# A Discrete Particle Swarm Optimization Algorithm for Dynamic Scheduling of Transmission Tasks

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## Abstract

**:**

## 1. Introduction

#### 1.1. Related Works

#### 1.2. Contributions

- It is necessary to establish a mathematical model suitable for the DPSO of the DSTT;
- It is necessary to solve the DPSO’s mathematical-description problems of particle position, direction, and velocity.
- It is necessary to design specific particle-update methods.

- We build a mathematical model of the DSTT, including a task model, an evaluation model, an evaluation function, and an output of the Schedule—the mathematical model of the transmission plan—and propose a one-dimensional code to describe the Schedule, making it suitable for the calculation of the DPSO;
- We propose a DPSO to define the particle position, particle-update direction and target definition, and solve the mathematical description of the DPSO for specific problems;
- Based on the basic idea of the DPSO, and taking into account inertia retention, particle best, and global best, we use the probability-selection model to realize the particle update, and we propose random perturbation to improve the diversity of the particle population.

## 2. Preliminaries

**Definition 1.**

#### 2.1. Task Queue

#### 2.2. Value Matrix

#### 2.3. Task-Scheduling Result

#### 2.4. Schedule

#### 2.5. Fitness Function

#### 2.6. Example

## 3. Methodologies

#### 3.1. PSO

#### 3.2. Algorithm Description

- Definition of particle position: in combination with the DSTT and the example, see Formula (15) for the definition of particle position.

- 2.
- Definition of particle-motion direction: in combination with the characteristics of data discretization in DSTT, there is no direct association management between each task. Binary processing is adopted when defining particle-motion direction, that is, each particle-motion direction is each task that can change the equipment, and is recorded as:

- 3.
- Definition of particle-motion target: the velocity displacement is defined as the serial number of the equipment to be replaced by the node representing the motion direction of particles in Schedule. The particle-motion target suitable for the operation of DSTT is defined as ${VT}_{i}$, which is recorded as:

- 4.
- Definition of particle-position update: according to the characteristics of DSTT, the operation of particle-velocity update is to calculate the motion direction of particles and the motion target of particles. The evaluation value of each particle task is calculated according to the particle position, and ${XV}_{i}$ is recorded as:

#### 3.3. Parameter

- According to Table 2, when the number of equipment and time periods is [4, 7], the influence of the parameters on the algorithm results is small. When the PBF is small and the GBF is large, the algorithm’s success rate is high. Taking the IRF of 0.1 as an example, as the PBF increases, the GBF decreases, and the success rate of the algorithm decreases gradually.
- According to Table 3, when the number of equipment and time periods is small [4, 7], the algorithm performance is evaluated by the weighted average of the number of iterations of the algorithm required to reach the global-best solution. The algorithm parameters have a great impact on the number of iterations of the algorithm. Among the parameter groups with a success rate of 100%, the parameter groups (0.2,0.2,0.6) have the lowest number of iterations.
- According to Table 4, the interval between the number of equipment and the number of time periods [4, 12] is considered globally. In the test of fixed iterations, the DPSO only achieves the maximum value of multiple parameters when the number of equipment and the number of time periods are 8. In [9, 12], some different parameter groups achieved maximum values, including (0.3,0.1,0.6), (0.5,0.1,0.4), (0.2,0.1,0.7), and (0.4,0.1,0.5).
- The groups (0.3,0.1,0.6) are better in the iterative-weighting calculation in the previous two comparison tables, but the success rate is slightly lower. The groups (0.2,0.2,0.6)’ weighted-average number of iterations is minimal. In order to ensure the comprehensiveness of the subsequent multi-algorithm experiments, use 5 groups of parameters to carry out experiments in the subsequent comparison experiments of DPSO. The list is in Table 5.

