Error : Unable to use a value of type optim.problemdef.OptimizationVariable as an index.

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Maria 2023-12-7

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评论： Matt J 2023-12-20

Hello !

I am working on a problem-based optimization task where I need to assign 4 subtasks to 4 different nodes. My approach involves defining an optimization variable as a vector with integer elements ranging from 1 to 4, each representing the node assigned to a subtask.

Here's a snippet of my current setup:

numSubtasks = 4;
numNodes = 4;
taskAssignmentVector = optimvar('taskAssignmentVector', numSubtasks, 'Type', 'integer', 'LowerBound', 1, 'UpperBound', numSubtasks);

My goal is to reshape this vector into a 4x4 binary assignment matrix within the optimization framework. Each row of this matrix should correspond to a subtask, and each column to a node, with '1' indicating the assignment.

I attempted to implement this by creating a function to generate the assignment matrix based on the vector, but I'm facing challenges in using the optimization variable as an index, leading to errors.

 AssignedMatrix = zeros(numSubtasks, numNodes);
        for s = 1:numSubtasks
          nodeAssigned = taskAssignmentVector(s); % Node assigned for each subtask
           AssignedMatrix(s, nodeAssigned) = 1;
        end

Could you please advise on the best approach to reshape this vector into a matrix form within the problem-based optimization framework? I am looking for a way to link the task assignments in the vector with a binary matrix that I can use in my objective function and constraints.

Thank you for your assistance!

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Matt J 2023-12-7

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编辑：Matt J 2023-12-7

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It sounds like the better approach would be to have the 4x4 binary matrix AssignedMatrix be the fundamental unknown optimization variable.

AssignedMatrix = optimvar('AssignedMatrix', [4,4], 'Type', 'integer', 'LowerBound', 0, 'UpperBound', 0);

Once you've done so, the taskAssignmentVector is easily expressed as a linear expression of the AssignedMatrix:

prob=optimproblem;
prob.Constraints.OneToOne1=sum(AssignedMatrix,1)==1;
prob.Constraints.OneToOne2=sum(AssignedMatrix,2)==1;
taskAssignmentVector=AssignedMatrix*(1:4)';

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Maria 2023-12-7

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@Matt J

Thank you, i tried already but I am facing an issue with correctly setting up and utilizing the assignment matrix in the optimization problem. I would like to ensure that my implementation of the assignment matrix and the way it interacts with the calculation of offloading times and the objective function is correct.

%Problem Based optimization 
function [solution, exitflag] = ProblemBasedOptimization()numSubtasks = 4;
numNodes = 4;
assignmentMatrix = optimvar('assignmentMatrix', numSubtasks, numNodes, 'Type', 'integer', 'LowerBound', 0, 'UpperBound', 1);
function maxOffloadingTime = calculateMaxOffloadingTime(taskAssignmentVector)
    Offloading_time_subtask = calculateOffloadingTime(x_UAV, y_UAV, z_UAV,x_positions,y_positions,x_haps,y_haps,z_haps,num_vehicles,numUAVs, Task_assignment, taskAssignmentVector, all_subtasks,reordered_tasks,initial_data_sizes,dependency_matrix,transmission_time,P_tx,P_Haps,f_c, c, eta_LoS_Ls,numRBs,B_RB_aerial,Noise_aerial,B_RB_dl,Noise_dl,G_u_linear,G_h_linear,h_LoS,kB,Ts,min_value,max_value,Fmax,coverageRadius,a,b,eta_NLoS_Ls);
    maxOffloadingTime = max(Offloading_time_subtask(:)); 
end
function satisfactionRate = objectiveFunction(assignmentMatrix, QoS_values)
    maxTime = calculateMaxOffloadingTime(taskAssignmentVector);
    satisfactionRate = (maxTime <= QoS_values); % 1 if constraint is satisfied, 0 otherwise
end
prob = optimproblem('ObjectiveSense', 'maximize');
prob.Objective = objectiveFunction(assignmentMatrix, QoS_values); 
% Add constraints
prob.Constraints.OneToOne1=sum(assignmentMatrix,1)==1;
prob.Constraints.OneToOne2=sum(assignmentMatrix,2)==1;
taskAssignmentVector=assignmentMatrix*(1:4)';
 [sol, fval, exitflag, output] = solve(prob);
if exitflag > 0
    optimalAssignment = solution.assignmentMatrix;
else
    disp('No feasible solution found.');
 end
end

this is the error :

