A LVS weight scheduling method and system based on IPSO algorithm

Abstract

The present invention belongs to the field of computer science and network communication technology, and specifically relates to an LVS weight scheduling method and system based on the IPSO algorithm. First, the load information of each server node is collected; then the collected load information of the server node is transmitted to the LVS system; then the initial particle population and parameters are set, and the fitness function is constructed using the load information; then the improved IPSO algorithm is used to iteratively solve the global optimal solution; the solved global optimal solution is transmitted to the LVS system kernel; the LVS system performs LVS weight scheduling based on the global optimal solution. The dynamic allocation of load balancing weights according to the real-time load situation is realized, and the weight scheduling is made more accurate through comprehensive consideration of multiple indicators, which can better reflect the actual load capacity of the server. The performance of the entire load balancing system is optimized, ensuring that the resources of each server are optimally utilized, and improving the throughput and response speed of the system.

Description

Technical Field

[0001] The invention belongs to the field of computer science and network communication technology, and in particular relates to an LVS weight scheduling method and system based on an IPSO algorithm. Background Art

[0002] In today's highly networked and distributed computing environment, load balancing technology is essential to improving system performance and ensuring reliability. Load balancing ensures optimal use of system resources by rationally allocating tasks and requests to multiple servers, avoiding server overload or resource waste. However, traditional load balancing algorithms often face a series of challenges, especially in dynamic environments, where it is difficult to adapt to changes in system load and it is impossible to fully utilize the performance advantages of each server.

[0003] In the LVS system, i.e., the load balancing system, the existing scheduling algorithms, including the round-robin scheduling algorithm RR, the weighted round-robin scheduling algorithm WRR, the minimum connection scheduling algorithm LC, and the weighted minimum connection scheduling algorithm WLC, have achieved some success in certain scenarios, but they still have some inherent problems. Among them, the weights in the weighted minimum connection scheduling algorithm WLC and the weighted round-robin scheduling algorithm WRR cannot be adjusted dynamically, resulting in the system being unable to adapt to changes in load in real time, and the weight reference factors of the WLC algorithm are relatively single, and it is impossible to fully consider the multi-indicator load status, which may lead to inaccurate weight settings. The round-robin scheduling algorithm RR only allocates tasks through a simple polling method, without considering the actual load of the server, which may lead to uneven load distribution, and lacks a dynamic adjustment mechanism, and cannot make corresponding adjustments according to the real-time changes in the server load, which may cause some servers to be overloaded while other servers are idle. The minimum connection scheduling algorithm LC only considers the number of connections as the load standard, while ignoring other important server load indicators, resulting in incomplete load balancing, and using the number of connections as a metric may not accurately reflect the actual load of the server, especially for the server resource occupancy of different types of requests.

[0004] Therefore, how to solve the above technical problems existing in the existing LVS system is a technical problem that urgently needs to be solved. Summary of the invention

[0005] The purpose of the present invention is to provide a LVS weight scheduling method based on the IPSO algorithm to solve the above technical problems.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0007] In a first aspect, a LVS weight scheduling method based on an IPSO algorithm is provided, comprising the following steps:

[0008] S1: Collect the load information of each server node;

[0009] S2: Transmit the collected server node load information to the LVS system;

[0010] S3: Set the initial particle population and parameters, and use the load information to build the fitness function;

[0011] S4: Use the improved IPSO algorithm to iteratively solve the global optimal solution;

[0012] S5: Transmit the global optimal solution to the LVS system kernel;

[0013] S6: The LVS system performs LVS weight scheduling based on the global optimal solution.

[0014] Preferably, in step S1, the load information includes key indicators of CPU occupancy, memory occupancy, network bandwidth occupancy and disk IO occupancy.

[0015] Preferably, in step S2, the specific process is: the server node and the LVS system communicate in real time through the communication module, and the load information is transmitted to the LVS system in real time.

[0016] Preferably, constructing the fitness function in step S3 includes the following specific processes:

[0017] S31: Calculate the load balancing degree of the server cluster;

[0018] S32: Calculate the adaptability of the LVS system through the designed fitness function.

[0019] Preferably, in step S31, the formula for calculating the load balancing degree of the server cluster is set as follows:

[0020] ;

[0021] In step S32, the formula for setting the fitness function is as follows:

[0022] .

