A method for designing a peptide vaccine based on evolutionary multi-objective optimization
By reconstructing the peptide vaccine design problem into a bi-objective optimization problem and applying a multi-objective evolutionary algorithm and a hot-start and repair strategy, the problems of local optima and insufficient coverage in peptide vaccine design are solved, achieving more efficient peptide subset selection and broader population coverage.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV
- Filing Date
- 2024-06-04
- Publication Date
- 2026-07-21
Smart Images
Figure CN118737316B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a peptide vaccine design method, and more particularly to a peptide vaccine design method based on an evolutionary multi-objective optimization algorithm. Background Technology
[0002] Peptide vaccine design is a vaccine development approach that selects specific protein fragments (called peptides) that mimic antigenic sites on the surface of pathogens, thereby stimulating an immune response and providing an increasingly important clinical treatment tool for a variety of diseases. These vaccines have shown great potential in combating diseases such as HIV, Alzheimer's disease, and various types of cancer. Compared to traditional vaccine designs, such as those using attenuated or inactivated pathogens, peptide vaccines offer a highly specific and safe alternative. This is because they contain only key antigenic portions of the pathogen, rather than the entire live pathogen, significantly reducing the risk of infection while precisely targeting the immune response to the pathogen. Furthermore, the synthesis process of peptide vaccines is relatively simple and easy to standardize, enabling rapid responses to emerging epidemics.
[0003] Epitopes on peptides can bind to major histocompatibility complex (MHC) molecules in the human body, thereby eliciting a specific immune response. Machine learning plays a crucial role in identifying peptide epitopes that can trigger an immune response in this process. The application of this technology has greatly advanced research in this field, particularly in improving the accuracy of peptide prediction methods. After identifying potential peptide epitopes, the main challenge in peptide vaccine design lies in screening an effective subset of peptides. This process is exceptionally complex due to the allelic diversity of human MHC molecules, as peptide binding to MHC varies significantly among individuals. Therefore, selecting a diverse set of peptides that can cover a broad population and exert a universal effect has become a challenging task.
[0004] Previous studies on peptide vaccine design have largely relied on discrete optimization methods, such as integer linear programming and genetic algorithms, aiming to maximize population coverage. Liu et al. emphasized the importance of incorporating redundancy into the design to enhance the likelihood of effective immunogenic peptide presentation. They viewed the peptide vaccine design problem as a maximization problem... The problem of secondary coverage is that the goal is to select a set of peptides that ensure each individual has at least one. Secondary immunogenic peptides interact with MHC molecules, and this problem can be addressed using heuristic methods. However, maximizing... The sub-coverage problem is inherently NP-hard, and due to its lack of submodality, it cannot achieve a constant-factor approximate solution in polynomial time. Furthermore, in a set of peptides that have not reached... Before double coverage, this method often underestimates the actual utility of peptides.
[0005] Dai et al. modeled peptide vaccine design as a constrained optimization problem, aiming to maximize the expected number of peptides binding to MHC molecules in the population. They introduced cardinality constraints to limit the number of peptides in the selected subset and pairwise constraints to limit redundancy caused by peptide structural similarity. The objective function, i.e., the expected number of peptides binding to MHC molecules in the human body (peptide-MHC) in a broad population, was shown to be both monotonic and submodal, enabling their greedy algorithm Optivax-P to provide... An approximate guarantee, where , This represents the optimal function value. It represents the optimal function value under additional constraints. However, the performance of greedy algorithms may be limited by their greedy nature. Summary of the Invention
[0006] Purpose of the invention: To address the problem that existing greedy algorithms for peptide vaccine design are prone to getting trapped in local optima and have limited performance, a peptide vaccine design method based on evolutionary multi-objective optimization is proposed.
[0007] Technical Solution: A peptide vaccine design method based on evolutionary multi-objective optimization. Peptide vaccine design aims to maximize the expected peptide-MHC binding rate in a broad population by selecting a subset of peptides that satisfy certain constraints from a given set of peptides. A formal definition of the peptide vaccine design problem is now given.
