Multi-objective multitask optimization method for identifying individual patient network biomarkers

Abstract

The application discloses a multi-objective multi-task optimization method for identifying individual patient network biomarkers, simultaneously identifies drug target markers and disease signal markers from the gene network of an individual patient, forms a multi-objective multi-task optimization model according to a dynamic network biomarker physical theory and a multi-objective network control theory, and then adopts a multi-objective multi-task evolution algorithm to identify network biomarkers. The application utilizes the dynamic network biomarker physical theory and the multi-objective network control theory to respectively construct an unconstrained disease signal detection model and a constrained drug target identification model, and further constructs a multi-objective multi-task optimization problem, and then utilizes the multi-objective multi-task optimization method to identify the two types of markers, which can explore and utilize useful knowledge between the two models, and simultaneously improves the identification precision of the two types of markers.

Description

Technical Field

[0001] This invention relates to the field of cancer individual biomarker identification technology, and more specifically, to a multi-objective, multi-task optimization method for identifying network biomarkers of individual patients. Background Technology

[0002] Cancer is a leading cause of death, and identifying disease signals and developing new drugs are two important research areas. For disease signal detection, personalized dynamic biomarker theory can leverage the high-dimensional dynamic data of individual patients using single-sample network techniques, thus avoiding the analytical challenges associated with large-scale data. Specifically, patient genetic data is constructed into a personalized gene interaction network (PGIN), and then a set of genes is identified from the PGIN as biomarkers by analyzing the interactions between genes. These biomarkers can be further used to analyze disease signals. For drug development, an important task is identifying drug targets. Several network-based methods identify biomarkers from the PGIN and further identify targets through drug activation. Among these, structured network control criteria are a popular approach because they can accurately describe how to control the transition of the PGIN between normal and disease states. Summary of the Invention

[0003] To address the aforementioned problems, this invention utilizes dynamic network biomarker theory and multi-objective network control theory to construct an unconstrained disease signal detection model and a constrained drug target identification model, respectively. These models are further categorized into multi-objective, multi-task optimization problems. The invented multi-objective, multi-task optimization method is then used to identify the two types of biomarkers. This method can explore and utilize useful knowledge between the two models while simultaneously improving the identification accuracy of the two types of biomarkers.

[0004] The technical solution adopted in this invention is a multi-objective, multi-task optimization method for identifying network biomarkers of individual patients, comprising the following steps:

[0005] S1, the disease signal detection task and the drug target identification task are constructed as a multi-objective, multi-task optimization problem, with the following formula:

[0006] {x1,x2,…,x k}=arg min(F1(x1),F2(x2),…,F k (x k ))

[0007] stG1(x1),G2(x2),…,G k (x k )

[0008] x k ={x k,1 ,xk,2 ,…,x k,NP}, k∈{1,2,…,K}

[0009] In the formula: k is the number of optimization tasks; F k Let G be the objective function for the k-th optimization task. k For the constraints of the k-th optimization task, x k Let represent the decision variable for the k-th optimization task, which contains NP individuals;

[0010] The formula for the disease signal detection task T1 is:

[0011]

[0012] In the formula: f1(x) represents the minimum number of nodes; f2(x) represents the minimum form that maximizes the number of prior nodes; V represents the number of nodes in PGIN; V p x represents the number of prior nodes in PGIN; 1,i It is a 0 / 1 variable; if the i-th node is selected, then x... i It equals 1, otherwise it equals 0; i It is an indicator variable; if the i-th node is a priori node, then l i It equals 1, otherwise it equals 0.

[0013] The formula for drug target identification task T2 is:

[0014]

[0015] In the formula: In the Minimal Dominant Set (MDS) model, Represents the index of the neighboring nodes of the i-th node; if the i-th node and the j-th node are connected by an edge, then the j-th node is called the neighbor of the i-th node; in the nonlinear control model (NCUA) of the undirected network algorithm, |E| represents the number of edges in PGIN, e j Represents the j-th edge in E; when the selected node is connected to e... j When connected, e j It equals 1, otherwise it equals 0;

[0016] S2, randomly initialize (NP-2) individuals as P 11 ;

[0017] S3 generates two single-objective optimal solutions, which serve as P. 12 ;

[0018] S4, merge P 11 and P 12 P1 is used as the initial population of T1, and P1 is evaluated on T1.

