A mobile edge computing offloading scheduling method based on predator swarm intelligence evolution

Abstract

A mobile edge computing offloading scheduling method based on predator swarm intelligence evolution. The method is a model strategy that optimizes time delay, energy consumption and cost together, which is closer to the cost consideration in the real scene. Chaos mapping is used to increase population diversity during population initialization, and then the marine predator algorithm combined with the differential evolution algorithm completes the scheduling of task offloading. The mutation advantage of the differential evolution algorithm is used to jump out of local convergence. Compared with other heuristic algorithms, the offloading scheduling method given here can effectively reduce the time delay and power consumption of edge computing offloading. The test results also show that MPA-DE can effectively reduce premature convergence and has good global search ability, and can efficiently handle more dimensional complex NP-complete problems.

Claims

1. A mobile edge computing offloading scheduling method based on predator swarm intelligence evolution, characterized in that... The method includes the following steps: First, initialize the population by calling the logistic chaotic mapping; 2. Calculate the initial fitness and the global optimal solution; 3. Set the maximum number of iterations and initialize the counter; 4. The three-stage search of the Marine Predator Algorithm (MPA); 4.1, the first 1 / 3 of iterations, Brownian motion global search; 4.2 The middle third of the iterations, balancing exploration and development; 4.3, the last 1 / 3 of iterations, partial development; 5. FAD effect + DE enhancement; 5.1 Trigger FAD perturbation and randomly change direction to search for a solution; 5.2 When FAD is not triggered, combine DE mutation to escape local optima; 6. Update the global optimal solution; 7. Output the global optimal solution.

2. The mobile edge computing offloading scheduling method based on predator swarm intelligence evolution as described in claim 1, characterized in that, In step 1, the logistic chaotic mapping is called to initialize the population, that is, the initial population position is randomly generated using the chaotic mapping according to formula (1). Each individual's location is within the search space. , Within this area, the uniformity of the initial solution is enhanced, preventing individuals from concentrating in local regions. (1) in the formula Represents the nth generation of chaotic particles; This represents the chaos coefficient, with a value of 4, indicating that the system is in a completely chaotic state. Represents the (n+1)th generation chaotic particle, used to generate the initial population position. This process generates uniformly distributed chaotic particles through iterative generation of the Logistic chaotic map, and then maps them to the search space boundary. , Within this framework, an initial task unloading scheme population covering the entire space is finally obtained, providing a foundation of evenly distributed and sufficiently diverse initial solutions for subsequent algorithm iterations.

3. The mobile edge computing offloading scheduling method based on predator swarm intelligence evolution as described in claim 1, characterized in that, In step 2, the initial fitness and the global optimal solution are calculated, that is, the fitness value of each individual is calculated, and the individual's quality is evaluated according to the objective function using formula (2), and the current optimal solution Elite is selected. Formula (2) is shown below: (2) This formula is the prey matrix, where : Represents the position component of the i-th prey individual in the j-th dimension, representing the coordinates of the prey in one dimension of the search space; n: Represents the total number of prey individuals, corresponding to the number of rows in the matrix; d: represents the number of dimensions of the search space, corresponding to the number of columns in the matrix. Each prey individual has d dimensions of positional information. First, construct the prey matrix Prey based on formula (2): This step organizes the location information of all prey individuals in matrix form. Each row of the matrix represents a prey individual, and each column corresponds to a dimension of the search space, ensuring that the location information of all prey can be uniformly managed and called. Subsequently, this matrix serves as the foundational data for subsequent iterations: in each iteration, the algorithm updates the individual positions in the prey matrix based on the elite matrix, thereby achieving dynamic exploration of the entire search space.

4. The mobile edge computing offloading scheduling method based on predator swarm intelligence evolution as described in claim 1, characterized in that, Step 3 sets the maximum number of iterations and initializes the counter, i.e., sets the maximum number of iterations. And initialize the iteration counter to t=0; First, set the maximum number of iterations for the algorithm: This step presets an upper limit for iterations based on the complexity of the problem and the computing resources to prevent the algorithm from getting stuck in a meaningless infinite loop. Then, initialize the iteration counter to t=0: This provides an initial benchmark for the accumulation of subsequent iterations and the determination of termination conditions.