[0008] make Represents a collection of peptides. This indicates the observation of a set of MHC genotypes in the population. Peptide vaccines work by selecting a group of effective peptides that are displayed on the cell surface as MHC proteins. The resulting peptide-MHC complex activates the cellular immune system. Let... peptide Based on an individual's MHC genotype The probabilities are shown, and it is assumed that these probabilities are independent between different peptides. The presented event is called a peptide-MHC hit, indicated by an indicator function. This indicates that the function value is 1 if the event occurs. Different MHC alleles have different peptide-binding properties, therefore, triggering multiple peptide-MHC bindings in vaccines is crucial to ensure T cell redundancy activation in individuals. Given a selected subset of peptides... For MHC genotype , The number of peptides displayed can be expressed as Since excessive redundancy can lead to an unnecessary burden on the immune system, a threshold parameter is used. To limit until the individual reaches The additional benefits up to the second hit, namely Therefore, for subsets The entire MHC genotype set The expected number of peptides bound to MHC is
[0009] in Indicates having a genotype The weights corresponding to the proportion of the population. To calculate... It is necessary to calculate each of Then, these expected values are summed. Assume the indicator variable... For each MHC genotype It is independent. For a given MHC genotype ,let express Center front A subset of peptides (assuming) The peptides in the peptides have an arbitrary order. express The sum of independent Bernoulli trials. The distribution is ordinary. Iterative calculations are possible. The distribution ,in Indicating new peptides MHC genotype The displayed probability. Then, The distribution satisfies ,and ,in That's right Then, the expected value is calculated using the obtained distribution.
[0010] The peptide vaccine design problem is subject to two types of constraints. The first is cardinality constraint, which ensures that the selected peptide subset... No more than the given size ,Right now This is crucial for increasing vaccine stability and reducing production costs. The second type involves pairwise constraints to prevent subsets... Any two peptides are similar. Maintaining the difference between peptides is crucial for vaccine design, as similar peptides may fail for the same reasons, thus reducing the overall effectiveness of the vaccine. Represent a graph where vertices correspond to sets of peptides. V Edges connect peptides considered similar. Solutions satisfying pairwise constraints correspond to the graph. G=(V,E) An independent set in a subset; that is, for a subset Any two peptides ,exist There is no border in the middle Peptide vaccine design has been envisioned as maximizing an objective function while satisfying cardinal constraints and a set of pairwise constraints. The problem is as follows: Given a set of peptides A group of MHC genotypes Each peptide With each MHC genotype The probability of combination between Corresponding to each MHC genotype Weighting function of population percentage Threshold ,Budget and similarity graph The goal of peptide vaccine design is to find a subset of peptides. ,make Maximize under the constraints of size constraints and a set of pairwise constraints. That is:
[0011] (2) The technical solution proposed in this invention is as follows: A novel peptide vaccine design framework based on evolutionary multi-objective optimization, termed PVD-EMO, is proposed. (Subset) It can be naturally derived from a Boolean vector. It indicates that the first one Bit If and only if The first in Each peptide was Includes. For symbolic convenience, no distinction is made. and its corresponding subset PVD-EMO first reformulates the original peptide vaccine design problem as a bi-objective maximization problem: , (3) in , In other words, the first goal equal to the original target (i.e., the expected number of peptide-MHC bindings in a broad population), for feasible solutions that satisfy the cardinality and pairwise constraints, and -1 for infeasible solutions; the second objective It is the opposite of the size of the subset. Use dominance relations to compare solutions: for two solutions... and 1) If Then it is called weak dominance (Right now, Compare Better, indicated as ); 2) If Then it is called Dominate (Right now, Compare Strict is better, expressed as ); 3) and They are incomparable, if they are neither No A solution is Pareto optimal if no other solution can dominate it. The set of objective vectors of all Pareto optimal solutions is called the Pareto front.
[0012] After constructing the bi-objective problem in formula (3), PVD-EMO applies a multi-objective evolutionary algorithm (MOEA) to solve it. Evolutionary algorithms (EAs), inspired by Darwin's theory of evolution, are general stochastic heuristic optimization algorithms that simulate mutation and natural selection. An evolutionary algorithm starts with an initial population of solutions, iteratively proliferates offspring solutions through crossover and mutation, and selects better solutions from both parent and offspring solutions to form the next population. The population-based search of EAs meets the requirements of multi-objective optimization, meaning that EAs can generate a set of Pareto optimal solutions by running only once. Therefore, evolutionary algorithms have become the most popular tool for multi-objective optimization, and the corresponding algorithms are also called MOEAs. After multiple iterations, the best feasible solution (i.e., the one that satisfies the constraints while having the maximum) is selected from the final population. f The solution to the value is taken as the output. Note that the goal of PVD-EMO is to find a good solution to the original peptide vaccine design problem, rather than the Pareto frontier of the restated bi-objective problem in Equation (3). That is, the bi-objective restatement is an intermediate process. Introducing the second objective Nature can bring about a diverse population, which may lead to better performance optimization. The detailed process of the PVD-EMO framework is as follows: Algorithm Flow 1: The process of applying a multi-objective evolutionary algorithm to solve the peptide vaccine design problem using the PVD-EMO framework. Input: Example of peptide vaccine design problem, budget A similarity graph
[0013] Output: A value with a maximum size of of subset 1. Construct two objective functions and To maximize it, as shown in formula (3); 2. Apply the Multi-Objective Evolutionary Algorithm (MOEA) to solve bi-objective problems; 3. Return the best feasible solution from the final population generated by the multi-objective evolutionary algorithm. PVD-EMO can be used with any multi-objective evolutionary algorithm, employing GSEMO and NSGA-II. To improve efficiency, warm-start and repair strategies are incorporated into the multi-objective evolutionary algorithm, and a strategy to accelerate objective evaluation is designed. These will be described in detail below.