Unrecognized function or variable 'taskAssignmentVector'.
Error in ProblemBasedOptimization/objectiveFunction (line 158)
    maxTime = calculateMaxOffloadingTime(taskAssignmentVector);

Maria 2023-12-7

编辑：Maria 2023-12-7

在 MATLAB Online 中打开

@Matt J Thank you for your guidance on using taskAssignmentVector directly in the optimization problem. I have attempted to follow your advice, but I'm encountering an issue when it comes to the calculations within my functions.

When I attempt to use assignmentMatrix in my calculations, it seems that the functions are not recognizing it as a regular matrix but rather as an OptimizationVariable object, and I'm unable to perform the necessary calculations. I'm aware that functions should be set up to work with OptimizationExpression objects, but I'm not sure how to adjust my existing functions to accommodate this.

assignmentMatrix(3, 1) + 2*assignmentMatrix(3, 2) + 3*assignmentMatrix(3, 3) + 4*assignmentMatrix(3, 4) 
assignmentMatrix(2, 1) + 2*assignmentMatrix(2, 2) + 3*assignmentMatrix(2, 3) + 4*assignmentMatrix(2, 4)
assignmentMatrix(3, 1) + 2*assignmentMatrix(3, 2) + 3*assignmentMatrix(3, 3) + 4*assignmentMatrix(3, 4)
assignmentMatrix(4, 1) + 2*assignmentMatrix(4, 2) + 3*assignmentMatrix(4, 3) + 4*assignmentMatrix(4, 4)

For instance, when I pass assignmentMatrix to the calculateMaxOffloadingTime function, I notice that it take the input as optimvar instead of binary matrix

I appreciate any further assistance you can provide.

Maria 2023-12-8

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@Matt J yes , but it wasn't the same problem and i tried to follow same steps but there is some issues.

@Torsten thank you for your suggestion.I've attempted to implement the changes, but I'm still encountering the same index out-of-bounds error when solving the problem using the genetic algorithm. The error message is as follows:

Solving problem using ga.
Error using optim.problemdef.OptimizationProblem/solve
Index in position 2 exceeds array bounds. Index must not exceed 3.

This issue seems to arise from the size of the assignmentMatrix not being appropriate within my function. Here's the relevant portion of my modified code for your reference:

function maxOffloadingTime = calculateMaxOffloadingTime(assignmentMatrix)
 
    Offloading_time_subtask = calculateOffloadingTime(x_UAV, y_UAV, z_UAV,x_positions,y_positions,x_haps,y_haps,z_haps,num_vehicles,numUAVs, Task_assignment, assignmentMatrix, all_subtasks,reordered_tasks,initial_data_sizes,dependency_matrix,transmission_time,P_tx,P_Haps,f_c, c, eta_LoS_Ls,numRBs,B_RB_aerial,Noise_aerial,B_RB_dl,Noise_dl,G_u_linear,G_h_linear,h_LoS,kB,Ts,min_value,max_value,Fmax,coverageRadius,a,b,eta_NLoS_Ls);
    maxOffloadingTime = max(Offloading_time_subtask(:)); 
end
maxOffloadingTimeExpr = fcn2optimexpr(@calculateMaxOffloadingTime, assignmentMatrix, 'OutputSize', [1, 1]);
prob.Objective = maxOffloadingTimeExpr;

It seems to be related to how the assignmentMatrix is used within the optimization problem, but I'm not certain how to resolve it.

Maria 2023-12-9

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@Matt J @Torsten Thank you for your guidance. I understand the need for a complete code to fully grasp the issue, but unfortunately, it's complex with multiple interconnected functions. However, I can provide a simplified example to illustrate the core problem.

