How to check if my linear constraints and bounds are infeasible & reduce execution time?

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Muhammad Kahari Pranata
评论： Muhammad Kahari Pranata 2024-6-17
Hello,
I'm making a code where it creates an optimized engine usage schedule based on engine's reliability using genetic algorithm solver. The following is the code that I've made:
tic
clear
% Create arrays to store total Hour & daily result
totalHourWeekday = zeros(5,13);
result = zeros(5,13);
% Calculate the maximum engine by adding all of the engine's status
engineStatus = ones(1,13);
maxEngine = sum(engineStatus);
% Initialize optimization problem
rel = zeros(1,13);
decision = optimproblem("ObjectiveSense","max");
engine = optimvar('engine',13,'Type','integer','LowerBound',0,'UpperBound',1);
% Define days
for day = 1:5
% calculate maximum duration
maxDuration = 24*max(day);
% Initialize demand
for demand = 1:5
disp(['Day: ',num2str(day),' Demand: ',num2str(demand)])
switch demand
case 1
hourDemand = 3;
engineDemand = 9;
% Calculate reliability based on the sum between the hour
% demand & previous hour
if day == 1
timeCalc = hourDemand + totalHourWeekday(demand,:);
else
timeCalc = hourDemand + result(day-1,:);
end
rel = exp(-(4.44*10^-5*timeCalc));
relSys = 1-((1-engine(1)*rel(1,1))*(1-engine(2)*rel(1,2))*(1-engine(3)*rel(1,3))*(1-engine(4)*rel(1,4))*(1-engine(5)*rel(1,5))*(1-engine(6)*rel(1,6))*(1-engine(7)*rel(1,7))*(1-engine(8)*rel(1,8))*(1-engine(9)*rel(1,9))*(1-engine(10)*rel(1,10))*(1-engine(11)*rel(1,11))*(1-engine(12)*rel(1,12))*(1-engine(13)*rel(1,13)));
% Set reliability as objective function
decision.Objective = relSys;
% Initialize constraint #1: engines should be equal to the
% demand
engineMaintOrNot = sum(engine*engineStatus);
decision.Constraints.engineDemandConstraint = engineMaintOrNot == engineDemand;
% Initialize constraint #2: engine's hour should be less
% than max duration
if day == 1
decision.Constraints.durationConstraint = engine*totalHourWeekday(demand,:) <= maxDuration;
else
decision.Constraints.durationConstraint = engine*result(day-1,:) <= maxDuration;
end
% Solve optimization problem
sol = solve(decision);
% Add the hour demand to the chosen engines
for i = 1:13
if sol.engine(i) == 1
totalHourWeekday(demand,i) = totalHourWeekday(demand,i) + hourDemand;
end
end
case 2
hourDemand = 2;
engineDemand = 6;
timeCalc = hourDemand + totalHourWeekday(demand-1,:);
rel = exp(-(4.44*10^-5*timeCalc));
relSys = 1-((1-engine(1)*rel(1,1))*(1-engine(2)*rel(1,2))*(1-engine(3)*rel(1,3))*(1-engine(4)*rel(1,4))*(1-engine(5)*rel(1,5))*(1-engine(6)*rel(1,6))*(1-engine(7)*rel(1,7))*(1-engine(8)*rel(1,8))*(1-engine(9)*rel(1,9))*(1-engine(10)*rel(1,10))*(1-engine(11)*rel(1,11))*(1-engine(12)*rel(1,12))*(1-engine(13)*rel(1,13)));
decision.Objective = relSys;
engineMaintOrNot = sum(engine*engineStatus);
decision.Constraints.engineDemandConstraint = engineMaintOrNot == engineDemand;
decision.Constraints.durationConstraint = engine*totalHourWeekday(demand-1,:) <= maxDuration;
sol = solve(decision);
for i = 1:13
if sol.engine(i) == 1
totalHourWeekday(demand,i) = totalHourWeekday(demand,i) + hourDemand;
end
end
case 3
hourDemand = 5;
engineDemand = 10;
timeCalc = hourDemand + totalHourWeekday(demand-1,:);
rel = exp(-(4.44*10^-5*timeCalc));
relSys = 1-((1-engine(1)*rel(1,1))*(1-engine(2)*rel(1,2))*(1-engine(3)*rel(1,3))*(1-engine(4)*rel(1,4))*(1-engine(5)*rel(1,5))*(1-engine(6)*rel(1,6))*(1-engine(7)*rel(1,7))*(1-engine(8)*rel(1,8))*(1-engine(9)*rel(1,9))*(1-engine(10)*rel(1,10))*(1-engine(11)*rel(1,11))*(1-engine(12)*rel(1,12))*(1-engine(13)*rel(1,13)));
decision.Objective = relSys;
engineMaintOrNot = sum(engine*engineStatus);
decision.Constraints.engineDemandConstraint = engineMaintOrNot == engineDemand;