[0014] The PVD-EMO algorithm, combined with the GSEMO algorithm and employing both warm-start and repair strategies, is termed PVD-GSEMO-WR. PVD-GSEMO-WR first constructs the biobjective problem in equation (3). Then, it starts with an initial population created by the warm-start strategy and iteratively improves the population. The quality of the solution. The warm-start strategy will... For each size in the equation, a feasible solution is randomly generated, while for a size of... The solution uses the output of the previous greedy algorithm Optivax-P. Among these solutions, non-dominated solutions will be included in the initial population. For details, please refer to algorithm flow 3. In each iteration, from the current population... A parent solution is selected uniformly and randomly from the middle. Sub-solutions are generated through position-by-position mutation. That is, based on probability Independent flipping Each one of them. Then, the sub-solution. It will undergo a repair strategy that can repair sub-solutions. This will prevent it from violating pairwise constraints, which will be discussed later. If If it is already feasible, then the repaired sub-solution equal Then, use Update population .if Not Dominated by any solution, it will be added Meanwhile, those who were Weakly dominant solutions will be removed. This update process makes the population... It always contains incomparable solutions. Furthermore, Feasible solutions are always included because 1) the repair strategy can correct violations of pairwise constraints; 2) according to formula (3), solutions that violate constraints have bad values on both objectives and will not be included in the population. The specific process of the PVD-GSEMO-WR algorithm is as follows: Algorithm Flow 2: The process of using the multi-objective evolutionary algorithm PVD-GSEMO-WR to solve the peptide vaccine design problem Input: Example of peptide vaccine design problem, budget and similarity graph
[0015] Output: A value with a maximum size of of subset 1. Construct two objective functions and To maximize it, as shown in formula (3); 2. Initialize the population using a warm-start strategy. ; 3. Repeat the following cyclical process: 4. From Uniform random selection ; 5. By using probability Flip Each one of them came to create ; 6. Repair strategy algorithm ( , , ) 7. If Make : 8.
[0016] 9. Meeting certain conditions 10. Return to the population The best feasible solution Algorithm Flow 3: Hot Start Strategy to Generate Initial Population Input: The solution output by the greedy algorithm Optivax-P
[0017] 1. ; 2. From Traversal : 3. Randomly generate a size of Feasible solution ; 4. If Make : 5.
[0018] 6. Return to the initial population
[0019] Repair strategy algorithm checks parent solution and offspring solution Each and every one of them. In their place from The 0 in the middle is flipped to When it is 1, it will recognize Middle and edge sets peptides Connected index sets Then, the algorithm randomly maintains... An index Unchanged, and will The other connection bits are set to 0. This ensures The former The bits do not violate pairwise constraints. After processing all bits, the corrected result will be returned. (No pairwise constraint violations exist). The specific process of the repair strategy algorithm is as follows: Algorithm Flow 4: The repair strategy repairs solutions that violate pairwise constraints into feasible solutions. Input: Similar image , parent solution and offspring solution
[0020] 1. From Traversal : 2. If 0, then 3. ; 4. From Uniform random selection ; 5. Set to 0, for any ; 6. Return to child solution
[0021] Furthermore, the multi-objective evolutionary algorithm NSGA-II was applied to the PVD-EMO framework. NSGA-II combines two important features: non-dominated ordering and crowding distance. PVD-EMO uses NSGA-II for multi-objective optimization and incorporates warm-start and repair strategies, referred to as PVD-NSGA-II-WR.
[0022] In each iteration of the PVD-EMO framework, a newly generated solution needs to be evaluated. The target value, i.e. ,in yes The corresponding subset. For each ,random variable yes An independent Bernoulli trial The sum can be obtained through iterative convolution. The probability distribution, which requires spending time The time. Then It can be done To calculate, where This requires Time. Therefore, calculation The total time is This is very expensive. Next, we will provide an assessment. The acceleration strategy. For each ,make Represents random variables The probability distribution, Indicates from peptide subset get The probability of a hit, i.e. The probability distribution of the empty subset Satisfy: For all , To expedite the evaluation process, in the distribution and A recursive relationship was established between them, where yes The parent solution. Specifically, it can be based on... calculate Add from recursively The peptides, and then recursively delete those from Peptides. Distribution based on Update:
[0023] Similarly, probability distribution By from Backtracking for updates:
[0024] Note that the position-by-position mutation operator commonly used in multi-objective evolutionary algorithms will expect to flip a single bit, meaning it will expect to add or delete a peptide. Therefore, calculating the offspring solution... probability distribution The expected time complexity is This is more efficient than direct calculation. Time is of the essence. The utility function... Stored in a data structure that supports random access, such as an array, this allows us to... The expected value is calculated within a given time. By implementing these optimizations, the total time required to compute the objective function can be reduced from [the time required for computation]. Reduce to .
