A diesel engine multi-objective combustion control parameter optimization method based on divide-and-conquer-tree non-dominated sorting
By using the improved NSGA-II algorithm with divide-and-conquer and tree-based non-dominated sorting, the problem of balancing NOx and CO2 in diesel engines is solved, achieving efficient and coordinated optimization of diesel engine combustion control parameters, and improving computational efficiency and emission reduction effect.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUILIN UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2026-01-27
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies cannot efficiently resolve the trade-off between NOx and CO2 in diesel engines. Traditional single-objective optimization algorithms have high computational overhead, which limits the emission reduction potential of diesel engines.
An improved NSGA-II algorithm based on divide-and-conquer and tree-based non-dominated sorting is adopted. By combining the hierarchical method with segment trees, the dominance comparison efficiency is optimized, and the Pareto optimal solution set is quickly screened to achieve the collaborative optimization of diesel engine combustion control parameters.
It significantly improves the calculation efficiency of diesel engine combustion control parameters, achieves synergistic emission reduction of NOx and CO2, and is suitable for large-scale population processing.
Smart Images
Figure CN122151497A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of diesel engine combustion performance optimization technology, and in particular to a method for optimizing multi-objective combustion control parameters of diesel engines based on divide-and-conquer tree-structured non-dominated sorting. Background Technology
[0002] Despite the rapid pace of electrification, diesel engines remain irreplaceable in key sectors such as heavy-duty commercial vehicles, ocean-going vessels, large construction machinery, and agricultural equipment, thanks to their high thermal efficiency, superior reliability, and powerful torque output. Their energy efficiency is crucial for ensuring national energy security and the stable operation of the economy. However, while contributing significant power, diesel engines are also major sources of nitrogen oxides (NOx) and carbon dioxide (CO2), key greenhouse gases. Since NOx is primarily generated under high-temperature, oxygen-rich combustion conditions, methods to reduce its emissions typically include delaying fuel injection and increasing exhaust gas recirculation rates, but these measures reduce combustion efficiency. CO2, an inevitable byproduct of carbon-based fuel combustion, is directly related to fuel consumption. Reducing CO2 necessitates higher combustion efficiency, which usually requires optimizing the combustion process, such as increasing combustion temperature, but this leads to a surge in NOx emissions. This trade-off makes it impossible for traditional single-objective optimization algorithms to systematically reveal the global optimal solution, thus significantly limiting the further exploration of diesel engine emission reduction potential. Therefore, diesel engine combustion system optimization faces an inherent, trade-off-based multi-objective trade-off problem. To address this multi-objective optimization challenge, multi-objective optimization algorithms have been introduced into the field, providing a series of Pareto optimal solutions to intuitively demonstrate the trade-off between NOx and CO2. However, when dealing with such problems, classic algorithms (such as NSGA-II) suffer from a significant increase in computational cost in their core non-dominated sorting step as the population size grows, becoming a bottleneck restricting optimization efficiency. Summary of the Invention
[0003] The purpose of this invention is to provide a multi-objective combustion control parameter optimization method for diesel engines based on divide-and-conquer-tree non-dominated sorting, solving the technical problem that existing methods cannot resolve the trade-off between NOx and CO2 in diesel engines. It aims to improve computational efficiency and achieve collaborative optimization of key combustion control parameters, thereby providing an efficient and practical technical path to overcome the dilemma of NOx and CO2 trade-offs.
[0004] This method uses a hierarchical tree-like sorting mechanism to quickly complete the screening of non-dominated solutions, thereby efficiently achieving global optimization of diesel engine combustion control parameters and ultimately improving the synergistic emission reduction effect of NOx and CO2.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0006] A method for optimizing multi-objective combustion control parameters of a diesel engine based on divide-and-conquer tree-structured non-dominated sorting includes the following steps:
[0007] Step S1: Set up a diesel engine test bench and determine the list of diesel engine operating conditions;
[0008] Step S2: According to the list of operating conditions, conduct experiments on the diesel engine test bench, accurately collect and record engine operating status data and controller parameters under each operating condition;
[0009] Step S3: Process and analyze the experimental data to determine the optimization objective function of the multi-objective algorithm, the decision variables of the optimization process, and the constraints that must be followed.