## 4. Experiments

#### 4.1. Comparison Algorithm and Method

#### 4.2. Algorithm Comparison Experiment

#### 4.3. Summary of Experimental Analysis

#### 4.4. Simulation Experiment

- In the simulation experiment of multiple time periods, the evaluation values of the transmission effect for all time periods are averaged. The DPSO improved the evaluation value by 3.012295% compared to the GR, and the DPSO improved the evaluation value by 0.1111146% compared to the IGA.
- In the simulation experiment with a maximum period of 48, the results of the DPSO were better than that of the IGA. In almost 60% of the 100 experiments, the IGA achieved the same results as the DPSO while other results were lower than that of the DPSO. The DPSO improved the evaluation value by 0.11115% compared to the IGA.
- In the simulation experiment with a maximum period of 48, in 100 experiments the average execution time of the DPSO was 3.195 s, and the average execution time of the IGA was 10.388 s. The DPSO improved the execution efficiency by 69.246%.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Parameter | Explain |
---|---|

$m$ | number of Schedule definition periods |

$n$ | number of equipment defined in Schedule |

$p$ | number of Schedule tasks |

${Task}_{k}$ | task of the k-th Schedule, including $<TaFr,Start,Span>$ |

${TaskResult}_{k}$ | data description of the k-th result, including $<Task,TransNo>$ |

${Va}_{ij}$ | evaluation value of the transmitting effect of the i-th equipment in the j-th frequency band |

${FreqBand}_{ij}$ | Schedule node data, frequency code of the i-th equipment working in the j-th time period |

$ScheduleResult$ | The output result of Schedule is composed of p piece of $TransNo$ code values |

Parameter | Number of Equipment and Time Periods | Total | |||||
---|---|---|---|---|---|---|---|

IRF | PBF | GBF | 4 | 5 | 6 | 7 | |

0.8 | 0.1 | 0.1 | 100 | 100 | 100 | 99 | 399 |

0.7 | 0.1 | 0.2 | 100 | 100 | 100 | 100 | 400 |

0.6 | 0.2 | 0.2 | 100 | 100 | 100 | 99 | 399 |

0.6 | 0.1 | 0.3 | 100 | 100 | 100 | 100 | 400 |

0.6 | 0.2 | 0.2 | 100 | 100 | 100 | 99 | 399 |

0.6 | 0.3 | 0.1 | 100 | 100 | 99 | 97 | 396 |

0.5 | 0.1 | 0.4 | 100 | 100 | 100 | 100 | 400 |

0.5 | 0.2 | 0.3 | 100 | 100 | 100 | 100 | 400 |

0.5 | 0.3 | 0.2 | 100 | 100 | 98 | 98 | 396 |

0.5 | 0.4 | 0.1 | 100 | 100 | 97 | 93 | 390 |

0.4 | 0.1 | 0.5 | 100 | 100 | 100 | 100 | 400 |

0.4 | 0.2 | 0.4 | 100 | 100 | 100 | 99 | 399 |

0.4 | 0.3 | 0.3 | 100 | 100 | 100 | 99 | 399 |

0.4 | 0.4 | 0.2 | 100 | 99 | 96 | 90 | 385 |

0.4 | 0.5 | 0.1 | 100 | 99 | 96 | 96 | 391 |

0.3 | 0.1 | 0.6 | 100 | 100 | 100 | 99 | 399 |

0.3 | 0.2 | 0.5 | 100 | 100 | 100 | 97 | 397 |

0.3 | 0.3 | 0.4 | 100 | 99 | 99 | 97 | 395 |

0.3 | 0.4 | 0.3 | 100 | 100 | 97 | 96 | 393 |

0.3 | 0.5 | 0.2 | 100 | 99 | 98 | 94 | 391 |

0.3 | 0.6 | 0.1 | 100 | 99 | 97 | 93 | 389 |

0.2 | 0.1 | 0.7 | 100 | 100 | 100 | 100 | 400 |

0.2 | 0.2 | 0.6 | 100 | 100 | 100 | 100 | 400 |

0.2 | 0.3 | 0.5 | 100 | 99 | 99 | 95 | 393 |

0.2 | 0.4 | 0.4 | 100 | 98 | 98 | 97 | 393 |

0.2 | 0.5 | 0.3 | 100 | 99 | 94 | 92 | 385 |

0.2 | 0.6 | 0.2 | 100 | 95 | 97 | 89 | 381 |

0.2 | 0.7 | 0.1 | 99 | 98 | 89 | 87 | 373 |

0.1 | 0.1 | 0.8 | 100 | 100 | 100 | 99 | 399 |

0.1 | 0.2 | 0.7 | 100 | 100 | 100 | 99 | 399 |

0.1 | 0.3 | 0.6 | 100 | 100 | 98 | 99 | 397 |

0.1 | 0.4 | 0.5 | 100 | 96 | 98 | 94 | 388 |

0.1 | 0.5 | 0.4 | 100 | 96 | 99 | 90 | 385 |

0.1 | 0.6 | 0.3 | 100 | 97 | 95 | 93 | 385 |

0.1 | 0.7 | 0.2 | 99 | 98 | 90 | 89 | 376 |

0.1 | 0.8 | 0.1 | 99 | 96 | 89 | 87 | 371 |

Parameter | Number of Equipment and Time Periods | Average Weighted | |||||
---|---|---|---|---|---|---|---|

