Intelligent short message channel resource allocation method oriented to multi-target multi-constraint coupling

Abstract

The invention discloses an intelligent short message channel resource allocation method oriented to multi-target multi-constraint coupling. The method comprises the following steps: S1, acquiring a data source of short message channel resources; s2, obtaining product related configuration from the data source, and converting the product related configuration into a triple constraint equation through product modeling; s3, obtaining channel related configuration from the data source, and converting the channel related configuration into a six-tuple constraint equation through channel modeling; s4, modeling according to the distribution schemes of the products and the channels and constraint conditions, and constructing a target function; the problem of short message channel resource allocation is converted into the problem of multi-constraint multi-objective optimization. S5, initializing a population of the improved genetic algorithm according to various basic constraints of the product and the channel; and S6, circularly executing a plurality of rounds of selection, crossover and mutation operator iteration to approach a globally optimal solution, and selecting an individual with the maximum fitness as a final allocation scheme.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication resource allocation, and in particular relates to a method for intelligently allocating short message channel resources oriented to multi-objective and multi-constraint coupling. Background Art

[0002] With the continued expansion of mobile internet marketing, SMS has become a core medium for reaching users, and its allocation efficiency directly impacts the conversion rate of marketing campaigns. However, traditional manual allocation models have significant limitations when it comes to coordinating allocation tasks across multiple products and channels.

[0003] First, the constraints between products and channels exhibit multi-dimensional coupling. Specifically, there are: First, available channel constraints: a single product can be distributed through multiple channels, and a single channel must support the marketing of multiple products. However, some special products are restricted to designated dedicated channels. Second, channel volume constraints: these include both the minimum volume threshold required by the channel provider (to ensure stable business partnerships) and the upper limit on channel capacity (to ensure that allocated volumes can be processed promptly). Third, service quality constraints: for example, requirements for SMS delivery success rates of at least 70% and user click-through rates of at least 10%.

[0004] Secondly, channel selection and volume allocation must simultaneously meet multi-objective optimization requirements. In real-world operations, operators tend to prioritize channels with lower unit prices in cost-conscious scenarios; whereas, in time-sensitive scenarios, they prioritize channels with high success rates and fast transmission speeds. Because these objectives inherently conflict (for example, high-success-rate channels often come with high costs), business decisions require a dynamic balance between multiple objectives, placing extremely high demands on the flexibility and expertise of manual configuration.

[0005] Finally, large-scale operations further highlight the efficiency bottlenecks of manual models. As the number of marketing products and channels grows exponentially, manual screening requires multiple rounds of trial and error and parameter tuning to arrive at the ideal solution. This time cost increases dramatically with the increasing complexity of the combination. Furthermore, the complex constraints of product-channel matching and the exponential possibilities of volume allocation make traditional manual models ineffective in meeting the demands of ultra-large-scale operations.

[0006] In summary, the manual configuration mode of the existing SMS channel resource intelligent allocation method cannot achieve the automatic and efficient allocation of SMS channel resources under the coupling of multiple constraints and multiple objectives. Summary of the Invention

[0007] Aiming at the problem that the manual configuration mode of the existing SMS channel resource intelligent allocation method cannot realize the automatic and efficient allocation of SMS channel resources under the coupling of multiple constraints and multiple objectives, the present invention provides an SMS channel quality indicator adaptive estimation method based on dynamic time series analysis.

[0008] In order to achieve the above technical objectives, the technical solutions adopted by the present invention are as follows:

[0009] A method for intelligently allocating short message channel resources based on multi-objective and multi-constraint coupling, comprising the following steps:

[0010] S1. Obtain the data source of SMS channel resources;

[0011] S2, obtain product-related configurations from the data source and convert them into triple constraint equations through product modeling;

[0012] S3, obtain channel-related configuration from the data source and convert it into a six-tuple constraint equation through channel modeling;

[0013] S4. Model the product and channel allocation plan and constraints, and construct the objective function; the SMS channel resource allocation problem is transformed into a multi-constraint and multi-objective optimization problem.

[0014] S5. Initialize the population of the improved genetic algorithm according to the basic constraints of products and channels;

[0015] S6. Execute several rounds of selection, crossover, and mutation operators iteratively to approach the global optimal solution, and select the individual with the largest fitness as the final allocation solution.