[0023] in, is the CPU usage, is the memory usage, is the network bandwidth utilization rate, is the disk IO usage, a , b , c , dThey are the corresponding weights of CPU usage, memory usage, network bandwidth usage, and disk IO usage.

[0024] Preferably, step S4 includes the following specific process:

[0025] S41: calculating the individual moving speed by setting the speed formula of the iterative update of the server individual;

[0026] S42: Calculate updated position information of each individual;

[0027] S43: By adding a random disturbance term in the PSO algorithm, the global optimal solution is optimized.

[0028] 1. Preferably, in step S41, the speed formula for iterative update of the server individual load is set as follows:

[0029] ;

[0030] in, Indicates that the d-th dimension position of individual n is k The particle velocity after iterations; and They represent the particle velocity and particle position of the d-th dimension position of individual n after the k-1th iteration respectively; ω is the inertia weight; C 1, C 2 are the individual learning coefficient and the social learning coefficient respectively; r 1, r 2 are the individual random coefficient and the social random coefficient respectively;

[0031] In step S42, the formula for calculating the updated position information of each individual is as follows:

[0032] ;

[0033] in, , Respectively represent the d-th dimension position of individual n in k The particle position after the k-1th iteration and the particle velocity after the k-1th iteration, Indicates that the d-th dimension position of individual n is k - Particle position after 1 iteration;

[0034] In step S43, the speed update formula with the random disturbance term added is as follows:

[0035] ;

[0036] in, is a Gaussian perturbation, μ is the mathematical expectation of the disturbance term, is the variance; is the constraint factor.

[0037] Preferably, in step S41, the individual learning coefficient in the speed formula for iterative update of the server individual C 1 and social learning coefficient C 2 is improved, and the improved individual learning coefficient C 1 and social learning coefficient C 2The formula is as follows:

[0038] ;

[0039] in, , are the minimum individual learning coefficient and the maximum individual learning coefficient respectively; , are the minimum social learning coefficient and the maximum social learning coefficient, respectively; and They are individual change factors and social change factors. The change factors here can be adjusted accordingly according to different models. The smaller the value, the stronger the individual learning ability of the population. Similarly, under certain conditions, stronger individual learning ability is required, and the , the same goes for social learning ability; k and are the current iteration number and maximum iteration number of the population respectively.

[0040] In a second aspect, a LVS weight scheduling system based on the IPSO algorithm is provided, which is used to implement any of the above-mentioned LVS weight scheduling methods based on the IPSO algorithm, including an information collection module, a communication module, a processing module and an IPSO algorithm module;

[0041] The information collection module is used to collect various load information of the server nodes;

[0042] The communication module is used to transmit the collected load information of the server nodes to the processing module;

[0043] The processing module is used to set the initial particle population and corresponding parameters based on the acquired load information, and construct a fitness function using the load information;

[0044] The IPSO algorithm module is used to find the global optimal solution for load balancing.

[0045] The beneficial effects of the present invention include:

[0046] The LVS weight scheduling method and system based on the IPSO algorithm provided by the present invention first collects the load information of each server node; then transmits the collected load information of the server node to the LVS system; then sets the initial particle population and parameters, and constructs a fitness function using the load information; then uses the improved IPSO algorithm to iteratively solve the global optimal solution; transmits the solved global optimal solution to the LVS system kernel; and the LVS system performs LVS weight scheduling based on the global optimal solution.

[0047] The dynamic allocation of load balancing weights is realized according to the real-time load situation, which enhances the adaptability and makes the system more flexible; through comprehensive consideration of multiple indicators, the weight scheduling is more accurate and can better reflect the actual load capacity of the server. The performance of the entire load balancing system is optimized, ensuring the optimal utilization of the resources of each server and improving the throughput and response speed of the system.

[0048] First, by setting the formula for calculating the load balancing degree of the server cluster and the formula for the fitness function, the load balancing degree and fitness value of the server cluster can be calculated in real time, providing a specific data basis for subsequent load scheduling and ensuring the high precision and accuracy of subsequent load scheduling.