5. The mobile edge computing offloading scheduling method based on predator swarm intelligence evolution as described in claim 1, characterized in that, In step 4.1, the first stage of the three-stage search of the Marine Predator Algorithm (MPA), i.e., the first 1 / 3 of the iterations, is a global search using Brownian motion. Individuals are updated using Brownian motion through formulas (3) and (4), simulating the behavior of a predator searching for prey at a long distance. Formulas (2) and (3) are shown below: (3) (4) in the formula Let be the step size of the i-th individual; R is a vector containing uniformly random numbers between 0 and 1. It is a Brownian motion distribution The vector represents a step-by-step multiplication; This represents the global optimal solution corresponding to the i-th individual; This represents the unloading scheme for the i-th individual task; A simulation representing the movement of prey; P is a constant with a value of 0.5; This indicates the process of adjusting the stride length during prey movement; First, the position update step size for each individual is calculated based on formula (3). This step involves determining the location of the globally optimal solution. With the individual's current location The difference, combined with the random coefficient of Brownian motion The perturbation generates a randomized step size, ensuring that the step size is both related to the current optimal information and covers a wider search space; subsequently, the individual position is updated using formula (4): the step size is adjusted. through After secondary randomization, then scaling factor is applied. Adjust the step size and finally superimpose it onto the individual's current position. This allows individuals to perform random walks within the search space; Step 4.2 is the second stage of the three-stage search of the Marine Predator Algorithm (MPA), specifically the middle third of the iterations. It balances exploration and exploitation, employing Brownian / Levy flight with local augmentation (DE). In this stage, the population is divided into two parts: (a) First half of the individuals: Formulas (5) and (6) continue to use Brownian motion / Levy flight updates to maintain global exploration capabilities. Formulas (5) and (6) are shown below: (5) (6) in It is a vector containing random numbers based on the Levy distribution, representing the Levy movement of the predator population; Prey i simulates prey movement using the levy method, adding a step length to the prey's position to simulate its movement; This indicates that the real-time location of the prey is updated randomly based on the current random coefficient R; First, the position update step size for each individual is calculated based on formula (5). This step uses the globally optimal position. Current location of prey The difference, combined with the Levy distribution random vector The perturbation generates a step size with Levy characteristics, ensuring that the step size is both related to the current optimal information and matches the long jump characteristics of Levy flight to cover a wider search space; then the prey position is updated by formula (6): the step size is adjusted. After further randomization by the random coefficient R, the result is superimposed onto the prey's current position. This enables prey to move randomly within the search space in accordance with Levy characteristics; (b) The second half of the individuals: The differential evolution DE operator of formulas (7), (8), and (9) is used for updating: a new solution U is generated by the differential mutation formula and the crossover operation. If the fitness of U is better than that of the original individual, the original individual is replaced. Formulas (7) and (8) are shown below: (7) (8) in the formula It is a mutated individual; , , These are three different individuals randomly selected from the population during the mutation phase; F is the scaling factor, which controls the magnitude of the difference variation; This represents the crossover vector of the i-th individual in the j-th dimension; Indicates a variant individual The component in the j-th dimension; Represents the original individual The component in the j-th dimension; This represents the j-th estimate of a random number generator that generates random numbers between [0, 1]. ∈ (1, 2, ..., D), representing a randomly selected sequence; CR represents the crossover operator, whose value range is [0, 1]. First, the mutation vector is generated based on formula (7). This step involves selecting three different individuals from the population and using a scaling factor F to amplify / reduce the individual differences, generating a mutation vector with population information perturbation. This ensures that the vector is related to the characteristics of existing solutions in the population and can also expand new search directions. Subsequently, the crossover operation is performed using formula (8) to obtain the experimental vector. Using the crossover probability CR as a threshold, combined with the random dimension , will the mutation vector With the original individual vector The dimensions are randomly replaced to achieve the fusion of two types of vector information; After mutation and crossover operations, the differential evolution algorithm compares the trial vector with the target vector in the current population according to the greedy criterion. In the next generation, if the target vector is better, the target vector is selected; if the trial vector is better, the trial vector is selected. The formula is as follows: (9) in Let i represent the i-th individual in the (t+1)-th generation; Represents the fitness function; Based on formula (9), a greedy selection operation is performed: this step is performed using the fitness function. , test vector With the current target vector The fitness values ​​are compared, and if the experimental vector is better, it is retained as the next generation individual; otherwise, the original target vector is used. This selection rule completes the population iterative update: the better vector is determined as the individual in generation t+1. This enables iterative filtering that "retains better solutions and eliminates worse solutions"; Step 4.3 is the third stage of the three-stage search of the Ocean Predator Algorithm (MPA), which is the last 1 / 3 of the iterations. It mainly involves local development. In this stage, the individual updates according to formulas (10) and (11) of the MPA local development formulas to approach the current global optimal solution Elite and strengthen the local search capability. Formulas (10) and (11) are shown below: (10) (11) in The movement of the predator is simulated using the levy method, which adds a step size to the predator's position to simulate its movement, and this helps to update its position; CF is an adaptive parameter that controls the predator's stride length; This represents the predator's step size based on the control factor CF. Perform targeted scaling adjustments; First, the position update step size for each predator is calculated based on formula (10). This step involves determining the globally optimal predator position. Current predator location The difference, combined with the perturbation of the Levy distribution random vector RL, generates a step size with Levy characteristics, ensuring that the step size is both related to the current optimal information and matches the long jump characteristics of Levy flight to expand the exploration range; then the predator's position is updated by formula (11): the step size is changed. After adaptive scaling by the CF control factor, the results are superimposed to the globally optimal position. This enables predators to move in a directional manner within the search space in accordance with Levy characteristics.