[0016] Further, product modeling:

[0017] The product triple is defined as (i,Q i ,R i ), where: i∈I is the unique identifier of the product; Q i ≥0 is the total marketable quantity of the product (unit: piece); R i ≥0 is the expected revenue per unit click (unit: yuan / item).

[0018] Furthermore, channel modeling: SMS channel six-tuple is defined as (j,S j ,T j ,C j ,L j ,U j ), where: j∈J is the unique identifier of the channel; S j ∈[0,1] is the average channel sending success rate; T j ∈[0,1] is the average click rate of the channel; C j≥0 is the expected cost per unit (unit: yuan / item); L j ≥0 is the lower limit of the channel allocation level (unit: bar); U j ≥L j Assign a magnitude upper limit to the channel (unit: bar).

[0019] Furthermore, the allocation scheme is modeled:

[0020] The allocation scheme triple is defined as (i, j, x ij ), where: x ij ∈Z ≥0 represents the magnitude of product i allocated to channel j (unit: bar);

[0021] Constraint modeling includes:

[0022] Upper limit constraints on product marketing scale Channel level lower limit constraint Channel magnitude upper limit constraint Non-negativity constraints: Channel availability constraints where Y ’ i represents the set of available channels for product i.

[0023] Furthermore, construct the objective function: according to different goals, design different optimization objective functions, including: maximizing total benefits: Maximize delivery success rate and click-through rate: Multi-objective equilibrium optimization: T j In actual application scenarios, it can be flexibly adjusted according to business objectives.

[0024] Coding: The product set I and channel set J have been defined above, and the allocation scheme triple is defined as (i, j, x ij ), then the magnitude distribution scheme of all products on all channels can be defined as a matrix x, where rows represent channels and columns represent products, x ij represents the magnitude of the product allocated to that channel. Each matrix x represents a possible allocation scheme, and the set of all x's constitutes X, which is the algorithm's solution space. Therefore, the matrix x is used for encoding individual products, and the process of finding the optimal solution is to traverse the solution space and find the optimal product-channel magnitude allocation scheme.

[0025]

[0026] Furthermore, determining the channel selection and magnitude distribution scheme is to solve the function:

[0027]

[0028] Furthermore, initialize the population of the improved genetic algorithm:

[0029] First, set the unavailable channel level to 0;

[0030] Then, for the remaining channels, the double mean method is used to generate random numbers. Under this product, the magnitude assigned to each channel is a random number between 1 and the mean of the remaining magnitudes (which must satisfy the non-negative constraint).

[0031] The final channel obtains all remaining levels, ensuring that the average of each random amount is equal and that the sum equals the total available level for the product. For each product (each column), the above method is used for random initialization to obtain an alternative allocation plan x′. This is then summed row by row, and the row sum is tested to see if it falls between the upper and lower limits of the available level for the corresponding channel. If the test passes, the alternative plan is included in the initial population; if not, the randomization is repeated until an alternative plan that meets all constraints is generated.

[0032] The upper limit constraint on the product marketing level requires that the sum of each column is exactly equal to the product available level Q i ;

[0033] The channel level constraint requires that the sum of each row is within the channel level lower limit L j and the upper limit of the channel magnitude U j between;

[0034] The non-negativity constraint requires that every x ij All are greater than or equal to 0;

[0035] The product channel availability constraint will make some x ij = 0. Since the product available level constraint requires the sum to be equal, during the population initialization process.

[0036] Furthermore, the selection operators include the elite selection algorithm and the roulette wheel algorithm. The elite selection strategy will directly copy a portion of the individuals with the highest fitness to the next generation, which helps to retain the currently found optimal solution;

[0037] Roulette wheel selection is a fitness-proportional selection method, in which the probability of each individual being selected is proportional to its fitness;

[0038] Crossover operator (within-group crossover): Each time a crossover occurs, two channels are randomly selected. Within these two rows, multiple crossover points are randomly selected and swapped to generate new offspring. After all points have been swapped, the sum is recalculated by row to verify whether the upper and lower limits of the channel's available magnitude are met. If so, the crossover is complete; if not, the random selection is repeated.

[0039] Because products must strictly meet the constraint of equal total volume, intra-group crossover must occur between rows. As shown in the following formula, rows p and q are randomly selected, and positions 1 and i are further randomly swapped.