I'm working with an assignment matrix, which is a binary matrix indicating the assignment of tasks to nodes after an original assignment already exist.Here's an example of an original assignment matrix for four tasks:

originalAssignmentMatrix = [
 1   0   0;
 1   0   0;
 1   0   0;
 1   0   0 ];

Each row represents a task, and each column represents a node. A '1' indicates that the task is assigned to that node. The constraint is that each task must be assigned to exactly one node, meaning the sum across each row should be 1.

The issue arises with the assignment matrix, which is derived from an optimization variable. The assignment matrix sometimes violates this constraint, assigning a task to multiple nodes or no nodes at all. For example, I get an error for a task assigned to multiple nodes:

original_node: 2, assignment_node: 1 2 3 4

But the function expecting this matrix requires exactly one node per task for its calculations.

I've tried implementing constraints to ensure that each task is assigned to only one node, but I'm still encountering issues with the dimension size and receiving errors related to this.

Could you please provide guidance on how to enforce this constraint properly within the optimization problem so that the updated assignment matrix always adheres to this one-node-per-task rule?

Maria 2023-12-10

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@Matt J @Torsten I've encountered difficulties while trying to solve my optimization problem initially with problem-based optimization techniques. After restructuring all my functions to accommodate problem-based optimization without success, I decided to transition to a solver-based approach using the Genetic Algorithm (GA).

I managed to solve the problem for a single user with four tasks. However, when I increased the number of users, I couldn't find any feasible solution using GA. Below is a brief outline of the code that works for one user and my attempt to scale it up for multiple users.

When I expanded the code to handle multiple users, I ensured that my fitness function and constraints were modified accordingly. Despite these changes, the GA doesn't seem to find a solution.

For a single user, the GA finds a solution quickly.
For multiple users, GA runs without finding a feasible solution.

numSubtasks = 4;
numNodes = 4; 
numGenes = numSubtasks * numNodes * num_users; 
% Lower and upper bounds for the representation
lb = zeros(1, numGenes);
ub = ones(1, numGenes);
function fitness = myFitnessFunction(chromosome)
    % Reshape chromosome into a matrix to represent task assignments
     assignmentMatrix = reshape(chromosome, [numSubtasks, numNodes, num_users]);
    
    % Calculate offloading time and satisfaction
    Offloading_time_subtask = calculateOffloadingTime(x_UAV, y_UAV, z_UAV,x_positions,y_positions,x_haps,y_haps,z_haps,num_vehicles,numUAVs, Task_assignment, assignmentMatrix, all_subtasks,reordered_tasks,initial_data_sizes,dependency_matrix,transmission_time,P_tx,P_Haps,f_c, c, eta_LoS_Ls,numRBs,B_RB_aerial,Noise_aerial,B_RB_dl,Noise_dl,G_u_linear,G_h_linear,h_LoS,kB,Ts,min_value,max_value,Fmax,coverageRadius,a,b,eta_NLoS_Ls); % Add the rest of your parameters
    Satisfaction_variable = computeSR(num_vehicles, numUAVs, Offloading_time_subtask, QoS_values);
    [E_totale] = Calculate_Total_Energy_Consumption(x_UAV, y_UAV, z_UAV,x_positions,y_positions,x_haps,y_haps,z_haps,num_vehicles,numUAVs, Task_assignment, assignmentMatrix, all_subtasks,reordered_tasks,initial_data_sizes,dependency_matrix,transmission_time,P_tx,P_Haps,f_c, c, eta_LoS_Ls,numRBs,B_RB_aerial,Noise_aerial,B_RB_dl,Noise_dl,G_u_linear,G_h_linear,h_LoS,kB,Ts,min_value,max_value,Fmax,coverageRadius,a,b,eta_NLoS_Ls,total_time);
    % Calculate objectives
    objective1 = MySatisfactionRate(Satisfaction_variable, reordered_tasks);
    objective2 = Compute_Remaining_Energy(E_max, E_HAPS, E_totale);
    
    % Calculate the fitness
    fitness = w1 * objective1 + w2 * objective2;
end
    function [cn, ceq] = nonlcon(chromosome)
    % Reshape chromosome into a matrix to represent task assignments
      assignmentMatrix = reshape(chromosome, [numSubtasks, numNodes, num_users]);
    