[0049] Secondly, by setting the speed formula for iterative update of individual servers based on the IPSO algorithm, the individual movement speed is calculated, the updated position information of each individual is calculated, and a random disturbance term is added to the PSO algorithm to optimize the global optimal solution. By setting the speed formula for iterative update of individual server loads, the load update status during the server load scheduling process is obtained, which optimizes the performance of the entire load balancing system, ensures that the resources of each server are optimally utilized, and improves the system's throughput and response speed.

[0050] Again, the individual learning coefficient QUOTE in the iterative update speed formula of the server individual and social learning coefficient C 2. Make improvements to optimize the iterative update process of server load. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of the LVS weight scheduling method based on the IPSO algorithm of the present invention.

[0052] Figure 2 It is a schematic diagram of the composition of the LVS weight scheduling system based on the IPSO algorithm of the present invention.

[0053] Figure 3 It is a schematic diagram of the IPSO algorithm flow in the LVS weight scheduling method based on the IPSO algorithm of the present invention. DETAILED DESCRIPTION

[0054] The following is combined with Figure 1~Figure 3 The present invention is further described in detail:

[0055] See attached Figure 1 As shown, a LVS weight scheduling method based on the IPSO algorithm includes the following steps:

[0056] S1: Collect the load information of each server node;

[0057] S2: Transmit the collected server node load information to the LVS system;

[0058] S3: Set the initial particle population and parameters, and use the load information to build the fitness function;

[0059] S4: Use the improved IPSO algorithm to iteratively solve the global optimal solution;

[0060] S5: Transmit the global optimal solution to the LVS system kernel;

[0061] S6: The LVS system performs LVS weight scheduling based on the global optimal solution.

[0062] In a server cluster, when the load weight of the cluster is allocated through the LVS system, the load information of each server node is first collected; then the collected load information of the server node is transmitted to the LVS system; then the initial particle population and parameters are set, and the fitness function is constructed using the load information; then the improved IPSO algorithm is used to iteratively solve the global optimal solution; the solved global optimal solution is transmitted to the LVS system kernel; the LVS system performs LVS weight scheduling based on the global optimal solution. The dynamic allocation of load balancing weights according to the real-time load situation is realized, the adaptability is enhanced, and the system is more flexible; the comprehensive consideration of multiple indicators makes the weight scheduling more accurate and can better reflect the actual load capacity of the server. The performance of the entire load balancing system is optimized, ensuring that the resources of each server are optimally utilized, and improving the throughput and response speed of the system.

[0063] In the above scheme, the load information in step S1 includes key indicators such as CPU occupancy, memory occupancy, network bandwidth occupancy and disk IO occupancy. Step S1 ensures that the load balancing system can obtain detailed load data of each node. The IPSO algorithm in this application dynamically adjusts the load weight based on multiple indicator information of the server, so that the LVS system can allocate tasks and weights more accurately, ensure that the resources of each server are optimally utilized, and improve the throughput and response speed of the system.

[0064] In step S2, the specific process is: the server node and the LVS system communicate in real time through the communication module, and transmit the load information to the LVS system in real time. The communication module installs a listener on each server node and the LVS system to establish a real-time communication mechanism. The communication module is responsible for transmitting the collected node load information to the LVS system to ensure timely transmission of data.

[0065] Constructing the fitness function in step S3 includes the following specific processes:

[0066] S31: Calculate the load balancing degree of the server cluster;

[0067] S32: Calculate the adaptability of the LVS system through the designed fitness function.

[0068] In step S31, the formula for calculating the load balancing degree of the server cluster is set as follows:

[0069] ;

[0070] In step S32, the formula for setting the fitness function is as follows:

[0071]

[0072] in, is the CPU usage, is the memory usage, is the network bandwidth utilization rate, is the disk IO usage, a , b , c , d They are the corresponding weights of CPU usage, memory usage, network bandwidth usage, and disk IO usage. The comprehensive load of the server node needs to consider the impact of each indicator on the node, including CPU usage, memory usage, network bandwidth usage, and disk IO usage. Considering that different indicators have different impacts on node performance and different impacts on the load balancing degree of the cluster, the load balancing degree of the cluster is positively correlated with each indicator.

[0073] F(X) is a continuous function about (x1,x2,···,xn). The larger the function value, the smaller the mean square error of the utilization of each resource in the cluster, and the more balanced the cluster load. From the knowledge of the function, we know that there must be an optimal solution within the value range of the function. The optimal solution is the optimal weight, which is the optimal scheduling solution. The weight indicates the proportion of requests that can be borne by the surplus of each node at present. Therefore, the node with more surplus performance must bear relatively more requests. If the request is scheduled according to this weight, the impact on the current cluster load is minimal.