[0040]

[0041] Mutation operator: The change in the magnitude of each product's distribution across different channels is manifested as an increase in the magnitude of one channel, followed by a decrease in the magnitude of another channel. After all points have been mutated, the sum is recalculated by row to verify whether the upper and lower limits of the available magnitude of the channel are met. If so, the mutation is complete; if not, the randomization is repeated.

[0042] Since the product needs to strictly meet the constraint of equal total level, the variation occurs within the column, as shown in the following formula: first, randomly select column c for variation, then randomly select points c1 and c2 for exchange, and then randomly generate the variation k, and finally randomly select x c1 、x c2 Increase or subtract k to complete the mutation.

[0043]

[0044] Evolutionary Process: After initializing the population based on the basic constraints for products and channels, several rounds of crossover, mutation, and selection operators are repeated until the iteration limit is reached or no further changes occur between iterations. At this point, the offspring with the highest fitness function is selected from the remaining population, which represents the product-channel magnitude allocation solution being solved.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] Addressing the three core challenges of SMS channel resource allocation in mobile internet marketing scenarios—multi-constraint coupling, multi-objective collaborative optimization, and scale efficiency bottlenecks—this approach achieves breakthroughs from both the perspectives of technological innovation and business value. Technically, through targeted genetic operator design, business constraints are embedded in the evolutionary mechanism. Dedicated channel restrictions between products and channels, magnitude threshold constraints, and quality of service constraints are explicitly incorporated into the genetic algorithm's encoding and evolutionary process, ensuring a naturally compliant solution space and resolving the inefficient allocation problem caused by conflicting constraints in traditional approaches. Furthermore, a multi-objective optimization function is designed as the genetic algorithm's fitness function, overcoming the limitations of static ranking methods, which are unable to balance multi-objective conflicts. On the business side, these technological innovations enable automated and intelligent allocation of SMS channel resources, reducing the manual configuration cycle from hours to minutes, significantly reducing operating costs, and helping enterprises achieve the dual goals of cost reduction, efficiency improvement, and compliant operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is an overall flow chart of a method for intelligently allocating SMS channel resources with multi-objective and multi-constraint coupling in an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of the estimated revenue of a product channel in an embodiment of the present invention;

[0049] Figure 3 A schematic diagram of initializing a genetic algorithm population in an embodiment of the present invention;

[0050] Figure 4 Schematic diagram of 500 rounds of iteration results of the genetic algorithm population in an embodiment of the present invention;

[0051] Figure 5 A schematic diagram of algorithm iteration visualization in an embodiment of the present invention;

[0052] Figure 6 Schematic diagram of the convergence process of the genetic algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and drawings. The contents mentioned in the embodiments are not intended to limit the present invention.

[0054] like Figure 1 As shown, this embodiment provides a method for intelligently allocating SMS channel resources based on multi-objective and multi-constraint coupling, including the following steps:

[0055] S1. Obtain the data source of SMS channel resources;

[0056] S2. Obtain product-related configurations from the data source and convert them into triple constraint equations through product modeling;

[0057] S3, obtain channel-related configuration from the data source and convert it into a six-tuple constraint equation through channel modeling;

[0058] S4. Model the product and channel allocation plan and constraints, and construct the objective function; the SMS channel resource allocation problem is transformed into a multi-constraint and multi-objective optimization problem.

[0059] S5. Initialize the population of the improved genetic algorithm according to the basic constraints of products and channels;

[0060] S6. Execute several rounds of selection, crossover, and mutation operators iteratively to approach the global optimal solution, and select the individual with the largest fitness as the final allocation solution.

[0061] Product Modeling:

[0062] The product triple is defined as (i,Qi ,R i ), where: i∈I is the unique identifier of the product; Q i ≥0 is the total marketable quantity of the product (unit: piece); R i ≥0 is the expected revenue per unit click (unit: yuan / item).

[0063] Channel modeling: SMS channel six-tuple is defined as (j,S j ,T j ,C j ,L j ,U j ), where: j∈J is the unique identifier of the channel; S j ∈[0,1] is the average channel sending success rate; T j ∈[0,1] is the average click rate of the channel; C j ≥0 is the expected cost per unit (unit: yuan / item); L j ≥0 is the lower limit of the channel allocation level (unit: bar); U j ≥L j Assign a magnitude upper limit to the channel (unit: bar).