    % Calculate the maximum offloading time
    Offloading_time_subtask = calculateOffloadingTime(x_UAV, y_UAV, z_UAV,x_positions,y_positions,x_haps,y_haps,z_haps,num_vehicles,numUAVs, Task_assignment, assignmentMatrix, all_subtasks,reordered_tasks,initial_data_sizes,dependency_matrix,transmission_time,P_tx,P_Haps,f_c, c, eta_LoS_Ls,numRBs,B_RB_aerial,Noise_aerial,B_RB_dl,Noise_dl,G_u_linear,G_h_linear,h_LoS,kB,Ts,min_value,max_value,Fmax,coverageRadius,a,b,eta_NLoS_Ls); % Add the rest of your parameters
    maxOffloadingTime = max(Offloading_time_subtask(:));
    [E_totale] = Calculate_Total_Energy_Consumption(x_UAV, y_UAV, z_UAV,x_positions,y_positions,x_haps,y_haps,z_haps,num_vehicles,numUAVs, Task_assignment, assignmentMatrix, all_subtasks,reordered_tasks,initial_data_sizes,dependency_matrix,transmission_time,P_tx,P_Haps,f_c, c, eta_LoS_Ls,numRBs,B_RB_aerial,Noise_aerial,B_RB_dl,Noise_dl,G_u_linear,G_h_linear,h_LoS,kB,Ts,min_value,max_value,Fmax,coverageRadius,a,b,eta_NLoS_Ls,total_time);
    % Nonlinear inequality constraints (c <= 0)
    c1 = maxOffloadingTime - QoS_values; % Assuming QoS_values is a scalar
    c2 =  E_totale - E_max_totale; 
    c1 = c1(:);
    c2 = c2(:);
    % Combine all inequality constraints into one vector
    cn = [c1; c2];
    % Nonlinear equality constraints (ceq == 0)
    ceq = sum(assignmentMatrix, 2) - 1;
    cn = real(cn);
    ceq = real(ceq);
end
% Create an initial population that adheres to the constraint that each subtask is assigned to one node
initialPopulation = zeros(100, numGenes);
for i = 1:100
    chromosome = zeros(1, numGenes);
    for v = 1:num_vehicles
        for j = 1:numSubtasks
            node = randi(numNodes);
            chromosome((v-1)*numSubtasks*numNodes + (j-1)*numNodes + node) = 1;
        end
    end
    initialPopulation(i, :) = chromosome;
end
% GA options
options = optimoptions('ga', ...
    'PopulationType', 'doubleVector', ...
    'PopulationSize', 100, ...
    'InitialPopulationMatrix', initialPopulation, ...
    'MaxGenerations', 100, ...
    'CrossoverFraction', 0.7, ...
    'EliteCount', 5, ...
    'FunctionTolerance', 1e-8, ...
    'MutationFcn', {@mutationuniform, 0.05}, ...
    'CrossoverFcn', @crossoverscattered, ...
    'NonlinearConstraintAlgorithm', 'penalty', ...
    'Display', 'iter');
[bestChromosome, bestFitness, exitflag, output] = ga(@myFitnessFunction, numGenes, [], [], [], [], lb, ub, @nonlcon, options);
% Check the results
if exitflag > 0
    bestAssignmentMatrix = reshape(bestChromosome, [numSubtasks, numNodes]);
    disp('Best Assignment Matrix:');
    disp(bestAssignmentMatrix);
    disp(['Best Fitness Value: ', num2str(bestFitness)]);
else
    disp('No feasible solution found.');
end
end

I am looking for recommendations on faster solver alternatives that can handle the increased complexity efficiently. Would you suggest any specific solver or MATLAB function that is known for faster performance on similar optimization problems?

Maria 2023-12-14

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i want to inform you that my problem was solved by GA.However, the solutions I'm getting are not optimal, and I suspect the issue may lie in the way I have defined my fitness function.

The goal of my fitness function is to maximize the 'satisfaction variable' while ensuring that the 'offloading time' for tasks does not exceed a certain QoS threshold. However, the current implementation seems to be producing suboptimal solutions.