[0010] Step S4: Construct an improved multi-objective combustion control parameter optimization model for the NSGA-II diesel engine based on divide-and-conquer and tree-structured non-dominated sorting. Use the algorithm to perform iterative calculations, search for and obtain the Pareto optimal solution set that reflects the trade-offs between the objectives.
[0011] Step S5: Verify the Pareto optimal solution set obtained from the optimization calculation, evaluate its effectiveness and accuracy, and finally output and determine the final optimization scheme and results.
[0012] Furthermore, the objective function of the multi-objective optimization algorithm, the decision variables of the optimization process, and the constraints that must be followed in step S3 specifically include:
[0013]
[0014]
[0015]
[0016] In the formula, To optimize the objective function, , Diesel engines Emissions and diesel engines There is usually a trade-off between reducing NOx emissions and reducing CO2 emissions. NOx is mainly generated under high temperature and oxygen-rich combustion conditions. Methods to reduce its emissions usually include delaying fuel injection and increasing exhaust gas recirculation rate, but these measures will reduce combustion efficiency. CO2 is an inevitable product of the complete combustion of carbon-based fuels. The higher the combustion efficiency, the less fuel is consumed and the less CO2 is produced. The decision variables consist of exhaust temperature, exhaust back pressure, intercooler-fed intake pressure, and intercooler-fed intake flow rate; the constraints are divided into inequality constraints. Sum of equality constraints .
[0017] Furthermore, in step S4, the steps for constructing the improved NSGA-II algorithm based on divide-and-conquer-tree non-dominated sorting are as follows:
[0018] First, initialize the first-generation parent population, generating an initial population of N individuals and calculating the objective function value for each individual. Sort the individuals in ascending order based on their objective function values to generate the parent population. Then, repeatedly perform selection, crossover, and mutation operations to generate a child population of size N. The selection operation uses a tournament-style random selection of two groups of individuals, choosing those with higher non-dominant levels as candidates. The crossover operation uses probability... Simulated binary crossover (SBX) is performed on the parent individual to generate two offspring individuals, and the mutation operation is performed probabilistically. Perform polynomial mutation on the offspring individuals; then merge the parent and offspring populations into a single population of size [missing information]. Merged population It performs fast non-dominated sorting, but traditional fast non-dominated sorting methods suffer from problems such as repeated comparisons due to the large number of pairwise comparisons between individuals, resulting in a high time complexity. Where M is the target number and N is the number of comparisons. Therefore, to improve efficiency, this invention proposes an optimization strategy based on a combination of hierarchical sorting and tree sorting. When the number of targets is small (e.g., 2-3), the time complexity of the fast dominance sorting step can be improved to [value missing]. Finally, individuals are added to the new population in order of increasing non-dominated level. If the number of individuals in a certain non-dominated level exceeds the remaining capacity, they are selected in order of decreasing crowding distance, eventually forming a new generation of parent population of size N. When the evolution reaches the maximum number of iterations, the algorithm outputs the set of individuals belonging to the first non-dominated level in the last generation population, which is the Pareto optimal solution set.
[0019] The efficient non-dominated sorting strategy based on hierarchical methods and tree-based sorting is implemented with the core engineering principle of optimizing the efficiency of dominance comparison through divide-and-conquer and segment trees. The specific implementation process is as follows: First, the algorithm sorts the entire merged population Rt in ascending order according to the first objective function value and recursively divides it into two subpopulations. Then, it performs independent non-dominated sorting on these two subpopulations in parallel or recursively. During the merge sorting process, for each non-dominated layer generated in the right half, the algorithm dynamically constructs a segment tree data structure for its corresponding left half non-dominated layer. This segment tree is used to efficiently maintain the minimum or maximum values of individuals in the left half across multiple objective function dimensions, thus transforming dominance comparison into efficient interval queries. By querying this segment tree, it is possible to quickly determine whether an individual in the right half is dominated by any individual in that layer of the left half. This process only filters and retains undominated individuals in the right half, forming the effective residual non-dominated set for that layer. Finally, the non-dominated layers of the left half are merged with the filtered right half residuals to form the global non-dominated layer. This divide-and-conquer, tree-building, query filtering, and merging process is executed recursively until all individuals are successfully assigned to their respective non-dominated layers. This design reduces the complexity of dominance comparisons from O(MN) using a tree structure. 2 It significantly reduces [the risk of infection], making it particularly suitable for handling large populations.