[0025] For the peptide vaccine design problem in formula (2), by simultaneously maximizing and PVD-GSEMO-WR and PVD-NSGA-II-WR can achieve the same theoretical guarantees as Optivax-P, as shown in Theorem 1.
[0026] Theorem 1. For the peptide vaccine design problem in formula (2), the PVD-GSEMO-WR or population size is at least [missing information]. The PVD-NSGA-II-WR algorithm can achieve the same approximation guarantee as the previous greedy algorithm Optivax-P.
[0027] Furthermore, through the following peptide vaccine design example, Theorem 2 shows that Optivax-P tends to get trapped in local optima, while PVD-GSEMO-WR can avoid them and find the global optimum. The global optimum in this example does not contain peptides. The proof's approach is that Optivax-P, due to its greedy property, first selects... And be misled, while PVD-GSEMO-WR avoids this through positional mutation. Alternatively, a repair strategy can be used to escape local optima, and then follow the path provided by the population to reach the global optimum.
[0028] set up and Similarity graph In this graph, the two nodes connected by each edge are considered similar. Each node in the graph has a degree of at most 1, meaning it can only form one edge with another node. Except for that, its degree is 2. Objective function It has the following attributes: For any feasible solution in ,and Make , established ; , , established ; Make , established .
[0029] Theorem 2. For the peptide vaccine design example given above, PVD-GSEMO-WR can achieve the expected results. It finds the optimal solution within a number of iterations, while the greedy algorithm Optivax-P cannot.
[0030] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the peptide vaccine design method based on evolutionary multi-objective optimization as described above.
[0031] A computer-readable storage medium storing a computer program that performs the evolutionary multi-objective optimization-based peptide vaccine design method as described above.
[0032] Beneficial Effects: This invention provides a peptide vaccine design method based on evolutionary multi-objective optimization. The proposed PVD-EMO framework reformulates peptide vaccine design as a bi-objective optimization problem, maximizing the expected number of peptide-MHC molecule bindings while minimizing the number of selected peptides, and employs a multi-objective evolutionary algorithm to solve it. PVD-EMO can be equipped with any multi-objective evolutionary algorithm to solve this bi-objective problem, employing the theoretically sound GSEMO and the popular NSGA-II multi-objective evolutionary algorithms. To improve efficiency, a hot-start and repair strategy is also embedded into the multi-objective evolutionary algorithm. We demonstrate that the hot-start strategy ensures that PVD-EMO maintains the same worst-case approximation guarantee as the previous greedy algorithm Optivax-P. Furthermore, using a peptide vaccine design example, we demonstrate that Optivax-P can get trapped in local optima, while PVD-EMO can avoid this. Experiments on peptide vaccine design for COVID-19 caused by the SARS-CoV-2 virus demonstrate that PVD-EMO can effectively escape local optima and obtain better solutions than the state-of-the-art algorithm Optivax-P. Attached Figure Description
[0033] Figure 1 This is the overall flowchart of the PVD-EMO framework; Figure 2 This is a process diagram of the PVD-EMO framework paired with the GSEMO algorithm, which incorporates hot start and repair strategies. Figure 3 This is a similarity graph of peptide vaccine design examples. , where vertices correspond to peptides, and edges exist between similar peptides; Figure 4 The difference lies in the average objective value between each algorithm and the Optivax-P algorithm; Figure 5 It is a graph showing how the average target value of each algorithm changes over time. Detailed Implementation
[0034] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.
[0035] This invention provides a peptide vaccine design method based on evolutionary multi-objective optimization. It re-objectives the original peptide vaccine design problem and applies a multi-objective evolutionary algorithm with embedded hot-start and repair strategies to solve it, which can obtain better results.
[0036] A novel peptide vaccine design framework based on evolutionary multi-objective optimization is called PVD-EMO. (Subset) It can be naturally derived from a Boolean vector. It indicates that the first one Bit If and only if The first in Each peptide was Includes. For symbolic convenience, no distinction is made. and its corresponding subset PVD-EMO first reformulates the original peptide vaccine design problem as a bi-objective maximization problem: , (3) in , In other words, the first goal equal to the original target (i.e., the expected number of peptide-MHC bindings in a broad population), for feasible solutions that satisfy the cardinality and pairwise constraints, and -1 for infeasible solutions; the second objective It is the opposite of the size of the subset. Use dominance relations to compare solutions: for two solutions... and 1) If Then it is called weak dominance (Right now, Compare Better, indicated as ); 2) If Then it is called Dominate (Right now, Compare Strict is better, expressed as ); 3) and They are incomparable, if they are neither No A solution is Pareto optimal if no other solution can dominate it. The set of objective vectors of all Pareto optimal solutions is called the Pareto front.