[0074] Step S3 is implemented by the processing module, by setting the initial particle population and corresponding parameters, and using the load information to construct the fitness function. In the particle population, each particle represents a weight combination. A reasonable initial population can provide a better initial state for the IPSO algorithm, which is conducive to the IPSO scheduling algorithm to quickly iterate the optimal particle solution.

[0075] Step S4 includes the following specific processes:

[0076] S41: calculating the individual moving speed by setting the speed formula of the iterative update of the server individual;

[0077] S42: Calculate updated position information of each individual;

[0078] S43: By adding a random disturbance term in the PSO algorithm, the global optimal solution is optimized.

[0079] Within a certain period of time, and when the number of parallel requests changes, the IPSO iterative operation is repeated until the exit condition is met or the listener is closed, so as to obtain the global optimal solution and provide a more optimal weight combination for load balancing scheduling.

[0080] In step S41, the speed formula of the iterative update of the individual is set as follows:

[0081] ;

[0082] in, Indicates that the d-th dimension position of individual n is k The particle velocity after iterations; and They represent the particle velocity and particle position of the d-th dimension position of individual n after the k-1th iteration respectively; ω is the inertia weight; C 1, C 2 are the individual learning coefficient and the social learning coefficient respectively; r 1, r 2 are the individual random coefficient and the social random coefficient respectively;

[0083] In step S42, the formula for calculating the updated position information of each individual is as follows:

[0084] ;

[0085] in, , Respectively represent the d-th dimension position of individual n in k The particle position after the k-1th iteration and the particle velocity after the k-1th iteration, Indicates that the d-th dimension position of individual n is k - Particle position after 1 iteration;

[0086] In step S43, the speed update formula with the random disturbance term added is as follows:

[0087] ;

[0088] in, is a Gaussian perturbation, μ is the mathematical expectation of the disturbance term, is the variance; is the constraint factor.

[0089] In step S41, the individual learning coefficient QUOTE in the speed formula of the individual iteration update and social learning coefficient C 2 is improved, and the improved individual learning coefficient C 1 and social learning coefficient C 2The formula is as follows:

[0090] ;

[0091] in, , are the minimum individual learning coefficient and the maximum individual learning coefficient respectively; , are the minimum social learning coefficient and the maximum social learning coefficient, respectively; and They are individual change factors and social change factors. The change factors here can be adjusted accordingly according to different models. The smaller the value, the stronger the individual learning ability of the population. Similarly, under certain conditions, stronger individual learning ability is required, and the , the same goes for social learning ability; k and are the current iteration number and maximum iteration number of the population respectively.

[0092] Choosing a reasonable individual learning coefficient can better utilize the historical position of each individual to deal with complex optimization problems. A reasonable social learning coefficient is conducive to improving the population's recognition of the global optimal solution and avoiding the population from falling into the local optimum. In the classic multi-objective particle swarm algorithm, a constant is used as the learning coefficient of the particle. Later, scholars conducted a more in-depth study on the selection of the learning coefficient through theoretical analysis, but the more common improvement methods are to change the two learning coefficients linearly or synchronously, without considering the correlation between the iteration process and the learning ability, resulting in the population being unable to reasonably control the learning ability of the global optimum according to the iteration progress, reducing the convergence speed of the algorithm to solve the global optimum. To address this problem, this paper proposes an adaptive learning coefficient, which adaptively regulates the individual and social learning coefficients according to the iteration progress of the population, increases the diversity of population evolution through asynchronous adjustment methods, and improves the global search ability of the algorithm.

[0093] The scheduling module in the LVS system introduces the global optimal solution calculated by the improved IPSO algorithm to ensure that the solution can be effectively transmitted in the system kernel, inject better weights into the system, and improve the load balancing system's adaptability to dynamic environmental changes. After obtaining the global optimal solution, the load balancing system re-schedules the load balancing. The key to this step is to make full use of the intelligent weights obtained by the IPSO algorithm and realize cluster adaptive weight load balancing through precise load scheduling methods, thereby improving system performance and optimizing resource utilization.

