# Reliability Optimization Design of Diesel Engine System Based on the GO Method
## 3 Problem Description and Model Building and Solution
### Algorithm Design  
The diesel engine optimization design model constructed in this paper is a three-objective optimization model. Concerning the solution of such a model, the weighted sum method is generally applied to convert the multi-objective optimization into single-objective optimization. This method is simple to realize. Nevertheless, it is required to determine the weight subjectively, and only one feasible solution can be given for each run. The NSGA-II algorithm, which is a multi-objective optimization algorithm, is proposed on the basis of a genetic algorithm, adding a fast non-dominated sorting strategy and crowding comparison operator [22] in the selection operation. A Pareto solution set can be obtained for each run, and users can choose different design schemes following actual demands. The particle swarm optimization algorithm has acquired increasing attention owing to its advantages in global search ability, convergence speed, and accuracy, and it is an intelligent algorithm with great application potential [23]. Particle swarm optimization algorithm can be adopted to accurately calculate the global optimal value of the reliability function and cost function on \(D(R_{low},R_{up})\). With the purpose of solving the three-objective reliability optimization design model, the PSO algorithm is embedded into the NSGA-II algorithm, and a hybrid NSGA-II-PSO algorithm based on the GO method in this paper is proposed. The specific steps are described as follows.  
Step 1:Initialize and generate initial population \(P0\). Initialize the variables and parameters of the algorithm. Determine the population size \(N\) and the maximum iterations \(G\)max. Generate \(P0\) by the PSO algorithm with the reliability of the diesel engine system and function as constraints.  
Step 1.1:Generate hyper-rectangle individuals. Within the range of \(m\) unit reliability, randomly generate \(m\) intervals to form an \(m\)-dimensional hyper-rectangle \(D\).  
Step 1.2: Initialize variables and parameters of the PSO algorithm, determine the population size \(M\), and set the maximum iterations \(K\)max.  
Step 1.3:Run the PSO algorithm to output the optimal reliability value of the diesel engine system and function.  
Step 1.4:Determine whether all constraints are satisfied. If not, generate new individuals again until the generated \(N\) individuals satisfy the conditions and use as initial population \(P0\).  
Step 2:Select, cross, and mutate individuals in population \(P0\) to obtain a new population \(Q0\) with a population size of \(N\).  
Step 3: Combine population \(P0\) and \(Q0\) to form a new population \(R0\) with a population size of \(2N\). Calculate the value of objective functions. In each hyper-rectangle satisfying the constraint conditions, solve the minimum reliability and maximum cost of the diesel engine system using the PSO optimization algorithm, and calculate the volume of the hyper-rectangle.  
Step 4: Perform fast non-dominated sorting on \(R0\) and calculate its crowding distance in accordance with the maximum system reliability, minimum cost, and maximum hyper-rectangle volume.  
Step 5: After sorting population \(R0\) according to Pareto rank and crowding distance, select \(N\) individuals as the next generation population \(P1\) by elitism strategy and competition strategy.  
Step 6: Determine whether \(G\) is equal to the maximum evolution generation. If not, return to Step 2.  
Step 7:Output Pareto optimal solution set, save the individual data of the optimal solution set, and finish the algorithm operation.  
The algorithm flow is presented in Figure 5.