decision.Constraints.durationConstraint = engine*totalHourWeekday(demand-1,:) <= maxDuration;
sol = solve(decision);
for i = 1:13
if sol.engine(i) == 1
totalHourWeekday(demand,i) = totalHourWeekday(demand,i) + hourDemand;
end
end
case 4
hourDemand = 8;
engineDemand = maxEngine-1;
timeCalc = hourDemand + totalHourWeekday(demand-1,:);
rel = exp(-(4.44*10^-5*timeCalc));
relSys = 1-((1-engine(1)*rel(1,1))*(1-engine(2)*rel(1,2))*(1-engine(3)*rel(1,3))*(1-engine(4)*rel(1,4))*(1-engine(5)*rel(1,5))*(1-engine(6)*rel(1,6))*(1-engine(7)*rel(1,7))*(1-engine(8)*rel(1,8))*(1-engine(9)*rel(1,9))*(1-engine(10)*rel(1,10))*(1-engine(11)*rel(1,11))*(1-engine(12)*rel(1,12))*(1-engine(13)*rel(1,13)));
decision.Objective = relSys;
engineMaintOrNot = sum(engine*engineStatus);
decision.Constraints.engineDemandConstraint = engineMaintOrNot == engineDemand;
decision.Constraints.durationConstraint = engine*totalHourWeekday(demand-1,:) <= maxDuration;
sol = solve(decision);
for i = 1:13
if sol.engine(i) == 1
totalHourWeekday(demand,i) = totalHourWeekday(demand,i) + hourDemand;
end
end
case 5
% Special case
for i = 1:13
if engineStatus(1,i) == 1
totalHourWeekday(demand,i) = totalHourWeekday(demand,i) + 6;
end
end
end
% Add the total hour from all hour demands within the day
if day == 1
result(day,:) = sum(totalHourWeekday);
else
result(day,:) = result(day-1,:) + sum(totalHourWeekday);
end
end
end
The code ran well until it reached 4th day. When calculating 4th day's 1st demand, it gave me the following error:
I guessed that, since it gave the infeasible linear constraints and bounds, an error was detected on line 57. That's why I am wondering how to solve this problem or how to check for linear constraints and bounds infeasibility?
Furthermore, is there any way to reduce the code's execution time?
Thank you in advance
  4 个评论
显示 2更早的评论
Torsten
Torsten 2024-6-14
I don't know the background of your problem, but usually - if you make schedules for a certain time span - you cannot do this successively (day by day), but for the complete period because decisions taken at day i influence decisions on days before and after day i.
Muhammad Kahari Pranata
Muhammad Kahari Pranata 2024-6-14
@Torsten I forgot to add some further information regarding this program. This code is just about one part of the whole project. The other part is to make sure that when one of the engines reached a certain operation hour, it must be maintained for certain period of days and make sure that maintenance happens only to one engine at a time (so multiple engines can't be maintained simultaneously). So the final output of this program is to generate a maintenance schedule that shows, for each engines, the day of the maintenance and the operating hour when the maintenance is executed. Can I still do it per week? or do I have no choice but to do it per day?

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采纳的回答

Nipun
Nipun 2024-6-17
Hi Kahari,
I understand that you are receiving an out of bounds error when indexing in a data structure in MATLAB and intend to know the root cause of this error.
You can create a filter to investigate the infeasibilities of the linear programming constraints in MATLAB. For more information on creating such filters, refer to the following MathWorks documentation: https://www.mathworks.com/help/optim/ug/investigate-linear-infeasibilities.html
Hope this helps.
Regards,
Nipun
  1 个评论
Muhammad Kahari Pranata
Muhammad Kahari Pranata 2024-6-17
Thank you for the answer, @Nipun. I've actually solved the problem by resetting the totalHourWeekday every new day instead of initializing it only once. But I will look into that if I encountered the error again. Now, the only problem is to reduce the code's execution time. Do you know how to reduce it?

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