[0094] In the above scheme, see Figure 3 , the specific process of calculating the global optimal solution using the improved IPSO algorithm is as follows:

[0095] First, initialize the algorithm IPSO parameters, including key parameters such as population size, number of iterations, and number of individual particles. Generate a random initial population, in which each particle represents a solution to a set of weights, and evaluate the fitness of the generated random initial population through the established fitness function. Next, perform a non-dominated sort on the evaluated population to determine the quality of each particle. At the same time, establish an elite individual archive to store the optimal solution in the non-dominated sort. Subsequently, calculate the learning coefficient and perturbation term for each particle. The learning coefficient includes the individual learning coefficient and the social learning coefficient, which are used to adjust the speed and position of the particle. This step takes into account the individual historical optimal position of the individual particle and the global optimal position of the entire population. Then, update the speed and position of the particle, and update the individual position at the same time. In this process, the feasibility of the solution is ensured by limiting the individuals that exceed the boundary. After each iteration, determine whether the termination condition is met. If it is met, the optimal solution is output; if not, the fitness of the population is re-evaluated and the next round of iterations is continued. This process is repeated until the termination condition is met.

[0096] An LVS weight scheduling system based on the IPSO algorithm, used to implement any one of the above-mentioned LVS weight scheduling methods based on the IPSO algorithm, comprising an information collection module, a communication module, a processing module and an IPSO algorithm module;

[0097] The information collection module is used to collect various load information of the server nodes;

[0098] The communication module is used to transmit the collected load information of the server nodes to the processing module;

[0099] The processing module is used to set the initial particle population and corresponding parameters based on the acquired load information, and construct a fitness function using the load information;

[0100] The IPSO algorithm module is used to find the global optimal solution for load balancing.

[0101] In summary, the LVS weight scheduling method based on the IPSO algorithm provided by the present invention first collects the load information of each server node; then transmits the collected load information of the server node to the LVS system; then sets the initial particle population and parameters, and uses the load information to construct a fitness function; then uses the improved IPSO algorithm to iteratively solve the global optimal solution; transmits the solved global optimal solution to the LVS system kernel; the LVS system performs LVS weight scheduling based on the global optimal solution.

[0102] The LVS weight scheduling policy system based on the IPSO algorithm of the present application can adaptively adjust the weight of the server according to the real-time load conditions, so as to adapt to the changing load environment more flexibly; and it takes into account multiple indicators and constructs a more comprehensive fitness function. Compared with the traditional algorithm, the comprehensive consideration of multiple indicators makes the weight scheduling more accurate and can better reflect the actual load capacity of the server; the present invention can optimize the performance of the entire system. The load balancer can allocate tasks more intelligently, ensure the optimal utilization of each server resource, and improve the throughput and response speed of the system. The load balancing system is more flexible and can cope with real-time load changes, thereby ensuring the stability of the entire system and having better performance.

Claims

1. A LVS weight scheduling method based on IPSO algorithm, It is characterized in that The following steps are involved: S1: Collect the load information of each server node; S2: Transmit the collected server node load information to the LVS system; S3: Set the initial particle population and parameters, and use the load information to build the fitness function; S4: Use the improved IPSO algorithm to iteratively solve the global optimal solution; S5: Transmit the global optimal solution to the LVS system kernel; S6: The LVS system performs LVS weight scheduling based on the global optimal solution; Among them, constructing the fitness function in step S3 includes the following specific processes: S31: Calculate the load balancing degree of the server cluster; S32: Calculate the adaptability of the LVS system through the designed fitness function; In step S31, the formula for calculating the load balancing degree of the server cluster is set as follows: ； In step S32, the formula for setting the fitness function is as follows: ； in, is the CPU usage, is the memory usage, is the network bandwidth utilization rate, is the disk IO usage, a , b , c , d They are the corresponding weights of CPU usage, memory usage, network bandwidth usage, and disk IO usage; Step S4 includes the following specific processes: S41: calculating the individual moving speed by setting the speed formula of the iterative update of the server individual; S42: Calculate updated position information of each individual; S43: By adding a random disturbance term in the PSO algorithm, the global optimal solution is optimized; In step S41, the speed formula for iterative update of the server individual load is set as follows: ； in, Indicates that the d-th dimension position of individual n is k The particle velocity after iterations; and They represent the particle velocity and particle position of the d-th dimension position of individual n after the k-1th iteration respectively; ω is the inertia weight; C 1 , C 2 They are the individual learning coefficient and the social learning coefficient; r 1 , r 2 They are individual random coefficient and social random coefficient respectively; In step S42, the formula for calculating the updated position information of each individual is as follows: ； in, , They represent the d-th dimension position of individual n in k The particle position after the k-1th iteration and the particle velocity after the k-1th iteration, Indicates that the d-th dimension position of individual n is k - Particle position after 1 iteration; In step S43, the speed update formula with the random disturbance term added is as follows: ； in, is a Gaussian perturbation, μ is the mathematical expectation of the disturbance term, is the variance; is the constraint factor.