[0019] S5, randomly generate three populations of size NP, which will be used as the three initial populations P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13, P14, P15, P16, P17, P18, P1 ... 21 and P 22 The three populations were evaluated on T2; where P2 was used to optimize two objectives and constraints, P 21 P is used to optimize the first objective and constraints. 22 Used to optimize the second objective and constraints;

[0020] S6, set the algebraic counter Cnt to 1;

[0021] S7, P1 uses a binary genetic algorithm to generate NP / 2 offspring individuals, denoted as OP1, and evaluates OP1 on T1;

[0022] S8 and P2 produce offspring, denoted as OP2;

[0023] S9, P 21 and P 22 The binary genetic algorithm is used to generate NP / 4 offspring individuals, denoted as OP. 21 and OP 22 ;

[0024] S10, P1 uses an unconstrained non-dominated selection strategy to select NP individuals from the set {P1, OP1} as the new P1;

[0025] S11, evaluate OP2 on T2, OP 21 and OP 22 ;

[0026] S12, P2 uses the epsilon method to extract from the set {P2, OP2, OP...} 21 OP 22} Select NP individuals as the new P2;

[0027] S13, P 21 Use the epsilon method to extract from set {P 21 OP2, OP 21 OP 22} Select NP individuals as the new P 21 The f2 value of all individuals is set to 0.

[0028] S14, P 22 Use the epsilon method to extract from set {P 22 OP2, OP 21 OP 22} Select NP individuals as the new P 22 , where the f1 value of all individuals is set to 0;

[0029] S15, Cnt = Cnt + 1;

[0030] S16: If the maximum number of evaluations is reached, the algorithm stops and outputs P1 and P2; otherwise, jump to S7.

[0031] Furthermore, the specific steps of S3 include:

[0032] S31 generates a |V|-dimensional row vector, denoted as A, which is the optimal solution for the first objective;

[0033] S32 generates a |V|-dimensional row vector, denoted as B, where all dimension values ​​corresponding to the prior nodes are set to 1, which is the optimal solution for the second objective.

[0034] Furthermore, the specific steps of S8 are as follows:

[0035] S81, if the remainder of Cnt divided by 30 is 0, then jump to S82; otherwise, jump to S83.

[0036] S82, using the infeasible solution repair strategy to generate the offspring population OP2;

[0037] S83, P2 uses a binary genetic algorithm to generate NP / 2 offspring individuals, denoted as OP2.

[0038] Furthermore, the specific steps of S82 are as follows:

[0039] S821, randomly select NP / 2 individuals from P1, denoted as ST1;

[0040] S822, If the optimized network model is MDS, then jump to S823; if the optimized network model is NCUA, then jump to S828.

[0041] S823, set counter i = 1;

[0042] S824, for the i-th individual in ST1, is denoted as ST. 1,i ;

[0043] S825, for any j∈{1,2,…,|V|}, if ST 1,i If the node corresponding to the j-th dimension variable is selected or its neighbor node is selected, then the j-th dimension variable of ST1 remains unchanged; otherwise, randomly select a node from the j-th dimension node and its neighbors, and set the dimension of the newly selected node in ST1 to 1.

[0044] S826, Update counter i = i + 1;

[0045] S827, if i>NP, output ST1, otherwise jump to S824;

[0046] S828, set counter i = 1;

[0047] S829, for the i-th individual in ST1, denoted as ST 1,i Set j = 1;

[0048] S8210, for any j∈{1,2,…,|E|}, if ST 1,i If neither of the two nodes connected by the j-th edge in the corresponding PGIN is selected, then a node is randomly selected and its corresponding dimension is set to 1.

[0049] S8211, Update counter i = i + 1;

[0050] S8212, if i>NP, output ST1, otherwise jump to S829.

[0051] The beneficial effects of this invention are as follows:

[0052] (1) The problem of disease signal detection and drug target identification is modeled as a multi-task optimization problem. The algorithm's solution performance on both problems is improved by knowledge transfer between the two tasks.

[0053] (2) The two single-objective optimal solutions constructed in T1 improve the versatility of the algorithm for this task;

[0054] (3) The infeasible solution repair strategy set in T2 improves the effectiveness of knowledge transfer from T1 to T2. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method of the present invention;

[0056] Figure 2 This is a comparison chart of the evaluation metrics for early warning scores of the present invention and the unconstrained multi-objective algorithm;

[0057] Figure 3 This is a comparison chart of the evaluation metrics of the area under the curve of the present invention and the constrained multi-objective algorithm;

[0058] Figure 4 This is a comparison chart of the evaluation metrics for the early warning scores of this invention and the multi-objective multi-task algorithm;

[0059] Figure 5 This is a comparison chart of the area under the curve (AUC) evaluation metrics of the present invention and the multi-objective multi-task algorithm. Detailed Implementation

[0060] The invention will now be further described with reference to the accompanying drawings.

