Optimization of water distribution network, objective is to get optimal cost

I want to ask how I should use any optimization algorithm with EPANET to obtained optimal diameter and optimal cost?

After using the code attached, I am unable to get the optimal cost; it is always coming 'inf' even if I am using a minimum pressure requirement of 30 m for nodes, minimum velocity 0, and maximum velocity 'inf' for links. I am using the Hanoi network, which has 34 links, for hydraulic simulation, I am using EPANET I am also attaching the Matlab code that I am using. It would be very nice of you if anyone could help me with this.

% GENETIC ALGORITHM (GA) SETUP

clear; close('all'); clc;
start_toolkit;

%d = epanet('C:\Users\Admin\Desktop\PipeNetwork\PN_code\Hanoi.inp');

% Define GA options for optimization
options = optimoptions('ga', 'Display', 'iter', 'PopulationSize', 16, ...
    'MaxGenerations', 6, 'UseParallel', false);

% Define number of pipes in the network
nvars = 34; % Number of pipes

diameterOptions = [304.8, 406.4, 508, 609.6, 762, 1016]; % Available diameters in mm
costPerDiameter = [45.73, 70.4, 98.38, 129.333, 180.8, 278.3]; % Cost per unit length for each diameter


% Define lower and upper bounds for pipe diameters
lb = repmat(min(diameterOptions), 1, nvars); % Minimum diameter constraint
ub = repmat(max(diameterOptions), 1, nvars); % Maximum diameter constraint

% Run Genetic Algorithm (GA) for optimal pipe diameter selection
[optimalDiameters, optimalCost] = ga(@pipeNetworkObjective, nvars, [], [], [], [], lb, ub, [], options);

% Display optimization results
fprintf('Optimal Pipe Diameters:\n');
disp(optimalDiameters);
fprintf('Optimal Cost:\n');
disp(optimalCost);

function cost = pipeNetworkObjective(diameters)
    % Load EPANET-MATLAB Toolkit
    start_toolkit;
    d = epanet('Optimal_Configuration_eta_2.00.inp');
    
    % Set pipe diameters based on GA input
    for i = 1:length(diameters)
        d.setLinkDiameter(i, diameters(i));
    end
    
    % Run hydraulic simulation
    d.solveCompleteHydraulics;
    
    % Check constraints
    pressures = d.getNodePressure;
    velocities = d.getLinkVelocity;
    
    if any(pressures < 0) || any(velocities < 0) || any(velocities > inf)
        cost = inf; % Penalize infeasible solutions
    else
        % Calculate cost based on diameters
        cost = calculateCost(diameters);
    end
    
    % Close EPANET
    d.unload;
end

function totalCost = calculateCost(diameters)
    % Define cost per diameter (example values)
    diameterOptions = [304.8, 406.4, 508, 609.6, 762, 1016]; % Available diameters in mm
    costPerDiameter = [45.73, 70.4, 98.38, 129.333, 180.8, 278.3]; % Cost per unit length for each diameter
    
    % Calculate total cost
    totalCost = 0;
    for i = 1:length(diameters)
        idx = find(diameterOptions == diameters(i));
        totalCost = totalCost + costPerDiameter(idx);
    end
end

[Torsten]

I don't understand your coupling between EPANET and ga.

[surendra kumar]

I am doing this by using the pipeNetworkObjective function (code for the same is already in the chat). I first define the pipeNetworkObjective function and then apply GA to it.

But I am unable to understand what is wrong with that code as minimum pipe network criteria is not satisfying after running the code and optimal cost is always coming 'inf', if you have any suggestions please let me know.

[Sam Chak]

@surendra kumar,

From Google, EPANET is a computer program capable of performing extended hydraulic and water quality simulations for pressurized water distribution networks. However, I cannot run the optimization using only the two codes provided. Are you, by any chance, utilizing the OpenWaterAnalytics/EPANET-Matlab-Toolkit which can be obtained from File Exchange?

Google also says the Hanoi water network, located in Vietnam. It consists of 32 nodes, 34 pipes, and 3 loops, and is fed by gravity from a reservoir with a 100 m fixed head.

[surendra kumar]

yes, I am using OpenWaterAnalytics/EPANET-Matlab-Toolkit and calling it by start_toolkit, which calls epanet I have attached the code for your reference, now if you can find some solution for my query kindly let me know.