IRF | PBF | GBF | 4 | 5 | 6 | 7 | |

0.8 | 0.1 | 0.1 | 224 | 871 | 2655 | 21,824 | 3.9881 |

0.7 | 0.1 | 0.2 | 112 | 599 | 2217 | 10,548 | 2.3223 |

0.6 | 0.2 | 0.2 | 172 | 557 | 1650 | 8722 | 2.3816 |

0.6 | 0.1 | 0.3 | 121 | 591 | 1836 | 5129 | 1.9570 |

0.6 | 0.2 | 0.2 | 113 | 439 | 3923 | 9776 | 2.4696 |

0.6 | 0.3 | 0.1 | 178 | 452 | 3309 | 16,446 | 3.1171 |

0.5 | 0.1 | 0.4 | 149 | 512 | 1569 | 8560 | 2.1828 |

0.5 | 0.2 | 0.3 | 132 | 367 | 1469 | 5336 | 1.7257 |

0.5 | 0.3 | 0.2 | 118 | 432 | 2423 | 11,878 | 2.3078 |

0.5 | 0.4 | 0.1 | 112 | 307 | 6163 | 25,490 | 3.7425 |

0.4 | 0.1 | 0.5 | 122 | 522 | 1749 | 3791 | 1.7931 |

0.4 | 0.2 | 0.4 | 122 | 415 | 1270 | 7374 | 1.8020 |

0.4 | 0.3 | 0.3 | 124 | 334 | 975 | 8476 | 1.7363 |

0.4 | 0.4 | 0.2 | 119 | 780 | 8287 | 35,345 | 5.2982 |

0.4 | 0.5 | 0.1 | 109 | 1033 | 7520 | 21,687 | 4.5165 |

0.3 | 0.1 | 0.6 | 149 | 443 | 1619 | 7191 | 2.0399 |

0.3 | 0.2 | 0.5 | 110 | 453 | 1363 | 10,859 | 2.0050 |

0.3 | 0.3 | 0.4 | 127 | 843 | 3195 | 12,709 | 2.9862 |

0.3 | 0.4 | 0.3 | 104 | 351 | 6735 | 17,436 | 3.3739 |

0.3 | 0.5 | 0.2 | 754 | 628 | 4604 | 19,818 | 6.9327 |

0.3 | 0.6 | 0.1 | 103 | 1049 | 7460 | 22,095 | 4.5122 |

0.2 | 0.1 | 0.7 | 139 | 567 | 1450 | 4326 | 1.9032 |

0.2 | 0.2 | 0.6 | 109 | 415 | 1283 | 3175 | 1.4791 |

0.2 | 0.3 | 0.5 | 120 | 725 | 3347 | 14,749 | 2.9821 |

0.2 | 0.4 | 0.4 | 119 | 1037 | 4929 | 15,402 | 3.6608 |

0.2 | 0.5 | 0.3 | 109 | 554 | 9827 | 28,083 | 4.8906 |

0.2 | 0.6 | 0.2 | 107 | 4385 | 6990 | 37,551 | 8.7769 |

0.2 | 0.7 | 0.1 | 498 | 1632 | 16,425 | 46,448 | 10.6003 |

0.1 | 0.1 | 0.8 | 133 | 455 | 1978 | 5732 | 1.9499 |

0.1 | 0.2 | 0.7 | 115 | 378 | 1600 | 5762 | 1.6963 |

0.1 | 0.3 | 0.6 | 126 | 352 | 4289 | 4313 | 2.1971 |

0.1 | 0.4 | 0.5 | 146 | 2829 | 5560 | 13,826 | 5.6724 |

0.1 | 0.5 | 0.4 | 118 | 1822 | 2081 | 29,446 | 4.7190 |

0.1 | 0.6 | 0.3 | 116 | 3604 | 9047 | 19,192 | 7.3423 |

0.1 | 0.7 | 0.2 | 614 | 2266 | 15,314 | 39,792 | 11.2526 |

0.1 | 0.8 | 0.1 | 612 | 2278 | 18,466 | 36,460 | 11.7022 |

Parameter | Number of Equipment and Time Periods | Total | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