[0037] After constructing the bi-objective problem in Equation (3), PVD-EMO applies a multi-objective evolutionary algorithm (MOEA) to solve it. The goal of PVD-EMO is to find a good solution to the original peptide vaccine design problem, rather than the Pareto front of the restated bi-objective problem in Equation (3). In other words, the bi-objective restatement is an intermediate process. A second objective is introduced. Nature can bring about a diverse population, which may lead to better performance optimization. The detailed process of the PVD-EMO framework is as follows: Algorithm Flow 1: The process of applying a multi-objective evolutionary algorithm to solve the peptide vaccine design problem using the PVD-EMO framework. Input: Example of peptide vaccine design problem, budget A similarity graph
[0038] Output: A value with a maximum size of of subset Construct two objective functions and To maximize it, as shown in formula (3); Applying the Multi-Objective Evolutionary Algorithm (MOEA) to solve bi-objective problems; Return the best feasible solution in the final population generated by the multi-objective evolutionary algorithm.
[0039] PVD-EMO can be used with any multi-objective evolutionary algorithm, employing GSEMO and NSGA-II. To improve efficiency, warm-start and repair strategies are incorporated into the multi-objective evolutionary algorithm, and a strategy to accelerate objective evaluation is designed. These will be described in detail below.
[0040] The PVD-EMO algorithm, combined with the GSEMO algorithm and employing both warm-start and repair strategies, is termed PVD-GSEMO-WR. PVD-GSEMO-WR first constructs the biobjective problem in equation (3). Then, it starts with an initial population created by the warm-start strategy and iteratively improves the population. The quality of the solution. The warm-start strategy will... For each size in the equation, a feasible solution is randomly generated, while for a size of... The solution uses the output of the previous greedy algorithm Optivax-P. Among these solutions, non-dominated solutions will be included in the initial population. For details, please refer to algorithm flow 3. In each iteration, from the current population... A parent solution is selected uniformly and randomly from the middle. Sub-solutions are generated through position-by-position mutation. That is, based on probability Independent flipping Each one of them. Then, the sub-solution. It will undergo a repair strategy that can repair sub-solutions. This will prevent it from violating pairwise constraints, which will be discussed later. If If it is already feasible, then the repaired sub-solution equal Then, use Update population .if Not Dominated by any solution, it will be added Meanwhile, those who were Weakly dominant solutions will be removed. This update process makes the population... It always contains incomparable solutions. Furthermore, Feasible solutions are always included because 1) the repair strategy can correct violations of pairwise constraints; 2) according to formula (3), solutions that violate constraints have bad values on both objectives and will not be included in the population. The specific process of the PVD-GSEMO-WR algorithm is as follows: Algorithm Flow 2: The process of using the multi-objective evolutionary algorithm PVD-GSEMO-WR to solve the peptide vaccine design problem Input: Example of peptide vaccine design problem, budget and similarity graph
[0041] Output: A value with a maximum size of of subset Construct two objective functions and To maximize it, as shown in formula (3); Initialize the population using a warm-start strategy. ; Repeat the following cyclical process: from Uniform random selection ; By using probability Flip Each one of them came to create ; Repair strategy algorithm ( , , ) if Make :
[0042] Certain conditions must be met (such as using a certain number of evaluations or running for a certain period of time). Return to population The best feasible solution in the equation.
[0043] Algorithm Flow 3: Hot Start Strategy to Generate Initial Population Input: The solution output by the greedy algorithm Optivax-P
[0044] ; from Traversal : Randomly generated size is Feasible solution ; if Make :
[0045] Return to the initial population .
[0046] Repair strategy algorithm checks parent solution and offspring solution Each and every one of them. In their place from The 0 in the middle is flipped to When it is 1, it will recognize Middle and edge sets peptides Connected index sets Then, the algorithm randomly maintains... An index Unchanged, and will The other connection bits are set to 0. This ensures The former The bits do not violate pairwise constraints. After processing all bits, the corrected result will be returned. (No pairwise constraint violations exist). The specific process of the repair strategy algorithm is as follows: Algorithm Flow 4: The repair strategy repairs solutions that violate pairwise constraints into feasible solutions. Input: Similar image , parent solution and offspring solution
[0047] from Traversal : if 0, then ; from Uniform random selection ; Will Set to 0, for any ; Returning child solutions .
