar panels for time period 1(2.5hrs)

for i = 1:44

for j = 1: n(i,1)

eff3(i,j) = panelEfficiency(i,j,faces,rays(3,:));

end

end

%Getting the efficiency of solar panels for time period 1(1.5hrs)

for i = 1:44

for j = 1: n(i,1)

eff4(i,j) = panelEfficiency(i,j,faces,rays(4,:));

end

end

% optimum power output per placement of panel

P = zeros(44,120);

for i = 1:44

for j = 1:120

P(i,j) = 300*eff1(i,j)*1.8 + 300*eff2(i,j)*2.5 + 300*eff3(i,j)*2.2 ...

+ 300*eff4(i,j)*1.5;

end

end

% my optimization Procedures

% to get optimum performance

maxP = max(P, [], 'all');

% Get maximum efficiencies for each time period

maxEff1 = max(eff1,[],'all');

maxEff2 = max(eff2,[],'all');

maxEff3 = max(eff3,[],'all');

maxEff4 = max(eff4,[],'all');

% maximum efficiency(overall)

maxEff = max([maxEff1 maxEff2 maxEff3 maxEff4]);

%get maximum performance values for each facade

PMaxValues = max(P')';

% Generate the average

WeightedP = P./PMaxValues;

% get only the best placements for each row

for i=1:size(WeightedP,1)

for j = 1:size(WeightedP,2)

if (WeightedP(i,j) ~= 1)

WeightedP(i,j) = 0;

end

end

end

% Multiply by the performance vector

OptimumWeights = WeightedP .* P;

%----Optional --------------

% Let us set a performance benchmark for each solar panel of 900

% for i=1:size(WeightedP,1)

% for j = 1:size(WeightedP,2)

% if (OptimumWeights(i,j) < 700)

% OptimumWeights(i,j) = 0;

% end

% end

% end

% -----------------------------

% get the count of our remaining installations

count = 0;

for i=1:size(WeightedP,1)

for j = 1:size(WeightedP,2)

if (OptimumWeights(i,j) > 0)

count = count + 1;

end

end

end

% assuming i want to install at most 2,000 solar panels

% remove all minimums until we get to the top 2000 positions

% add a second constraint with respect to cost

% assuming i want to get a cost of not more than 1,000,000 USD

Cost = 0; % Initial Cost of zero

while count > 2000 || Cost > 1000000

un = min(OptimumWeights(OptimumWeights>0)); % Represents the smallest value in the matrix

for i=1:size(WeightedP,1)

for j = 1:size(WeightedP,2)

if (OptimumWeights(i,j) == un)

OptimumWeights(i,j) = 0;

end

end

end

count = 0;

for i=1:size(WeightedP,1)

%for i = 1:size(weightedP,1)

for j = 1:size(WeightedP,2)

if (OptimumWeights(i,j) > 0)

count = count + 1;

end

end

end

Cost = 800 * count;

end

% Compute the Energy Output of the installation

EnergyOutput = sum(OptimumWeights,"all");

% Compute installation cost

Cost = 800 * count;

% ---Generate text file report ----------

strOutput = "";

for i=1:size(WeightedP,1)

for j = 1:size(WeightedP,2)

if (OptimumWeights(i,j) > 0)

strOutput = append(strOutput, num2str(j), ",");

else

continue

end

end

strOutput = append(strOutput,newline);

end

fid = fopen('finalsolution.txt','wt');

fprintf(fid, strOutput);

fclose(fid);

Answer 1

[Umang Pandey]

Hi Chukwuemeka,

As per my understanding, you want to find appropriate objective functions which you can optimize based on provided code and obtain a pareto front.

For obtaining a pareto front, the nature of the objectives must be conflicting, i.e., achieving one goal impedes or contradicts the attainment of another. In the context of your code, following can be considered as potential objective functions -

• Maximizing Energy Output
• Minimizing Cost

Since, you have 2 objectives to optimize, this problem falls under the category of “Multi-Objective Optimization”.

You can refer to the following MathWorks discovery page for more information on this -

https://www.mathworks.com/discovery/multiobjective-optimization.html

As for obtaining a Pareto Front, refer to the following MATLAB example by running the following command in your MATLAB Command Window

openExample('globaloptim/ParetoFrontForMultiobjectiveOptimizationProblemBasedExample') 

Hope this helps!

Best,

Umang