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This article summary:SCI illustrations + multi-objective optimization! Transformer-GRU + NSGA-II process parameter optimization, engineering design optimization!
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1
Basic Introduction
1.Transformer-GRU + NSGA-II multi-objective optimization algorithm, process parameter optimization, engineering design optimization! (Complete Matlab source code and data)
Architecture of the Transformer-GRU model: Input layer: multiple variables as input, forming a multi-dimensional input tensor. Transformer Encoder: This encoder consists of multiple Transformer encoder layers, each containing a multi-head attention mechanism and a feedforward network. The encoder layers are used to learn the relationships between variables. GRU layer: After the Transformer encoder, the output sequence is input into the GRU layer. The GRU layer is used to process sequences, remember previous states, and generate hidden state sequences. Output layer: The hidden state sequence from the GRU layer is input into the output layer, which makes final predictions through a fully connected layer. The number of neurons in the output layer usually matches the dimensions of the prediction targets. During training, known input sequences and target sequences can be used to calculate prediction errors and update the model parameters using backpropagation algorithms. Common gradient descent methods, such as Adam, can be used as optimizers.
Multi-objective optimization refers to the optimization process that considers multiple objectives simultaneously in optimization problems. In multi-objective optimization, there are often multiple conflicting objectives, meaning that improving one objective may lead to the deterioration of another. Therefore, the goal of multi-objective optimization is to find a set of solutions that are optimal under multiple objectives, rather than just optimizing a single objective.
2. First, encapsulate the dependent variables (y1, y2, y3) and independent variables (x1, x2, x3, x4, x5) proxy model through Transformer-GRU, and then use NSGA-II to find the extreme values of y (max y1; min y2, y3) and provide the corresponding x1, x2, x3, x4, x5 Pareto solution set.
3. data is the dataset, with 5 input features and 3 output variables, NSGA-II algorithm seeks extreme values, obtaining the independent variables x1, x2, x3, x4, x5 when (max y1; min y2; min y3).
4. main1.m is the Transformer-GRU main program file, and main2.m is the NSGA-II multi-objective optimization algorithm main program file, which can be run sequentially; the rest are function files and do not need to be run.
5. The command window outputs evaluation indicators such as R2, MAE, MBE, MAPE, RMSE, outputs prediction comparison charts, error analysis charts, and Pareto solution set graphs for multi-objective optimization algorithms, which can be obtained in the download area.
6. Suitable for process parameter optimization, engineering design optimization, and other optimal feature combination fields.
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Basic ideas and technical routes of the NSGA-II algorithm
1) Randomly generate an initial population Pt of size N, undergo non-dominated sorting, selection, crossover, and mutation to produce a child population Qt, and combine the two populations to form a population Rt of size 2N;
2) Perform fast non-dominated sorting, and simultaneously calculate the crowding degree for individuals in each non-dominated layer, selecting suitable individuals based on non-dominance relationships and individual crowding degrees to form a new parent population Pt+1;
3) Generate a new child population Qt+1 through basic operations of genetic algorithms, merge Pt+1 and Qt+1 to form a new population Rt, and repeat the above operations until the program’s end conditions are met.
2
Dataset
Partial Code
%% Simulation test t_sim1 = sim(net, p_train); t_sim2 = sim(net, p_test ); %% Data reverse normalization T_sim1 = mapminmax('reverse', t_sim1, ps_output); T_sim2 = mapminmax('reverse', t_sim2, ps_output); %% Define result storage template empty.position = []; % Input variable storage empty.cost = []; % Objective function storage empty.rank = []; % Non-dominated sorting rank empty.domination = []; % Dominated individual collection empty.dominated = 0; % Number of dominated individuals empty.crowdingdistance = []; % Individual crowding distance pop = repmat(empty, npop, 1); %% 1. Initialize population for i = 1 : npop pop(i).position = create_x(var); % Generate input variables (individuals) pop(i).cost = costfunction(pop(i).position); % Calculate objective function end %% 2. Construct non-dominated set [pop,F] = nondominatedsort(pop); %% Calculate crowding distance pop = calcrowdingdistance(pop,F); %% Main program (selection, crossover, mutation)
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3
Effect Analysis
4
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