[0048] Furthermore, the multi-objective evolutionary algorithm NSGA-II was applied to the PVD-EMO framework. NSGA-II combines two important features: non-dominated ordering and crowding distance. PVD-EMO uses NSGA-II for multi-objective optimization and incorporates warm-start and repair strategies, referred to as PVD-NSGA-II-WR.
[0049] In each iteration of the PVD-EMO framework, a newly generated solution needs to be evaluated. The target value, i.e. ,in yes The corresponding subset. For each ,random variable yes An independent Bernoulli trial The sum can be obtained through iterative convolution. The probability distribution, which requires spending time The time. Then It can be done To calculate, where This requires Time. Therefore, calculation The total time is This is very expensive. Next, we will provide an assessment. The acceleration strategy. For each ,make Represents random variables The probability distribution, Indicates from peptide subset get The probability of a hit, i.e. The probability distribution of the empty subset Satisfy: For all , To expedite the evaluation process, in the distribution and A recursive relationship was established between them, where yes The parent solution. Specifically, it can be based on... calculate Add from recursively The peptides, and then recursively delete those from Peptides. Distribution based on Update:
[0050] Similarly, probability distribution By from Backtracking for updates:
[0051] Note that the position-by-position mutation operator commonly used in multi-objective evolutionary algorithms will expect to flip a single bit, meaning it will expect to add or delete a peptide. Therefore, calculating the offspring solution... probability distribution The expected time complexity is This is more efficient than direct calculation. Time is of the essence. The utility function... Stored in a data structure that supports random access, such as an array, this allows us to... The expected value is calculated within a given time. By implementing these optimizations, the total time required to compute the objective function can be reduced from [the time required for computation]. Reduce to .
[0052] For the peptide vaccine design problem in formula (2), by simultaneously maximizing and PVD-GSEMO-WR and PVD-NSGA-II-WR can achieve the same theoretical guarantees as Optivax-P, as shown in Theorem 1.
[0053] Theorem 1. For the peptide vaccine design problem in formula (2), the PVD-GSEMO-WR or population size is at least [missing information]. The PVD-NSGA-II-WR algorithm can achieve the same approximation guarantee as the previous greedy algorithm Optivax-P.
[0054] Furthermore, through the following peptide vaccine design example, Theorem 2 shows that Optivax-P tends to get trapped in local optima, while PVD-GSEMO-WR can avoid them and find the global optimum. The global optimum in this example does not contain peptides. The proof's approach is that Optivax-P, due to its greedy property, first selects... And be misled, while PVD-GSEMO-WR avoids this through positional mutation. Alternatively, a repair strategy can be used to escape local optima, and then follow the path provided by the population to reach the global optimum.
[0055] set up and Similarity graph like Figure 3 As shown, the two nodes connected by each edge are considered similar. Each node in the graph has a degree of at most 1, meaning it can only form one edge with another node. Except for that, its degree is 2. Objective function It has the following attributes: For any feasible solution in ,and Make , established ; , , established ; Make , established .
[0056] Theorem 2. For the peptide vaccine design example given above, PVD-GSEMO-WR can achieve the expected results. It finds the optimal solution within a number of iterations, while the greedy algorithm Optivax-P cannot.
[0057] Two variants of PVD-EMO, PVD-GSEMO-WR and PVD-NSGA-II-WR, were compared with Optivax-P to examine the performance of PVD-EMO in COVID-19 peptide vaccine design. Optivax-P, the state-of-the-art greedy algorithm, outperformed thirty other algorithms in peptide vaccine design. The same dataset used in previous studies was used to produce peptide vaccines against COVID-19, consisting of a set of candidate peptides (…). Genotypes of a group of major histocompatibility complex class I (MHC-I) ), their frequency (From different populations representing the global population) and the binding probability of each "peptide-MHC" pair generated by the NetMHCpa model based on the state-of-the-art neural network. Composition. The pairwise constraint set requires that any edit (insertion, deletion, or replacement) between any pair of peptides must be at least 6 times. Since PVD-EMO is a readily available algorithm, its performance will gradually improve with the number of iterations; therefore, the number of objective evaluations is set to... To balance performance and runtime, Optivax-P uses a certain number of evaluations. Furthermore, it is randomized, so it is run independently ten times and the average is reported. The specific procedures for PVD-GSEMO-WR and PVD-NSGA-II-WR are as follows: PVD-NSGA-II-WR: Step 1: Read in the peptide vaccine design example and re-divide the original single-objective problem in formula (2) into a binary objective according to formula (3).
[0058] Step 2: Generate the initial population using a warm-start strategy. The population size of PVD-NSGA-II-WR is set to twice the size of the Pareto front, i.e. The hot-start strategy creates two feasible solutions for each scale of PVD-NSGA-II-WR, where the output of Optivax-P is used as the scale. One of the solutions.
[0059] Step 3: Sort the individuals in the population into strata according to their dominance relationships. Each stratum contains individuals that are not dominant to each other and are better at optimizing the objective than the individuals in the next lower stratum.