[0020] The present invention, by adopting the above-described technical solution, has the following beneficial effects:
[0021] This invention constructs a multi-objective optimization problem for diesel engine operation, clearly defining the design variables, objective function, and constraints. It employs an improved NSGA-II algorithm based on divide-and-conquer and tree-structured non-dominated sorting for multi-objective optimization calculations, obtaining the Pareto optimal solution set, verifying the accuracy of the solution set, and outputting the final optimization results. This improves computational efficiency and achieves coordinated optimization of key combustion control parameters, thus providing an efficient and practical technical path to overcome the trade-off between NOx and CO2. The tree structure reduces the complexity of the dominance comparison from O(MN) to O(MN). 2 It significantly reduces [the risk of infection], making it particularly suitable for handling large populations. Attached Figure Description
[0022] Figure 1 This is a flowchart of the diesel engine multi-objective combustion control parameter optimization method of the present invention;
[0023] Figure 2 This is a flowchart of the NSGA-II algorithm based on divide-and-conquer tree-structured non-dominated sorting, which is the subject of this invention. Detailed Implementation
[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. However, it should be noted that many details listed in the specification are merely to provide the reader with a thorough understanding of one or more aspects of the present invention, and these aspects of the invention can be implemented even without these specific details.
[0025] like Figure 1 As shown, a method for optimizing multi-objective combustion control parameters of a diesel engine based on divide-and-conquer tree-structured non-dominated sorting is presented. The method includes the following steps:
[0026] Step S1: Set up a diesel engine test bench and determine the list of diesel engine operating conditions;
[0027] Step S2: According to the list of operating conditions, conduct experiments on the diesel engine test bench, accurately collect and record engine operating status data and controller parameters under each operating condition;
[0028] Step S3: Process and analyze the experimental data to determine the optimization objective function of the multi-objective algorithm, the decision variables of the optimization process, and the constraints that must be followed.
[0029] The objective function, decision variables, and constraints that must be followed in a multi-objective optimization algorithm specifically include:
[0030]
[0031]
[0032]
[0033] In the formula, To optimize the objective function, , Diesel engines Emissions and diesel engines There is usually a trade-off between reducing NOx emissions and reducing CO2 emissions. NOx is mainly generated under high temperature and oxygen-rich combustion conditions. Methods to reduce its emissions usually include delaying fuel injection and increasing exhaust gas recirculation rate, but these measures will reduce combustion efficiency. CO2 is an inevitable product of the complete combustion of carbon-based fuels. The higher the combustion efficiency, the less fuel is consumed and the less CO2 is produced. The decision variables consist of exhaust temperature, exhaust back pressure, intercooler-fed intake pressure, and intercooler-fed intake flow rate; the constraints are divided into inequality constraints. Sum of equality constraints .
[0034] Step S4: Construct an improved multi-objective combustion control parameter optimization model for the NSGA-II diesel engine based on divide-and-conquer and tree-structured non-dominated sorting. Use the algorithm to perform iterative calculations, search for and obtain the Pareto optimal solution set that reflects the trade-offs between the objectives.
[0035] Step S5: Verify the Pareto optimal solution set obtained from the optimization calculation, evaluate its effectiveness and accuracy, and finally output and determine the final optimization scheme and results.