[Sam Chak]

@surendra kumar, I am not an expert on graph optimization problems; however, I encourage forum users to describe their issues clearly so that other experts can provide advice or coding assistance without the need to search for missing files, such as the Hanoi.inp file, elsewhere on the Internet. For some individuals, it is often preferable to run the simulation directly within the forum or in MATLAB Online.

[Torsten]

Say you call EPANET with a list of 34 diameters for the 34 pipes. Is it really true that

any(pressures < 0) || any(velocities < 0) || any(velocities > inf)

are the only conditions that make a solution from EPANET infeasible ? Shouldn't the values for pressures and velocities somehow be constraint and/or influence the cost function for "ga" ? And if you compute costs that only depend on the tube diameters: don't you have to take into account the length of the tubes ?

But the main probem for the ga optimizer is that you only want it to choose between 6 different values for the diameters. As programmed, the optimizer will vary the input array "diameters" freely between 304.8 and 1016 such that the variable idx in

idx = find(diameterOptions == diameters(i));

will come out empty in almost all cases.

[surendra kumar]

@Sam Chak Thanks for your concern, In my 1st comment only I tried to upload the Hanoi.inp file but it showed File format is unsupported, one can easily get this file after downloading the OpenWaterAnalytics/EPANET-Matlab-Toolkit In the Network folder.

[surendra kumar]

@Torsten

• I am enforcing that at no node should the pressure drop below 30 m. The constraints on pressures and velocities (even if they appear simplistic in the code) serve as hard feasibility checks. If these constraints aren’t met, the simulation is marked as infeasible by assigning a high cost, which guides the GA away from those solutions.
• The cost function isn’t based solely on the diameters—it also accounts for the length of the tubes (as shown in the final cost-calculation function). So, while the diameters are the decision variables, the actual cost reflects both diameter and tube length, capturing the impact on material costs.
• I am indeed using a list of six allowed diameters. In practice, if a value outside this set is chosen (due to the GA’s continuous search space between 304.8 and 1016 mm), it fails to meet the constraints and is penalized heavily, effectively pushing the solution toward the nearest feasible option (often the lowest available diameter in that case)

[surendra kumar]

I request everyone, if you know clearly about OpenWaterAnalytics/EPANET-Matlab-Toolkit and GENETIC ALGORITHM (GA)Then, only comment on my question.

[Torsten]

Don't feel insulted by my comments - I just told you about the problems of your code in combination with EPANET.

I think a heuristic solution of your problem will make more sense than using an optimizer like "ga". I'd randomly take a portion of the 6^34 possible arrangements for the 6 diameters and 34 tubes (maybe starting from the lowest cost arrangements) and see if EPANET gives feasible results for pressure and velocity - however you may measure if a solution is feasible or not. Because your problem has a finite number of possible arrangements, I don't think that "ga" can do better.

If you want to stick to "ga", use the "intcon" option, define your vector of unknowns as a 34x1 vector where every element of this vector is an integer: either 1,2,3,4,5 or 6. This can be done by defining lb and ub as 1 and 6, respectively. These numbers then stand for the possible diameters of your tubes. Don't do it as you describe, namely to penalize deviations from the possible diameters you prescribe. But somehow "ga" needs to be told how "heavily" it violates the constraints on pressure and velocity if it offers a suggestion for the diameter vector. Simply returning "inf" for the cost in such cases doesn't help - you must create a cost function that penalizes infeasibility sensefully to give "ga" a chance to move in the right direction.

[surendra kumar]

@Torsten Thanks for your feedback. I read many research papers published in renowned journals. Many of them have successfully used GA for optimizing pipe networks. Many of them chose the Hanoi network for their case study and got the result for the constraint that no node should have a pressure drop below 30 m. There might be something missing in my code, which is why it is not working for me.

I am not familiar with intcon, but I will read about it if you have some resource or sample code for the same kindly share.

[Torsten]

@surendra kumar

From the documentation of "ga":

x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,intcon) or

x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,intcon,options)

requires that the variables listed in intcon take integer values.

Note

When there are integer constraints, ga does not accept nonlinear equality constraints, only nonlinear inequality constraints.

In your special case:

lb = ones(34,1);

ub = 6*ones(34,1);

intcon = 1:34;

[surendra kumar]

@Torsten Thank you, I wil try this one.