[0060] Step 4: Calculate the crowding degree for each individual: Within each layer, calculate the crowding degree of an individual, which is the density of solutions around that individual. Individuals with high crowding degree are considered to have better diversity.
[0061] Step 5: Select individuals for the next generation based on non-dominant ranking and crowding. Use tournament selection, prioritizing individuals with high ranking and high crowding.
[0062] Step 6: Apply single-point crossover and position-by-position mutation to the selected individuals with probabilities of 0.9 and 1, respectively, to generate new offspring. Then, use a repair strategy to ensure that the new offspring solutions do not violate the pairwise constraint.
[0063] Step 7: Merge the current population and offspring, and again use non-dominated sorting and crowding selection to select from them. The best individuals form a new population.
[0064] Step 8: Repeat steps 2 through 7 until the preset number of algebras is reached or the termination condition is met. Output the best feasible solution in the population that satisfies the constraints and maximizes the objective of the original problem.
[0065] PVD-GSEMO-WR: Step 1: Read in the peptide vaccine design example and re-divide the original single-objective problem in formula (2) into a binary objective according to formula (3).
[0066] Step 2: Hot start strategy for each scale of PVD-GSEMO-WR Create a feasible solution where the output of Optivax-P is used as the scale. One of the solutions.
[0067] Step 3: Select a parent solution from the population uniformly and randomly.
[0068] Step 4: Apply positional mutation to the selected individuals to generate new offspring, and then use a repair strategy to ensure that the new offspring solutions do not violate the pairwise constraints.
[0069] Step 5: Update the population according to the dominance rule: If no solution in the population can possess the offspring solution, then add the offspring solution to the population and remove the solution that is weakly dominated by the offspring solution from the population.
[0070] Step 8: Repeat steps 2 through 5 until the preset number of algebras is reached or the termination condition is met. Output the best feasible solution in the population that satisfies the constraints and maximizes the objective of the original problem.
[0071] set up , The result is as follows Figure 4 As shown, PVD-EMO performs at least as well as the competitive greedy algorithm Optivax-P. For relatively simple problems... Optivax-P might find the optimal solution, in which case PVD-EMO also performs well. However, as the problem complexity increases ( Both PVD-GSEMO-WR and PVD-NSGA-II-WR outperformed Optivax-P, demonstrating the superiority of the PVD-EMO framework. This is likely because PVD-EMO naturally maintains a diverse population of solutions through a bi-objective transformation, employs a position-by-position mutation operator with good global search capabilities, and the repair strategy further enhances the search ability. These characteristics contribute to a better ability to escape local optima. Among the two variants of PVD-EMO, PVD-GSEMO-WR outperforms PVD-NSGA-II-WR, possibly because the population of NSGA-II may contain redundant dominant solutions, leading to its poor performance.
[0072] To more clearly verify the effectiveness of the dual-objective reconstruction, a single-objective evolutionary algorithm was used. -EA conducted the experiment. For a fair comparison... -EA (population size is) Follow the PVD-GSEMO-WR settings and mark it as -EA-WR. The key difference is that... -EA-WR according to its objectives Values should be preserved optimally. The solution is used to update its population, while PVD-GSEMO-WR retains the non-dominated solution due to bi-objective refactoring. Furthermore, to evaluate the impact of warm-start and repair strategies, two variants were tested: PVD-GSEMO-R with only a repair strategy and PVD-GSEMO without a strategy. Figure 5 The curve showing the change of the target value over runtime is plotted in the image. Optivax-P is a fixed-time (close to) The algorithm used is PVD-GSEMO-R, while other algorithms are readily available and offer better performance, but their runtime is longer. Results show that even without a warm start, PVD-GSEMO-R and PVD-GSEMO outperform each other by [missing information - likely referring to performance improvements]. and The PVD-GSEMO-WR and PVD-GSEMO-R converge to the optimal objective value, with PVD-GSEMO-WR being faster due to its warm-start advantage. In contrast, despite employing two different strategies, -EA-WR still achieved the second-best objective value, thus validating the value of bi-objective reconstruction in maintaining a diverse population. Meanwhile, PVD-GSEMO, lacking a repair strategy, only achieved the third-best objective value, highlighting the crucial role of repair strategies in avoiding local optima, as shown in Theorem 2. These findings validate the effectiveness of bi-objective reconstruction, as well as warm-start and repair strategies.
[0073] Obviously, those skilled in the art should understand that the steps of the peptide vaccine design method based on evolutionary multi-objective optimization in the above embodiments of the present invention can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device. Furthermore, in some cases, the steps shown or described can be performed in a different order than presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the embodiments of the present invention are not limited to any particular hardware and software combination.