[0064] Allocation modeling:

[0065] The allocation scheme triple is defined as (i, j, x ij ), where: x ij ∈Z ≥0 represents the magnitude of product i allocated to channel j (unit: bar);

[0066] Constraint modeling includes:

[0067] Upper limit constraints on product marketing scale Channel level lower limit constraint Channel magnitude upper limit constraint Non-negativity constraints: Channel availability constraints where Y ’ i represents the set of available channels for product i.

[0068] Constructing objective functions: Designing different optimization objective functions according to different goals, including: Maximizing total benefits: Maximize delivery success rate and click-through rate: Multi-objective equilibrium optimization: In actual application scenarios, it can be flexibly adjusted according to business objectives.

[0069] Coding: The product set I and channel set J have been defined above, and the allocation scheme triple is defined as (i, j, xij ), then the magnitude distribution scheme of all products on all channels can be defined as a matrix x, where rows represent channels and columns represent products, x ij represents the magnitude of the product allocated to that channel. Each matrix x represents a possible allocation scheme, and the set of all x's constitutes X, which is the algorithm's solution space. Therefore, the matrix x is used for encoding individual products, and the process of finding the optimal solution is to traverse the solution space and find the optimal product-channel magnitude allocation scheme.

[0070]

[0071] Determining the channel selection and magnitude distribution scheme is to solve the function:

[0072]

[0073] Initialize the population of the improved genetic algorithm:

[0074] First, set the unavailable channel level to 0;

[0075] Then, for the remaining channels, the double mean method is used to generate random numbers. Under this product, the magnitude assigned to each channel is a random number between 1 and the mean of the remaining magnitudes (which must satisfy the non-negative constraint).

[0076] The final channel obtains all remaining levels, ensuring that the average of each random amount is equal and that the sum equals the total available level for the product. For each product (each column), the above method is used for random initialization to obtain an alternative allocation plan x'. This is then summed row by row, and the row sum is tested to see if it falls between the upper and lower limits of the available level for the corresponding channel. If the test passes, the alternative plan is included in the initial population; if not, the randomization is repeated until an alternative plan that meets all constraints is generated.

[0077] The upper limit constraint on the product marketing level requires that the sum of each column is exactly equal to the product available level Q i ;

[0078] The channel level constraint requires that the sum of each row is within the channel level lower limit L j and the upper limit of the channel magnitude U j between;

[0079] The non-negativity constraint requires that every x ij All are greater than or equal to 0;

[0080] The product channel availability constraint will make some x ij = 0. Since the product available level constraint requires the sum to be equal, during the population initialization process.

[0081] The selection operators include the elite selection algorithm and the roulette wheel algorithm. The elite selection strategy will directly copy some individuals with the highest fitness to the next generation, which helps to retain the currently found optimal solution.

[0082] Roulette wheel selection is a fitness-based selection method, where the probability of each individual being selected is proportional to its fitness; this means that individuals with higher fitness have a greater chance of being selected. During each iteration, an empirical selection algorithm first retains the upper 1 / 3 of the population's high-quality individuals. The entire population is then subjected to crossover and mutation, and the roulette wheel algorithm selects individuals from the upper 2 / 3 of the population from the resulting evolution.

[0083] Crossover operator (within-group crossover): Each time a crossover occurs, two channels are randomly selected. Within these two rows, multiple crossover points are randomly selected and swapped to generate new offspring. After all points have been swapped, the sum is recalculated by row to verify whether the upper and lower limits of the channel's available magnitude are met. If so, the crossover is complete; if not, the random selection is repeated.

[0084] Because products must strictly meet the constraint of equal total volume, intra-group crossover must occur between rows. As shown in the following formula, rows p and q are randomly selected, and positions 1 and i are further randomly swapped.

[0085]

[0086] Mutation operator: The change in the magnitude of each product's distribution across different channels is manifested as an increase in the magnitude of one channel, followed by a decrease in the magnitude of another channel. After all points have been mutated, the sum is recalculated by row to verify whether the upper and lower limits of the available magnitude of the channel are met. If so, the mutation is complete; if not, the randomization is repeated.

[0087] Since the product needs to strictly meet the constraint of equal total level, the variation occurs within the column, as shown in the following formula: first, randomly select column c for variation, then randomly select points c1 and c2 for exchange, and then randomly generate the variation k, and finally randomly select x c1 、x c2 Increase or subtract k to complete the mutation.