IRF | PBF | GBF | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |

0.8 | 0.1 | 0.1 | √ | √ | √ | 3 | ||||||

0.7 | 0.1 | 0.2 | √ | √ | √ | √ | 4 | |||||

0.6 | 0.2 | 0.2 | √ | √ | √ | 3 | ||||||

0.6 | 0.1 | 0.3 | √ | √ | √ | √ | 4 | |||||

0.6 | 0.2 | 0.2 | √ | √ | √ | 3 | ||||||

0.6 | 0.3 | 0.1 | √ | √ | 2 | |||||||

0.5 | 0.1 | 0.4 | √ | √ | √ | √ | √ | √ | 6 | |||

0.5 | 0.2 | 0.3 | √ | √ | √ | √ | 4 | |||||

0.5 | 0.3 | 0.2 | √ | √ | 2 | |||||||

0.5 | 0.4 | 0.1 | √ | √ | 2 | |||||||

0.4 | 0.1 | 0.5 | √ | √ | √ | √ | √ | √ | 6 | |||

0.4 | 0.2 | 0.4 | √ | √ | √ | 3 | ||||||

0.4 | 0.3 | 0.3 | √ | √ | √ | 3 | ||||||

0.4 | 0.4 | 0.2 | √ | 1 | ||||||||

0.4 | 0.5 | 0.1 | √ | 1 | ||||||||

0.3 | 0.1 | 0.6 | √ | √ | √ | √ | √ | 5 | ||||

0.3 | 0.2 | 0.5 | √ | √ | √ | 3 | ||||||

0.3 | 0.3 | 0.4 | √ | 1 | ||||||||

0.3 | 0.4 | 0.3 | √ | √ | 2 | |||||||

0.3 | 0.5 | 0.2 | √ | 1 | ||||||||

0.3 | 0.6 | 0.1 | √ | 1 | ||||||||

0.2 | 0.1 | 0.7 | √ | √ | √ | √ | √ | 5 | ||||

0.2 | 0.2 | 0.6 | √ | √ | √ | √ | 4 | |||||

0.2 | 0.3 | 0.5 | √ | 1 | ||||||||

0.2 | 0.4 | 0.4 | √ | 1 | ||||||||

0.2 | 0.5 | 0.3 | √ | 1 | ||||||||

0.2 | 0.6 | 0.2 | √ | 1 | ||||||||

0.2 | 0.7 | 0.1 | 0 | |||||||||

0.1 | 0.1 | 0.8 | √ | √ | √ | 3 | ||||||

0.1 | 0.2 | 0.7 | √ | √ | √ | 3 | ||||||

0.1 | 0.3 | 0.6 | √ | √ | 2 | |||||||

0.1 | 0.4 | 0.5 | √ | 1 | ||||||||

0.1 | 0.5 | 0.4 | √ | 1 | ||||||||

0.1 | 0.6 | 0.3 | √ | 1 | ||||||||

0.1 | 0.7 | 0.2 | 0 | |||||||||

0.1 | 0.8 | 0.1 | 0 |

Parameter | [4, 7] | [4, 12] | ||||
---|---|---|---|---|---|---|

IRF | PBF | GBF | Success Rate | Weighted Iteration | Maximum Number of Times | |

DPSO1 | 0.5 | 0.1 | 0.4 | 100% | 2.1828 | 6 |

DPSO2 | 0.4 | 0.1 | 0.5 | 100% | 1.7931 | 6 |

DPSO3 | 0.3 | 0.1 | 0.6 | 99.75% | 2.0399 | 5 |

DPSO4 | 0.2 | 0.1 | 0.7 | 100% | 1.9032 | 5 |

DPSO5 | 0.2 | 0.2 | 0.6 | 100% | 1.4791 | 4 |

Algorithm | Explain |
---|---|

ENU | Enumeration algorithm: The global-optimal solution can be obtained by traversing the running chart of all tasks and calculating the evaluation value. With the increase in the number of equipment and time periods, the iteration number increases rapidly and the algorithm’s execution time is long. |