Claims
1. A peptide vaccine design method based on evolutionary multi-objective optimization, characterized in that, The original peptide vaccine design problem is reformulated as a bi-objective maximization problem: , （3） in , The first goal equal to the original target That is, the expected peptide-MHC binding number in a broad population, which is -1 for feasible solutions satisfying the cardinality and pairing constraints, and -1 for infeasible solutions; the second objective It is the opposite of the size of the subset; Use dominance relations to compare solutions: for two solutions and 1) If Then it is called weak dominance ;2) If Then it is called Dominate ;3) and They are incomparable, if they are neither No If a solution has no other solution that can dominate it, then the solution is Pareto optimal; the set of objective vectors of all Pareto optimal solutions is called the Pareto front. After constructing the bi-objective problem in formula (3), the multi-objective evolutionary algorithm is applied to solve the bi-objective problem; the best feasible solution in the final population generated by the multi-objective evolutionary algorithm is returned; A hot start and repair strategy was added to the multi-objective evolution algorithm, and a strategy to accelerate objective evaluation was designed. Start with an initial population created by a warm-start strategy and iteratively increase the population. The quality of the solution; the hot start strategy will provide For each size in the equation, a feasible solution is randomly generated, while for a size of... The solution is obtained using the output of the greedy algorithm Optivax-P; non-dominated solutions will be included in the initial population. ; In each iteration, from the current population A parent solution is selected uniformly and randomly from the middle. Sub-solutions are generated through position-by-position mutation. That is, based on probability Independent flipping Each one; then, sub-solution It will undergo a repair strategy that can repair sub-solutions. This would prevent it from violating pairwise constraints; if If it is already feasible, then the repaired sub-solution equal Then, use Update population ;if Not Dominated by any solution, it will be added Meanwhile, those who were Weakly dominant solutions will be removed; this update process makes the population... It always contains incomparable solutions; the specific process of solving the peptide vaccine design problem using a multi-objective evolutionary algorithm is as follows: Input: Example of peptide vaccine design problem, budget and similarity graph Output: A value with a maximum size of of subset (1) Construct two objective functions and To maximize it, as shown in formula (3); (2) Initialize the population using a hot start strategy ; (3) Repeat the following cyclical process: from Uniform random selection ; By using probability Flip Each one of them came to create ; Repair strategy algorithm ( , , ) if Make : (4) The set conditions are met; (5) Return to the population The best feasible solution in the equation.
2. The peptide vaccine design method based on evolutionary multi-objective optimization according to claim 1, characterized in that, The process of generating the initial population using the warm-start strategy is as follows: Input: The solution output by the greedy algorithm Optivax-P （1） ； (2) From Traversal : (3) Randomly generate a size of Feasible solution ; (4) If Make : （5） (6) Return to the initial population .
3. The peptide vaccine design method based on evolutionary multi-objective optimization according to claim 1, characterized in that, Repair strategy algorithm checks parent solution and offspring solution Each and every one of them; in their place from The 0 in the middle is flipped to When 1 is identified, Middle and edge sets peptides Connected index sets Then, the algorithm randomly maintains... An index Unchanged, and will Other connection bits in the configuration are set to 0; ensure that The former The bits do not violate pairwise constraints; after processing all bits, the corrected result will be returned. The specific process of the repair strategy algorithm is as follows: Input: Similar image , parent solution and offspring solution (1) From Traversal : (2) If 0, then （3） ； (4) From Uniform random selection ; (5) Set to 0, for any ; (6) Return to child solution .
4. The peptide vaccine design method based on evolutionary multi-objective optimization according to claim 1, characterized in that, In each iteration, a newly generated solution needs to be evaluated. The target value, i.e. ,in yes The corresponding subset; for each ,random variable yes An independent Bernoulli trial The sum is obtained through iterative convolution. The probability distribution; pass To calculate, where ,calculate The total time is Provide an assessment The acceleration strategy, for each ,make Represents random variables The probability distribution, Indicates from peptide subset get The probability of a hit, i.e. Probability distribution of the empty subset Satisfy: For all , To expedite the evaluation process, in the distribution and A recursive relationship was established between them, where yes The parent solution; specifically, according to calculate Add from recursively The peptides, and then recursively delete those from peptides; distribution based on Update: Similarly, probability distribution By from Backtracking for updates: The multi-objective evolutionary algorithm's position-by-position mutation operator will expect to flip one bit, meaning it will expect to add or delete a peptide; calculating the offspring solution... probability distribution The expected time complexity is ; Utility function It is stored in a data structure that supports random access.
5. A computer device, characterized in that: The computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the peptide vaccine design method based on evolutionary multi-objective optimization as described in any one of claims 1-4.
6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that executes the peptide vaccine design method based on evolutionary multi-objective optimization as described in any one of claims 1-4.