[0061] S1, the disease signal detection task and the drug target identification task are constructed as a multi-objective, multi-task optimization problem, with the following formula:

[0062] {x1,x2,…,x k}=arg min(F1(x1),F2(x2),…,F k (x k ))

[0063] stG1(x1),G2(x2),…,G k (x k )

[0064] x k ={x k,1 ,x k,2 ,…,x k,NP}, k∈{1,2,…,K}

[0065] In the formula: k is the number of optimization tasks; F k Let G be the objective function for the k-th optimization task. k For the constraints of the k-th optimization task, x k Let represent the decision variable for the k-th optimization task, which contains NP individuals.

[0066] The formula for the disease signal detection task T1 is:

[0067]

[0068] In the formula: f1(x) represents the minimum number of nodes, f2(x) represents the minimum form that maximizes the number of prior nodes, and V represents the number of nodes in PGIN. p x represents the number of prior nodes in PGIN. 1,i It is a 0 / 1 variable; if the i-th node is selected, then x... i It equals 1, otherwise it equals 0; i It is an indicator variable; if the i-th node is a priori node, then l i It equals 1, otherwise it equals 0.

[0069] The formula for drug target identification task T2 is:

[0070]

[0071] In the formula: In the Minimal Dominant Set (MDS) model, Represents the index of the neighboring nodes of the i-th node; if the i-th node and the j-th node are connected by an edge, then the j-th node is called the neighbor of the i-th node; in the nonlinear control model NCUA of the undirected network algorithm, |E| represents the number of edges in PGIN, e j Represents the j-th edge in E; when the selected node is connected to e... j When connected, e j It equals 1, otherwise it equals 0;

[0072] S2, randomly initialize (NP-2) individuals as P 11 .

[0073] S3 generates two single-objective optimal solutions, which serve as P. 12 The specific steps include:

[0074] S31 generates a |V|-dimensional row vector, denoted as A, which is the optimal solution for the first objective and is all zeros.

[0075] S32 generates a |V|-dimensional row vector, denoted as B, where all dimension values ​​corresponding to the prior nodes are set to 1, which is the optimal solution for the second objective.

[0076] S4, merge P 11 and P 12 P1 is used as the initial population of T1, and P1 is evaluated on T1.

[0077] S5, randomly generate three populations of size NP, which will be used as the three initial populations P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13, P14, P15, P16, P17, P18, P1 ... 21 and P 22 The three populations were evaluated on T2; where P2 was used to optimize two objectives and constraints, P 21 P is used to optimize the first objective and constraints. 22 Used to optimize the second objective and constraints.

[0078] S6 sets the algebraic counter Cnt to 1.

[0079] S7, P1 uses a binary genetic algorithm to generate NP / 2 offspring individuals, denoted as OP1, and evaluates OP1 on T1.

[0080] S8 and P2 produce offspring, denoted as OP2; the specific steps include:

[0081] S81. If the remainder of Cnt divided by 30 is 0, then jump to S82; otherwise, jump to S83.

[0082] S82, using the infeasible solution repair strategy to generate the offspring population OP2; the specific steps are as follows:

[0083] S821, randomly select NP / 2 individuals from P1, denoted as ST1.

[0084] S822, if the optimized network model is MDS, then jump to S823; if the optimized network model is NCUA, then jump to S828.

[0085] S823, set counter i = 1.

[0086] S824, for the i-th individual in ST1, is denoted as ST. 1,i .

[0087] S825, for any j∈{1,2,…,|V|}, if ST 1,i If the node corresponding to the j-th dimension variable is selected or its neighbor node is selected, then the j-th dimension variable of ST1 remains unchanged; otherwise, randomly select a node from the j-th dimension node and its neighbors, and set the dimension of the newly selected node in ST1 to 1.

[0088] S826, update counter i = i + 1.

[0089] S827: If i > NP, output ST1; otherwise, jump to S824.

[0090] S828, set counter i = 1;

[0091] S829, for the i-th individual in ST1, denoted as ST 1,i Set j=1.

[0092] S8210, for any j∈{1,2,…,|E|}, if ST 1,i If neither of the two nodes connected by the j-th edge in the corresponding PGIN is selected, then a node is randomly selected and its corresponding dimension is set to 1.

[0093] S8211, update counter i = i + 1.