6. The mobile edge computing offloading scheduling method based on predator swarm intelligence evolution as described in claim 1, characterized in that, Step 5.1 involves the FAD effect plus DE enhancement. When the FAD perturbation is triggered, a random direction-changing search scheme is employed. In each iteration, individuals may also be affected by the fish swarming effect (FAD) and move to a random region with a certain probability. At that time, use formula (12) to increase population diversity: (12) In the formula, FAD is the probability of the FAD effect with a value of 0.

2. `r` is a binary vector containing an array of values ​​between 0 and 1. If an array value is less than 0.2, the array value changes from 0 to 1; if an array value is greater than 0.2, the array value changes from 1 to 0. `r` is a uniformly distributed random number between 0 and 1. and r1 and r2 are vectors representing the lower and upper bounds of the dimension, respectively, and represent the random exponents of the prey matrix. First, a dual-policy update of the prey position is performed based on formula (12): This step selects different update logics by comparing the random number r with the FAD effect probability of 0.

2. When r ≤ FADs, the control factor CF and boundary vector are used. , A perturbation step size is generated using a random flip vector U. When r > FADs, a step size is generated based on the positional differences of two other random prey, ensuring that the step size possesses both the random exploration capability under boundary constraints and the ability to correlate individual differences within the population. Subsequently, the prey position is updated using this dual-strategy rule: the generated step size is superimposed on the current prey position. This allows for dynamic adjustment of prey within the search space; Step 5.2 is the FAD effect + DE enhancement. When the FAD perturbation is not triggered, the DE mutation is combined to escape the local optimum. In this case, formulas (7), (8), and (9) are used to update the position based on the difference vector of two random individuals, thereby enhancing the ability to escape the local optimum.

7. The mobile edge computing offloading scheduling method based on predator swarm intelligence evolution as described in claim 1, characterized in that, Step 6 is to update the global optimum, that is, after each generation of iteration, the population fitness is re-evaluated and the global optimum Elite is updated. First, after each generation of iteration, the fitness value of all individuals in the population is re-evaluated: this step calculates the current performance of each individual through the fitness function and accurately identifies the best individual in the current population. Subsequently, the best individual is updated to the global optimal solution Elite: if the performance of the newly evaluated best individual is better than the original global optimal solution, the iterative replacement of the global optimal solution is completed; otherwise, the original global optimal solution is retained.

8. The mobile edge computing offloading scheduling method based on predator swarm intelligence evolution as described in claim 1, characterized in that, Step 7 is that when the maximum number of iterations is reached or the preset convergence condition is met, the algorithm terminates and outputs the global optimal solution. First, after each iteration, the algorithm checks whether the termination condition is met: this step will determine whether the current number of iterations has reached the preset maximum number of iterations, or whether the performance of the global optimal solution meets the preset convergence threshold. Then, if the termination condition is met, the algorithm is triggered to terminate: all iteration processes are stopped, and the current global optimal solution Elite is output as the final result. If the conditions are not met, continue to the next iteration.

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