Here's a simplified version of my fitness function:

function fitness = myFitnessFunction(x)
     %reshape
    assignmentMatrix = reshape(x, [numSubtasks, numNodes, num_vehicles]);
    assignmentMatrix = permute(assignmentMatrix, [2, 1, 3]);
     % Initialize satisfaction sum
      Satisfaction_variable = zeros(num_vehicles, 1);
    % Loop through each vehicle
      [Offloading_time_subtask,E_totale] = calculateOffloadingTime(...); 
      maxOffloadingTimes = zeros(1, num_vehicles); 
% Loop through each vehicle to find the maximum offloading time
for v = 1:num_vehicles
    % Extract the matrix for the current vehicle
    vehicleMatrix = Offloading_time_subtask(:, :, v);
    % Find the maximum offloading time for this vehicle
    maxOffloadingTimes(v) = max(vehicleMatrix(:)); 
    if maxOffloadingTimes(v) <= QoS_values(v)
        Satisfaction_variable(v) = 1;
    else
        Satisfaction_variable(v) = 0;
    end
       totalSatisfaction = sum (Satisfaction_variable,"all") /sum(Tasks,"all");    
end
     fitness = totalSatisfaction;
 end

I would greatly appreciate any suggestions on how to improve my fitness function to get more optimal results.

Maria 2023-12-20

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@Matt J @Torsten Hello!

after extensive testing and parameter tuning with GA, the results were consistently not good. In search of better solutions, I shifted to problem-based optimization. I used ILP approach, i decided to start with an initial assignment that had previously shown promising results. However, I've been surprised to find that the solutions from ILP are inferior to this initial assignment, raising concerns about the efficacy of both GA and ILP for my problem.

numSubtasks = 4;
numNodes = 4; 
% Binary association matrix A where ak,n = 1 means subtask k is offloaded to node n
A = optimvar('A', numSubtasks, numNodes,num_vehicles, 'Type', 'integer', 'LowerBound', 0, 'UpperBound', 1);
% Satisfaction variable (binary)
satisfaction = optimvar('satisfaction', 1,num_vehicles, 'Type', 'integer', 'LowerBound', 0, 'UpperBound', 1);
% Constraint: Each subtask is offloaded to exactly one node
% Use indexed variables for constraints
initialAssignment = My_initial_assignment;
% Loop variables
maxIterations = 100; % Maximum number of iterations
tolerance = 1e-03 ; % Tolerance for the stopping criterion
for iter = 1:maxIterations
[Offloading_time_subtask,Total_energy_consumption,E_ex] = calculateOffloadingTime(N,..initialAssignment,...)
  % Define a new optimization problem
    prob = optimproblem('ObjectiveSense', 'maximize');
    prob.Objective = sum(satisfaction);
% Constraint: Each subtask is offloaded to exactly one node
for v = 1:num_vehicles
    for k = 1:numSubtasks
        % sum over the third dimension (nodes) for a specific vehicle v and subtask k
         prob.Constraints.(['OneNodeForSubtask' num2str(k) 'Vehicle' num2str(v)]) = sum(A(k, :, v), 'all') == 1;
    end
end
for v = 1:num_vehicles
    vehicleMatrix = Offloading_time_subtask(:, :, v);
maxOffloadingTime = max(vehicleMatrix(:)); 
prob.Constraints.(['SatisfactionVehicle' num2str(v)]) = satisfaction(v) == (maxOffloadingTime <= QoS_values(v));
end
 % Solve the optimization problem
 show(prob);
    [sol, fval, exitflag, output] = solve(prob);
    newAssignment = reshape([sol.A], size(initialAssignment));
 % Check for convergence
    if norm(newAssignment - initialAssignment, 'fro') < tolerance
        break;
    end
    
    % Update the assignment for the next iteration
    initialAssignment = newAssignment;
end
end

Maria 2023-12-20

I'm talking about the result just for the satisfaction rate it didn't improve compared with other solutions, I thought that with optimization I will get more satisfied tasks but I get less.

Matt J 2023-12-20

Two remarks,

(1) You are not using my alternative objective function. I recommended that function because it is continuous and might be easier to optimize.

(2) Your call to solve() does not specify an initialAssignment as an initial point. Therefore, the optimization does not know what it is supposed to try to improve upon.

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