[0094] S8212, if i>NP, output ST1, otherwise jump to S829.

[0095] S83, P2 uses a binary genetic algorithm to generate NP / 2 offspring individuals, denoted as OP2.

[0096] S9, P 21 and P 22 The binary genetic algorithm is used to generate NP / 4 offspring individuals, denoted as OP. 21 and OP 22 .

[0097] S10, P1 uses an unconstrained non-dominated selection strategy to select NP individuals from the set {P1, OP1} as the new P1.

[0098] S11, evaluate OP2 on T2, OP 21 and OP 22 .

[0099] S12, P2 uses the epsilon method to extract from the set {P2, OP2, OP...} 21 OP 22 Select NP individuals as the new P2.

[0100] S13, P 21 Use the epsilon method to extract from set {P 21 OP2, OP 21 OP 22} Select NP individuals as the new P 21 The f2 value of all individuals is set to 0.

[0101] S14, P 22 Use the epsilon method to extract from set {P 22 OP2, OP 21 OP 22} Select NP individuals as the new P 22 The f1 value of all individuals is set to 0.

[0102] S15, update the algebraic counter Cnt = Cnt + 1.

[0103] S16: If the maximum number of evaluations is reached, the algorithm stops and outputs P1 and P2; otherwise, jump to S7.

[0104] To verify the effectiveness of this invention, experiments were conducted. The experimental parameters were set as follows: population size NP was 100, the maximum number of evaluations for the first task was 50,000, and the maximum number of evaluations for the second task was 100,000. The experimental data consisted of BRCA (breast cancer) and LUND (lung cancer), containing data from 112 and 106 patients, respectively. Two basic PGIN models were used: MDS and NCUA.

[0105] The comparative experiment consists of three parts:

[0106] The first part compares the optimization method of this invention with unconstrained multi-objective algorithms to verify its effectiveness on T1. The comparison algorithms are DEAGNG, MOEAD, MSEA and DAEA, PREA.

[0107] The comparison results are as follows Figure 2 As shown, the evaluation index is the early warning score F.p The larger the value, the more accurately the algorithm can identify the critical state of the disease. As can be seen from the figure, the multi-task, multi-objective network biomarker identification method MMUR adopted in this invention achieves significantly better F-values ​​on both datasets and both models. p The value proves its validity.

[0108] The second part compares the optimization method of this invention with constrained multi-objective algorithms to verify its effectiveness on T2. ​​The comparison algorithms are CCMO, cDPEA, ICMA, IMTCMO, and LSCV_MCEA. The comparison results are as follows: Figure 3 As shown, the evaluation metric is the area under the curve (AUC), which assesses the proportion of drug targets found by the algorithm in the database; a larger AUC indicates better algorithm performance. Figure 3 As can be seen, MMUR achieved the highest AUC value across all cases, demonstrating its effectiveness.

[0109] The third part compares the optimization method of this invention with multi-objective, multi-task algorithms to verify its effectiveness on the proposed multi-task model. The comparison algorithms are EMT-ET, MO-EMEA, MO-MFEA, and MO-MFEA-II. The comparison results are as follows: Figure 4 and Figure 5 As shown, the evaluation indicators are the early warning score F. p The results show that, compared with multi-objective, multi-task comparison algorithms, the proposed method MMUR can achieve effective knowledge transfer and improve its effectiveness on both tasks.

