# Task Scheduling for Federated Learning in Edge Cloud Computing Environments by Using Adaptive-Greedy Dingo Optimization Algorithm and Binary Salp Swarm Algorithm

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## Abstract

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## 1. Introduction

- We propose an adaptive dingo optimization algorithm (DOA) based on greedy strategies to search for the optimal solution to the PA problem, called AGDOA. The DOA incorporates a greedy algorithm, to optimize the initial value of the DOA, which improves the convergence speed. It also makes its parameters adaptively adjusted according to the convergence speed of the algorithm, to prevent it from falling into a local optimum;
- We advocate utilizing a binary salp swarm algorithm (SSA) method, known as BSSA, for the JRORS problem. We can use our approach for federated learning tasks in edge cloud computing environments;
- Simulations showed that the individual improvements of AGDOA significantly improved on the original algorithm, in terms of optimization results and convergence speed, while the search results outperformed the traditional algorithm. BSSA had a superior performance compared to the conventional algorithm for different numbers of mobile users, different workloads, and different configurations.

## 2. Related Work

## 3. Preliminaries and Definitions

#### 3.1. Network Architecture

#### 3.2. Definition of JRORS

#### 3.3. Definition of PA

## 4. Proposed Approach

#### 4.1. BSSA Algorithm

#### 4.1.1. SSA Model

Algorithm 1: Salp Swarm Algorithm (SSA) |

Input: ub, lbOutput: fitness |

1: xi ←initial salp population considering ub and lb 2: function SSA()3: while end condition is not satisfied do4: Calculate the fitness of each search agent (salp) 5: Set F as the food source 6: for each salp (${x}_{i}$) do7: if The salp population is in the top half then8: Update the position of the leading salp using Equation (7) 9: else10: Update the position of the follower salp using Equation (8) 11: end if12: end for13: end while14: return F 15: end function |

#### 4.1.2. Proposed BSSA Algorithm

Algorithm 2: BSSA |

Input: user_profile , na_min, na_max, max_lter, NOutput: fval_BSSAInitialize parameters |

1: lb ← 0 2: ub ← 1 3: thres ← 0.5 4: max_lter ← 600 5: convlter ← 0 6: dim ← length(user_profile) 7: Q ← 0.7 8: beta1 ← −2 + 4 × rand() 9: beta2 ← −1 + 2 × rand() 10: nalni ← 2 11: na ← round(na_min + (na_max − na_min) × rand()) 12: while t <= max_lter do13: for i ← 1 to N do14: Calculate fitness fit(i) using JRORS function 15: Negate fit(i) 16: if fit(i) > fitF then17: Set Xf = X(i,:) and fitF = fit(i) 18: End if19: End for20: Update X as Leader Salp or Follower Salp 21: Set curve(t) ← fitF 22: Increment t 23: End while24: Convert binary positions to feature subsets 25: Determine Sf, Nf based on Xf 26: Calculate sFeat from user_profile and Sf 27: return fval_BSSA ← fitF |

- Initialize the population. Within the upper bound 1 and lower bound 0 of the search space, a salp swarm of size N × D whose position is binary is randomly initialized;
- Calculate the initial fitness. According to Equation (1), the fitness values of N salps in the JRORS problem are calculated;
- Choose food. The salp swarm is sorted according to the fitness value, and the position of the salp swarm with the best fitness in the first place is set as the current food position;
- Choose leaders and followers. After the food location is selected, there are N − 1 remaining salps in the group, and according to the ranking of the salp groups, the salps in the first half are regarded as leaders and the rest as followers;
- Location update. First, the position of the leader is updated according to Equation (7), and then the position of the follower is updated according to Equation (8);
- Calculate the fitness. Compute the fitness of the updated population. The updated fitness value of each individual salp sheath is compared with the fitness value of the current food. If the fitness value of the updated salp sheath is higher than that of the food, the salp sheath position with the higher fitness value is taken as the new food position;
- Repeat steps 4–6 until a certain number of iterations is reached, and the current food position is output as the estimated position of the target.

#### 4.2. AGDOA Algorithm

#### 4.2.1. DOA Model

#### 4.2.2. DOA Considering Greedy Strategies

Algorithm 3: Greedy Initialization |

Input: alloted_bs, U, puntOutput: initial_profile Initialize parameters: |

1: initial_profile ← Create a matrix of size (|U| × |n|) with initial values as pmax 2: function greedy_initialization(alloted_bs, U, punt)3: for each user u in U do4: Get the current allocated base station index n for user u 5: Set initial_profile[u,n] to punt[u,n] 6: end for7: return initial_profile8: end function |

#### 4.2.3. Proposed AGDOA Algorithm

Algorithm 4: Adjust Parameters Adaptively |

Input: Max_iter, Curve, tol, max_counter, vMinOutput: Adjusted value of na based on adaptive mechanism |

1: tol_counter ← 0 2: for t ← 1 to Max_iter do3: Calculate vMin for current iteration 4: if t > 1 then5: Calculate diff_vMin = abs(Curve(t) − Curve(t + 1)) 6: if diff_vMin < tol then7: Increase tol_counter by 1 8: else9: Reset tol_counter to 0 10: if tol_counter >= max_counter then11: Decrease na 12: else13: Increase na 14: end for15: return na |

Algorithm 5: AGDOA |

Input: Max_iter, Curve, conver_tol, conver_counter, na_min, na_maxOutput: vMinInitialize parameters |