[0088]

[0089] Evolutionary Process: After initializing the population based on the basic constraints for products and channels, several rounds of crossover, mutation, and selection operators are repeated until the iteration limit is reached or no further changes occur between iterations. At this point, the offspring with the highest fitness function is selected from the remaining population, which represents the product-channel magnitude allocation solution being solved.

[0090] To illustrate the distribution effect of this method, five products and five alternative SMS channels are used here. For the above products and channels, the channel sending success rate, channel click rate, product estimated revenue and other indicators of the past 30 days are obtained (such as Figure 2 (as shown in the figure), and the average is calculated as the basic indicator for products and channels. To simplify the analysis, the success rate, click-through rate, and estimated product revenue are linearly multiplied to calculate the revenue coefficient for each level. The potential revenue generated by a product allocated to a certain level in a channel is the allocated level multiplied by this coefficient.

[0091] The constraints are as follows: the minimum level assigned to each product in each channel must be no less than 1,000. The maximum levels for channels 1, 2, and 5 must not exceed 60,000, 80,000, and 80,000, respectively. The total level of products is set to 100,000. The optimization objective is to maximize total revenue, meaning the genetic algorithm's fitness function is the sum of the revenue generated by all products across all channels.

[0092] During the execution of the genetic algorithm, the population is first randomly initialized. Here, the population size is set to 1000 and the number of iterations is set to 1000. The initialized individuals are as follows: Figure 3 and 4 As shown in the figure, each channel has a magnitude assigned. It can be observed that for channels 1, 2, and 5, where a magnitude cap is set, the total magnitude assigned does not exceed the constraint. For channel 4, where no magnitude cap is set, the total magnitude assigned is approximately 200,000. The sum of each column satisfies the total product magnitude constraint and the non-negative constraint. The initialization scheme meets expectations.

[0093] After the population is initialized, it enters the iteration phase, cyclically using crossover, mutation, and selection operators to select the best offspring. The iterative process is as follows: Figure 5 As shown, the algorithm convergence effect is as follows Figure 6 As shown in Figure 2. It can be observed that the distribution of magnitudes gradually changes from the initial random disorder to the product channel combination with the highest return. In this process, the total maximum return also gradually increases. After 500 rounds of iteration, the algorithm has achieved a good convergence effect. Figure 3As shown, it can be verified that, due to the constraint of the lower limit of the product channel magnitude, the lower limit of the magnitude allocated to each product in each channel is not less than 1000; the magnitude upper limits of channels 1, 2, and 5 do not exceed 60,000, 80,000, and 80,000, respectively; in the statistical profit coefficient, product 4 will obtain the maximum profit on channel 4, and the actual allocation result is also in line with this expectation; in addition, product 1 performs best on channel 2, product 3 performs best on channel 5, and product 5 performs best on channel 1, so the main magnitudes of these three products are allocated to the best channels. However, due to the magnitude constraints of channels 1, 2, and 5, product 2 can no longer allocate more magnitudes on these three channels, so product 2 is mainly allocated to channel 3. According to the above analysis process, it can also be seen that the method proposed by the present invention can achieve intelligent allocation of SMS channel resources under the coupling of multiple objectives and multiple constraints.

[0094] Compared with the prior art, the present invention has the following beneficial effects:

[0095] Addressing the three core challenges of SMS channel resource allocation in mobile internet marketing scenarios—multi-constraint coupling, multi-objective collaborative optimization, and scale efficiency bottlenecks—this approach achieves breakthroughs from both the perspectives of technological innovation and business value. Technically, through targeted genetic operator design, business constraints are embedded in the evolutionary mechanism. Dedicated channel restrictions between products and channels, magnitude threshold constraints, and quality of service constraints are explicitly incorporated into the genetic algorithm's encoding and evolutionary process, ensuring a naturally compliant solution space and resolving the inefficient allocation problem caused by conflicting constraints in traditional approaches. Furthermore, a multi-objective optimization function is designed as the genetic algorithm's fitness function, overcoming the limitations of static ranking methods, which are unable to balance multi-objective conflicts. On the business side, these technological innovations enable automated and intelligent allocation of SMS channel resources, reducing the manual configuration cycle from hours to minutes, significantly reducing operating costs, and helping enterprises achieve the dual goals of cost reduction, efficiency improvement, and compliant operations.