GR | Greedy algorithm: Find out the tasks that can obtain the best allocation among all tasks. According to this principle, until all tasks are allocated, the algorithm’s execution time is stable, the number of algorithm iterations is related to the task period, and the conflicts encountered in the allocation are backtracked [4]. |

IGA | Improved genetic algorithm: Select the elitist-retention strategy, the discontinuous cycle replacement group crossover strategy for crossover, and the overall equipment task switching strategy for mutation. The three parameters are set as the algorithm’s optimal parameter array, with a selection factor = 0.8, a crossover factor = 0.1, and a mutation factor = 0.1. Refer to previous research results for the selection of parameters [3]. |

DPSO | Discrete particle swarm optimization algorithm: The parameters are calculated according to the five sets of parameters in Table 5, and the corresponding statistical calculations are performed. |

Eq. | ENU | GR | IGA | DPSO | ||
---|---|---|---|---|---|---|

[min, max] | Avg. | Stdea. | ||||

4 | 100 | 25 | 100 | [100, 100] | 100 | 0.000000 |

5 | 100 | 8 | 100 | [100, 100] | 100 | 0.000000 |

6 | 100 | 5 | 100 | [99, 100] | 99.8 | 0.447214 |

7 | 100 | 2 | 99 | [98, 100] | 99.6 | 0.894427 |

8 | N/A | 1 | 89 | [99, 100] | 99.8 | 0.447214 |

9 | N/A | 0 | 70 | [92, 99] | 97.2 | 2.949576 |

10 | N/A | 0 | 62 | [93, 100] | 97.8 | 2.774887 |

11 | N/A | 0 | 35 | [93, 98] | 96.8 | 2.167948 |

12 | N/A | 0 | 39 | [83, 97] | 93.2 | 5.932959 |

13 | N/A | 0 | 20 | [90, 100] | 94.8 | 3.701351 |

14 | N/A | 0 | 4 | [77, 97] | 88.6 | 8.049845 |

15 | N/A | 0 | 10 | [67, 94] | 87.4 | 11.436783 |

Total | 400 | 41 | 728 | [1124, 1182] | 1155 | 26.870058 |

Eq. | GR | IGA | DPSO | ||
---|---|---|---|---|---|

[min, max] | Avg. | Stdea. | |||

4 | 0.815214 | 0.838134 | [0.838134, 0.838134] | 0.838134 | 0.000000 |

5 | 0.874183 | 0.895642 | [0.895642, 0.895642] | 0.895642 | 0.000000 |

6 | 0.856763 | 0.883459 | [0.883458, 0.883459] | 0.8834588 | 0.000000 |

7 | 0.899497 | 0.916141 | [0.916114, 0.916156] | 0.9161528 | 0.000007 |

8 | 0.892468 | 0.913266 | [0.91355, 0.913556] | 0.9135548 | 0.000003 |

9 | 0.858319 | 0.881545 | [0.882189, 0.882289] | 0.8822652 | 0.000043 |

10 | 0.874637 | 0.898784 | [0.89988, 0.899956] | 0.8999352 | 0.000031 |

11 | 0.873344 | 0.896935 | [0.898354, 0.898388] | 0.898379 | 0.000014 |

12 | 0.878253 | 0.902085 | [0.903259, 0.90338] | 0.9033514 | 0.000052 |

13 | 0.878391 | 0.914041 | [0.916594, 0.916635] | 0.9166176 | 0.000018 |

14 | 0.904408 | 0.931707 | [0.934612, 0.934725] | 0.9346716 | 0.000048 |

15 | 0.891888 | 0.917394 | [0.920402, 0.920621] | 0.920569 | 0.000094 |

Avg. | 0.874780 | 0.899094 | [0.900205, 0.900242] | 0.9002276 | 0.000018 |

Eq. | IGA | DPSO | ||
---|---|---|---|---|

[min, max] | Avg. | Stdea. | ||

4 | 643 | [105, 132] | 116.4 | 10.0 |

5 | 2692 | [340, 552] | 446.8 | 88.4 |

6 | 7452 | [1674, 2088] | 1812.4 | 179.8 |

7 | 15,095 | [4355, 9186] | 5893.8 | 1963.8 |

8 | 74,431 | [7719, 11,447] | 9395.8 | 1465.2 |

9 | 266,112 | [36,169, 69,736] | 48,312.8 | 13,134.6 |

10 | 421,878 | [42,925, 88,540] | 63,079 | 16,922.1 |