[0036] Reference Figure 2 This paper demonstrates the improved NSGA-II algorithm based on divide-and-conquer tree-based non-dominated sorting, specifically the following steps:
[0037] First, initialize the first-generation parent population, generating an initial population of N individuals and calculating the objective function value for each individual. Sort the individuals in ascending order based on their objective function values to generate the parent population. Then, repeatedly perform selection, crossover, and mutation operations to generate a child population of size N. The selection operation uses a tournament-style random selection of two groups of individuals, choosing those with higher non-dominant levels as candidates. The crossover operation uses probability... Simulated binary crossover (SBX) is performed on the parent individual to generate two offspring individuals, and the mutation operation is performed probabilistically. Perform polynomial mutation on the offspring individuals; then merge the parent and offspring populations into a single population of size [missing information]. Merged population It performs fast non-dominated sorting, but traditional fast non-dominated sorting methods suffer from problems such as repeated comparisons due to the large number of pairwise comparisons between individuals, resulting in a high time complexity. Where M is the target number and N is the number of comparisons. Therefore, to improve efficiency, this invention proposes an optimization strategy based on a combination of hierarchical sorting and tree sorting. When the number of targets is small (e.g., 2-3), the time complexity of the fast dominance sorting step can be improved to [value missing]. Finally, individuals are added to the new population in order of increasing non-dominated level. If the number of individuals in a certain non-dominated level exceeds the remaining capacity, they are selected in order of decreasing crowding distance, eventually forming a new generation of parent population of size N. When the evolution reaches the maximum number of iterations, the algorithm outputs the set of individuals belonging to the first non-dominated level in the last generation population, which is the Pareto optimal solution set.
[0038] The efficient non-dominated sorting strategy based on hierarchical methods and tree-based sorting is implemented with the core engineering principle of optimizing the efficiency of dominance comparison through divide-and-conquer and segment trees. The specific implementation process is as follows: First, the algorithm sorts the entire merged population Rt in ascending order according to the first objective function value and recursively divides it into two subpopulations. Then, it performs independent non-dominated sorting on these two subpopulations in parallel or recursively. During the merge sorting process, for each non-dominated layer generated in the right half, the algorithm dynamically constructs a segment tree data structure for its corresponding non-dominated layer in the left half. This segment tree is used to efficiently maintain the minimum (or maximum) values of individuals in the left half across multiple objective function dimensions, thus transforming dominance comparison into efficient interval queries. By querying this segment tree, it is possible to quickly determine whether an individual in the right half is dominated by any individual in that layer of the left half. This process only filters and retains the undominated individuals in the right half, forming the effective residual non-dominated set for that layer. Finally, the non-dominated layers of the left half are merged with the filtered residuals of the right half to form the global non-dominated layer. This divide-and-conquer, tree-building, query filtering, and merging process is executed recursively until all individuals are successfully assigned to their respective non-dominated layers. This design reduces the complexity of dominance comparisons from O(MN) using a tree structure. 2 It significantly reduces [the risk of infection], making it particularly suitable for handling large populations.
[0039] Matters not covered in this invention are common knowledge.
[0040] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for optimizing multi-objective combustion control parameters of a diesel engine based on divide-and-conquer tree-structured non-dominated sorting, characterized in that, The method includes the following steps: Step S1: Set up a diesel engine test bench and determine the list of diesel engine operating conditions; Step S2: According to the list of operating conditions, conduct experiments on the diesel engine test bench, collect and record engine operating status data and controller parameters under each operating condition; Step S3: Process and analyze the experimental data to determine the optimization objective function, decision variables of the optimization process, and constraints that must be followed for several target algorithms; Step S4: Construct an optimization process for several target combustion control parameters of a diesel engine based on the improved NSGA-II algorithm of divide-and-conquer-tree non-dominated sorting. Use the algorithm to perform iterative calculations, search for and obtain the Pareto optimal solution set that reflects the trade-off relationship between the targets. Step S5: Verify the Pareto optimal solution set obtained from the optimization calculation, evaluate its effectiveness and accuracy, and finally output and determine the final optimization scheme and result.