2. According to the LVS weight scheduling method based on the IPSO algorithm according to claim 1, It is characterized in that In step S1, the load information includes key indicators of CPU occupancy, memory occupancy, network bandwidth occupancy and disk IO occupancy.

3. According to the LVS weight scheduling method based on the IPSO algorithm described in claim 1, It is characterized in that In step S2, the specific process is: the server node and the LVS system communicate in real time through the communication module, and the load information is transmitted to the LVS system in real time.

4. According to claim 1, a LVS weight scheduling method based on IPSO algorithm, It is characterized in that In step S41, the individual learning coefficient in the speed formula of the iterative update of the server individual and social learning coefficient C 2 After improvement, the individual learning coefficient C 1 and social learning coefficient C 2 The formula is as follows: ； in, , are the minimum individual learning coefficient and the maximum individual learning coefficient respectively; , are the minimum social learning coefficient and the maximum social learning coefficient, respectively; and They are individual change factors and social change factors. The change factors here can be adjusted accordingly according to different models. The smaller the value, the stronger the individual learning ability of the population. Similarly, under certain conditions, stronger individual learning ability is required, and the , the same goes for social learning ability; k and are the current iteration number and maximum iteration number of the population respectively.

5. A LVS weight scheduling system based on the IPSO algorithm, used to implement the LVS weight scheduling method based on the IPSO algorithm described in any one of claims 1 to 4, It is characterized in that It includes information collection module, communication module, processing module and IPSO algorithm module; The information collection module is used to collect various load information of the server nodes; The communication module is used to transmit the collected load information of the server nodes to the processing module; The processing module is used to set the initial particle population and corresponding parameters based on the acquired load information, and construct a fitness function using the load information; The IPSO algorithm module is used to solve the global optimal solution of load balancing; Among them, constructing the fitness function includes the following specific processes: Calculate the load balancing degree of the server cluster; The adaptability of the LVS system is calculated through the designed fitness function; In calculating the load balancing degree of the server cluster, the formula for setting the load balancing degree of the server cluster is as follows: ； The adaptability of the LVS system is calculated by the designed fitness function. The formula for setting the fitness function is as follows: ； in, is the CPU usage, is the memory usage, is the network bandwidth utilization rate, is the disk IO usage, a , b , c , d They are the corresponding weights of CPU usage, memory usage, network bandwidth usage, and disk IO usage; The IPSO algorithm module solves the global optimal solution of load balancing, including the following specific processes: The individual movement speed is calculated by setting the speed formula of the iterative update of the server individual; Calculate the updated position information of each individual; By adding a random disturbance term to the PSO algorithm, the global optimal solution can be optimized; The formula for iterative update speed of the server individual load setting is as follows: ； in, Indicates that the d-th dimension position of individual n is k The particle velocity after iterations; and They represent the particle velocity and particle position of the d-th dimension position of individual n after the k-1th iteration respectively; ω is the inertia weight; C 1 , C 2 They are the individual learning coefficient and the social learning coefficient; r 1 , r 2 They are individual random coefficient and social random coefficient respectively; The formula for calculating the updated position information of each individual is as follows: ； in, , They represent the d-th dimension position of individual n in k The particle position after the k-1th iteration and the particle velocity after the k-1th iteration, Indicates that the d-th dimension position of individual n is k - Particle position after 1 iteration; The speed update formula with the addition of random disturbance terms is as follows: ； in, is a Gaussian perturbation, μ is the mathematical expectation of the disturbance term, is the variance; is the constraint factor.

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