11 | 899,103 | [108,956, 208,574] | 132,676.2 | 42,597.5 |

12 | 1,210,932 | [209,287, 407,190] | 309,613.4 | 90,217.6 |

13 | 2,211,539 | [362,240, 765,968] | 498,789 | 166,816.1 |

14 | 3,241,904 | [493,569, 1,381,226] | 841,163.8 | 328,465.6 |

15 | 4,141,849 | [735,817, 2,595,418] | 1,297,816.8 | 746,327.9 |

Eq. | Availability | Accuracy | Efficiency | Evaluation |
---|---|---|---|---|

ENU | high | N/A | N/A | bad |

GR | low | low | N/A | bad |

IGA | middle | high | low | better |

DPSO | high | high | high | best |

Periods | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|

GR | 0.893972 | 0.901704 | 0.913778 | 0.881862 | 0.879343 | 0.889435 | 0.906143 | 0.884089 | 0.896052 |

IGA | 0.917416 | 0.92164 | 0.934022 | 0.90367 | 0.904581 | 0.907794 | 0.932187 | 0.911542 | 0.920281 |

DPSO | 0.918031 | 0.922333 | 0.935052 | 0.904655 | 0.905095 | 0.909001 | 0.933586 | 0.912695 | 0.921244 |

Periods | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |

GR | 0.893406 | 0.881768 | 0.89654 | 0.907105 | 0.89874 | 0.860929 | 0.864331 | 0.894956 | 0.8873 |

IGA | 0.921019 | 0.910778 | 0.916936 | 0.93331 | 0.920762 | 0.88272 | 0.890827 | 0.921293 | 0.914671 |

DPSO | 0.922169 | 0.911839 | 0.91786 | 0.93453 | 0.921716 | 0.883748 | 0.891933 | 0.922291 | 0.915707 |

Periods | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

GR | 0.885542 | 0.885767 | 0.885219 | 0.87728 | 0.880179 | 0.87955 | 0.852032 | 0.883815 | 0.863596 |

IGA | 0.910287 | 0.912008 | 0.910358 | 0.904637 | 0.912072 | 0.902095 | 0.884231 | 0.909096 | 0.888886 |

DPSO | 0.911239 | 0.913564 | 0.911396 | 0.906042 | 0.912925 | 0.90334 | 0.885226 | 0.910536 | 0.889882 |

Periods | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |

GR | 0.890629 | 0.89359 | 0.857689 | 0.866087 | 0.873645 | 0.883004 | 0.867741 | 0.88413 | 0.867158 |

IGA | 0.915545 | 0.91956 | 0.885552 | 0.889054 | 0.899454 | 0.910442 | 0.890941 | 0.914558 | 0.897373 |

DPSO | 0.916702 | 0.920654 | 0.886297 | 0.89005 | 0.900186 | 0.911575 | 0.891782 | 0.915296 | 0.898685 |

Periods | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 |

GR | 0.862168 | 0.867621 | 0.86952 | 0.848084 | 0.876947 | 0.863869 | 0.875981 | 0.905513 | 0.858482 |

IGA | 0.884312 | 0.896044 | 0.895931 | 0.872597 | 0.907236 | 0.887478 | 0.899854 | 0.930317 | 0.889568 |

DPSO | 0.884925 | 0.896671 | 0.897014 | 0.873367 | 0.908403 | 0.888566 | 0.900728 | 0.931161 | 0.890556 |

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## Share and Cite

**MDPI and ACS Style**

Wang, X.; Yao, W. A Discrete Particle Swarm Optimization Algorithm for Dynamic Scheduling of Transmission Tasks. *Appl. Sci.* **2023**, *13*, 4353.
https://doi.org/10.3390/app13074353

**AMA Style**

Wang X, Yao W. A Discrete Particle Swarm Optimization Algorithm for Dynamic Scheduling of Transmission Tasks. *Applied Sciences*. 2023; 13(7):4353.
https://doi.org/10.3390/app13074353

**Chicago/Turabian Style**

Wang, Xinzhe, and Wenbin Yao. 2023. "A Discrete Particle Swarm Optimization Algorithm for Dynamic Scheduling of Transmission Tasks" *Applied Sciences* 13, no. 7: 4353.
https://doi.org/10.3390/app13074353