2. The method for optimizing multi-objective combustion control parameters of a diesel engine based on divide-and-conquer tree-structured non-dominated sorting as described in claim 1, characterized in that, In step 3, the objective function for optimizing several target algorithms is determined as follows: in, To optimize the objective function, , Diesel engines Emissions and diesel engines There is a trade-off between reducing NOx emissions and reducing CO2 emissions. It is generated under combustion conditions where the temperature and oxygen content are both above a fixed value, thus reducing... Emission control measures include delaying fuel injection and increasing exhaust gas recirculation, but these reduce combustion efficiency. CO2 is an inevitable byproduct of the complete combustion of carbon-based fuels. The higher the combustion efficiency, the less fuel is consumed and the less CO2 is produced.
3. The method for optimizing multi-objective combustion control parameters of a diesel engine based on divide-and-conquer tree-structured non-dominated sorting as described in claim 1, characterized in that: In step 3, the decision variables for the optimization process are: , The constraints are: As decision variables, These represent exhaust temperature, exhaust back pressure, intercooler-fed intake pressure, and intercooler-fed intake flow rate, respectively. The constraints are divided into inequality constraints. Sum of equality constraints .
4. The method for optimizing multi-objective combustion control parameters of a diesel engine based on divide-and-conquer tree-structured non-dominated sorting as described in claim 1, characterized in that: In step 4, the specific process of constructing the improved NSGA-II algorithm based on divide-and-conquer-tree-structured non-dominated sorting is as follows: First, initialize the first-generation parent population, generate an initial population containing N individuals, and calculate the objective function value for each individual. Sort the individuals in ascending order according to the first objective function value to generate the parent population. Repeatedly execute selection, crossover, and mutation operations to generate a child population of size N. The selection operation uses a tournament-style approach to randomly select two groups of individuals and chooses individuals with higher non-dominated levels as candidates. The crossover operation uses probability... Simulated binary crossover is performed on the parent individual to generate two offspring individuals, and mutation operations are performed probabilistically. Perform several polynomial mutations on the offspring individuals, and then merge the parent and offspring populations into a population of size [missing information]. Merged population And perform a fast non-dominated sort.
5. The method for optimizing multi-objective combustion control parameters of a diesel engine based on divide-and-conquer tree-structured non-dominated sorting as described in claim 1, characterized in that: The optimization strategy for improving the NSGA-II algorithm in step 4 is to increase the time complexity of the dominant sorting step to a value that is set when the number of targets is small. Individuals are added to the new population in order of non-dominance level from low to high. If the number of individuals in a certain non-dominance level exceeds the remaining capacity, they are selected in order of crowding distance from large to small, and finally a new generation of parent population of size N is formed. When the evolution reaches the maximum number of iterations, the set of individuals belonging to the first non-dominance level in the last generation is output, which is the Pareto optimal solution set.
6. The method for optimizing multi-objective combustion control parameters of a diesel engine based on divide-and-conquer tree-structured non-dominated sorting as described in claim 5, characterized in that: In the optimization strategy, the efficiency of dominance comparison is optimized through divide-and-conquer and segment trees. Specifically, the entire merged population Rt is sorted in ascending order according to the first objective function value, and recursively divided into two subpopulations. Then, the two subpopulations are sorted independently in parallel or recursively. When merging the sorting results, for each non-dominated layer generated in the right half, a segment tree data structure is dynamically constructed for the corresponding non-dominated layer in the left half. The segment tree is used to maintain the minimum or maximum value of individuals in the left half in several objective function dimensions, thereby transforming the dominance comparison into an interval query. By querying the segment tree, it is determined whether an individual in the right half is dominated by any individual in the corresponding layer in the left half. Only individuals that are not dominated in the right half are filtered and retained to form the effective residual non-dominated set of the corresponding layer. Finally, the non-dominated layer in the left half is merged with the filtered residual in the right half to form the global non-dominated layer. This process of divide-and-conquer, tree construction, query filtering, and merging is executed recursively until all individuals are successfully assigned to their respective non-dominated layers.