Claims

1. A multi-objective multi-task optimization method for identifying individual patient network biomarkers, characterized in that, The method comprises the following steps: S1, constructing a disease signal detection task and a drug target identification task into a multi-objective multi-task optimization problem, and the formula is: {x1,x2,…,x k}=arg min(F1(x1),F2(x2),…,F k (x k )) s.t. G1(x1), G2(x2),..., G k (x k ) x k = {x k,1 , x k,2 , …, x k,NP}, k e {1, 2, …, K} where: k is the number of optimization tasks; F k Gk is the objective function for the kth optimization task, x k hk is the constraint condition for the kth optimization task, x k xk represents the decision variable of the kth optimization task, which contains NP individuals; The formula of the disease signal detection task T1 is: where: f1(x) represents the minimization of the number of nodes; f2(x) represents the maximization of the minimum form of the number of prior nodes; V represents the number of nodes in the PGIN; V p represents the number of prior nodes in the PGIN; x 1,i is a 0 / 1 variable, if the ith node is selected, x i equals 1, otherwise equals 0; l i is an indicator variable, if the ith node is a prior node, l i equals 1, otherwise equals 0; The formula of the drug target identification task T2 is: wherein: in the model of the minimum dominating set (MDS), index of the neighbor node representing the ith node; if the ith node and the jth node are connected by an edge, the jth node is called the neighbor of the ith node; in the nonlinear control model of the undirected network algorithm (NCUA), |E| represents the number of edges in PGIN, e j represents the jth edge in E; when the selected node is connected with e j , e j equals 1, otherwise equals 0; S2, randomly initialize (NP-2) individuals as P 11 ; S3, generate two single-objective optimal solutions as P 12 ; S4, merge P 11 and P 12 , as initial population P1 at T1 and evaluate P1 at T1; S5, randomly generate three populations of size NP as three initial populations P2, P3 and P4 of T2, respectively 21 and P4 22 , and evaluate the three populations on T2; where P2 is used to optimize both objectives and constraints, P3 is used to optimize the first objective and constraints, and P4 is used to optimize the second objective and constraints 21 and P4 22 , and evaluate the three populations on T2; where P2 is used to optimize both objectives and constraints, P3 is used to optimize the first objective and constraints, and P4 is used to optimize the second objective and constraints S6, setting an algebraic counter Cnt equal to 1; S7, P1 generates NP / 2 offspring individuals using a binary genetic algorithm, denoted as OP1, and evaluates OP1 on T1; S8, P2 generates offspring, denoted as OP2; S9, P 21 and P 22 NP / 4 offspring individuals are generated using a binary genetic algorithm, respectively denoted OP 21 and OP 22 ; S10, P1 uses an unconstrained non-dominated selection strategy to select NP individuals from the set {P1, OP1} as a new P1; S11, evaluate OP2, OP at T2 21 and OP 22 ; S12, P2 uses the epsilon method to select NP individuals from the set {P2, OP2, OP 21} as the new P2. 22} as the new P2. S13, P 21 Select NP individuals from the set {P 21 , OP2, OP 21 , OP 22} using the epsilon method as the new P 21 where the f2 value of all individuals is set to 0; S14, P 22 Select NP individuals from the set {P 22 , OP2, OP 21 , OP 22} as the new P 22 with all individuals' f1 values set to 0; S15, Cnt=Cnt+1; S16, if the maximum evaluation number is reached, the algorithm stops and outputs P1 and P2; otherwise, jump to S7.

2. The multi-objective, multi-task optimization method of identifying individual patient network biomarkers of claim 1, wherein, The specific steps of S3 comprise: S31, generating a |V| dimensional row vector all of which are 0, denoted as A, which is the optimal solution of the first objective; S32, generating a |V| dimensional row vector all of which are 0, denoted as B, wherein all the dimension values corresponding to the prior nodes are set to 1, which is the optimal solution of the second objective.

3. The multi-objective, multi-task optimization method of identifying individual patient network biomarkers of claim 1, wherein, The specific steps of S8 are: S81, if the remainder of Cnt divided by 30 is 0, jump to S82, otherwise jump to S83; S82, generating offspring population OP2 using an infeasible solution repair strategy; S83, P2 generates NP / 2 offspring individuals using a binary genetic algorithm, denoted as OP2.

4. The multi-objective, multi-task optimization method of identifying individual patient network biomarkers of claim 3, wherein, The specific steps of S82 are: S821, randomly selecting NP / 2 individuals from P1, denoted as ST1; S822, if the optimized network model is MDS, jump to S823; if the optimized network model is NCUA, jump to S828; S823, setting a counter i=1; S824, for the i-th individual in ST1, denoted as ST 1,i ; S825, for any j ∈ {1, 2, …, |V|}, if the j-th dimensional variable of ST 1,i corresponds to a selected node or its j-th dimensional corresponding node is a neighbor of a selected node, the j-th dimensional variable of ST1 does not change; otherwise, a node is randomly selected from the j-th dimensional corresponding node and its neighbors, and the dimension corresponding to the newly selected node in ST1 is set to 1; S826, updating the counter i=i+1; S827, if i>NP, output ST1, otherwise jump to S824; S828, setting a counter i=1; S829, for the i-th individual in ST1, denoted as ST 1,i , set j = 1; S8210, for any j ∈ {1, 2, …, |E|}, if ST 1,i If neither of the two nodes connected by the jth edge in the corresponding PGIN has been selected, a node is randomly selected and its corresponding dimension is set to 1. S8211, updating the counter i=i+1; S8212, if i>NP, output ST1, otherwise jump to S829.

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