[0096] The above describes in detail the method for intelligently allocating SMS channel resources for multi-objective, multi-constraint coupling provided by this application. The description of the specific embodiments is intended only to facilitate understanding of the method and core concepts of this application. It should be noted that those skilled in the art may make various improvements and modifications to this application without departing from the principles of this application, and such improvements and modifications fall within the scope of protection of the claims of this application.

Claims

1. A method for intelligent allocation of SMS channel resources based on multi-objective and multi-constraint coupling, characterized in that: Including steps: S1. Obtain the data source of SMS channel resources; S2, obtain product-related configurations from the data source and convert them into triple constraint equations through product modeling; S3, obtain channel-related configuration from the data source and convert it into a six-tuple constraint equation through channel modeling; S4. Model the product and channel allocation schemes and constraints and construct the objective function; S5. Initialize the population of the improved genetic algorithm according to the basic constraints of products and channels; S6. Execute several rounds of selection, crossover, and mutation operators iteratively to approach the global optimal solution, and select the individual with the largest fitness as the final allocation solution.

2. The method for intelligently allocating short message channel resources based on multi-objective and multi-constraint coupling according to claim 1, characterized in that: Product Modeling: The product triple is defined as (i,Q i ,R i ), where: i∈I is the unique identifier of the product; Q i ≥0 is the total marketable amount of the product; R i ≥0 is the expected revenue per unit click.

3. The method for intelligently allocating short message channel resources based on multi-objective and multi-constraint coupling according to claim 2, characterized in that: Channel modeling: SMS channel six-tuple is defined as (j,S j ,T j ,C j ,L j ,U j ), where: j∈J is the unique identifier of the channel, S j ∈[0,1] is the average channel sending success rate, T j ∈[0,1] is the average click rate of the channel, C j ≥0 is the expected cost of unit level, L j ≥0 is the lower limit of the channel allocation level, U j ≥L j Assign a magnitude cap to the channel.

4. The method for intelligently allocating short message channel resources based on multi-objective and multi-constraint coupling according to claim 3, characterized in that: Allocation modeling: The allocation scheme triple is defined as (i, j, x ij ), where: x ij ∈Z ≥0 represents the magnitude of product i allocated to channel j; Constraint modeling includes: Upper limit constraints on product marketing scale Channel level lower limit constraint Channel magnitude upper limit constraint Non-negativity constraints: Channel availability constraints where Y' i represents the set of available channels for product i.

5. The method for intelligently allocating short message channel resources based on multi-objective and multi-constraint coupling according to claim 4, characterized in that: Constructing objective functions: Designing different optimization objective functions according to different goals, including: Maximizing total benefits: Maximize delivery success rate and click-through rate: Multi-objective equilibrium optimization:

6. The method for intelligently allocating short message channel resources based on multi-objective and multi-constraint coupling according to claim 5, characterized in that: Initialize the population of the improved genetic algorithm: First, set the unavailable channel level to 0; Then, for the remaining channels, the double mean method is used to generate random numbers. Under this product, the magnitude assigned to each channel is a random number between 1 and the mean of the remaining magnitudes. The last channel obtains all remaining levels, thus ensuring that the average value of each random amount is equal and the sum is equal to the total available level of the product.

7. The method for intelligently allocating short message channel resources based on multi-objective and multi-constraint coupling according to claim 5, characterized in that: The selection operators include the elite selection algorithm and the roulette wheel algorithm. The elite selection strategy will directly copy some individuals with the highest fitness to the next generation, which helps to retain the currently found optimal solution. Roulette wheel selection is a fitness-proportional selection method, in which the probability of each individual being selected is proportional to its fitness; Crossover operator: Each time a crossover occurs, two channels are randomly selected. Within these two rows, multiple crossover points are randomly selected and swapped to generate new offspring. After all points have been swapped, the sum is recalculated by row to verify whether the upper and lower limits of the available channel magnitude are met. If so, the crossover is complete; if not, the random selection is repeated. Mutation operator: The change in the magnitude of each product on different channels is manifested as an increase in the corresponding magnitude of a channel, and a decrease in the corresponding magnitude of another channel. After all points are mutated, the sum is re-calculated by row to verify whether the upper and lower limits of the available magnitude of the channel are met. If so, the mutation is completed; if not, the randomization is repeated.

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