1: threshold ← 0.005 2: converged ← false 3: consecutive_iterations ← 10 4: iteration_count ← 0 5: convlter ← 0 6: P ← 0.5 7: Q ← 0.7 8: beta1 ← −2 + 4 × rand() 9: beta2 ← −1 + 2 × rand() 10: nalni ← 2 11: na ← round(na_min + (na_max − na_min) × rand()) 12: Positions ← initialize from Algorithm 313: for each position i in Positions do14: Calculate Fitness(i) 15: end for16: for each iteration t from 1 to Max_iter do17: for each agent r from 1 to SearchAgent_no do18: sumatory ← 0 19: if random number() < P then20: Calculate sumatory using Attack function 21: if random number() < Q then 22: Update Agent position using strategy for group attack by Equation (9) 23: else24: Update agent position using strategy for persecution by Equation (10) 25: end if26: else27: Update agent position using strategy for scavenging by Equation (11) 28: end if29: if survival rate is below 0.3 then30: Execute survival process to update agent position by Equation (12) 31: end if32: Calculate Fnew 33: if Fnew <= Fitness(r) then34: Update agent position and fitness value 35: end if36: if Fnew <= vMin then37: Count and update convlter 38: Update theBestVct and vMin 39: end if40: end for41: Update na by Algorithm 442: end for43: return vMin |

- Use Algorithm 3 to initialize the dingo population position through the greedy strategy;
- Calculate the survival probability;
- If the survival probability is greater than the set point, jump to step 4, otherwise jump to step 9;
- If the random value is less than P, jump to step 5, otherwise jump to step 8;
- If the random value is less than Q, jump to step 6, otherwise jump to step 7;
- Perform a group attack according to Equation (9) to update the agent location;
- Perform individual persecution according to Equation (10) to update the agent location;
- Perform the clearance strategy according to Equation (11) to update the agent location;
- Update the position of the group with low survival rate according to Equation (12);
- Update the fitness value and the agent location;
- If the maximum number of iterations is not reached, update the adaptive parameters according to Algorithm 4 and repeat steps 2–10, otherwise output the optimal fitness;

## 5. Experimental Setup

#### 5.1. Simulation Settings

#### 5.2. Comparative Experiments

#### 5.2.1. Comparative Experiments of BSSA

- Northern Goshawk Algorithm (NGO): NGO is a relatively new algorithm that has the advantage of diverse search strategies that may help to better explore the solution space [13];
- Genetic Algorithm (GA): The GA performs well in dealing with discrete problems and can effectively represent and manipulate discrete decision variables through the use of binary or integer coding [38].
- Binary Particle Swarm Optimization Algorithm (BPSO): BPSO is suitable for discrete optimization problems and it can represent the decision variables of the problem in binary [39].

#### 5.2.2. Comparative Experiments with AGDOA

- Greedy Particle Swarm Optimization (GPSO): The PSO application has advantages for multivariate problems and is suitable for solving PA problems involving power allocation decisions among multiple mobile users and multiple base stations. Meanwhile, the initialization of the particle swarm was optimized using a greedy strategy to obtain GPSO [40];
- Simulated Annealing PA: Simulated annealing (SA) is suitable for complex problems and can effectively solve discrete NP-hard problems [41];
- Subgradient-based non-cooperative game model (NCGG): the NCGG algorithm is usually used to solve the problem of optimal decision making for multiple participants in a game, and is suitable for optimizing the multi-user PA problem [42].

#### 5.3. Performance Metrics

#### 5.3.1. Convergence Speed

#### 5.3.2. System Response Rate

#### 5.3.3. Scheduling Dominance Degree (SDD)

## 6. Performance Evaluation and Analysis

#### 6.1. Performance of BSSA

#### 6.1.1. Impact of the Number of Mobile Users

#### 6.1.2. Impact of Request Workloads

#### 6.1.3. Impact of Request Workload Configuration

#### 6.2. Performance of AGDOA

#### 6.2.1. Ablation Experiments

#### 6.2.2. Energy Consumption vs. Number of Mobile Devices

#### 6.2.3. Convergence Properties of AGDOA

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**(

**a**) The overall variation in the welfare of each algorithm with different numbers of mobile users; (

**b**) the overall results of the system response rate of each algorithm with different numbers of mobile users; (

**c**) the overall results of the SSD of each algorithm with different numbers of mobile users.

**Figure 4.**(

**a**) The overall change in welfare for each algorithm when changing the request workload for different numbers of mobile users; (

**b**) the overall results in SSD for each algorithm when changing the request workload for different numbers of mobile users.

**Figure 5.**The result of the experiment under u = 40. (

**a**) The overall welfare results for each algorithm at different wq; (

**b**) the variation in SDD for each algorithm at different wq.

**Figure 6.**The result of the experiment under u = 100. (

**a**) The overall welfare results for each algorithm at different wq; (

**b**) the variation in SDD for each algorithm at different wq.

**Figure 7.**(

**a**) The overall welfare results for each algorithm with different Iq in the u = 40 condition; (

**b**) the overall welfare results for each algorithm with different Iq in the u = 80 condition.

**Figure 8.**A direct comparison of the energy consumption results of the different algorithms as the number of iterations increased. (

**a**) DOA versus GDOA; (

**b**) DOA versus ADOA; (

**c**) GDOA versus AGDOA; (

**d**) DOA, GDOA, ADOA, AGDOA.

**Figure 10.**(

**a**) Variation in energy consumption with the number of iterations when u = 12 and n = 3; (

**b**) variation in energy consumption with the number of iterations when u = 40 and n = 10.

Symbol | Description |
---|---|

${\overrightarrow{x}}_{i}\left(t+1\right)$ | New location for dingoes |

$\overrightarrow{{\phi}_{k}}\left(t\right)$ | Subset of search agents |

$\overrightarrow{{x}_{i}}\left(t\right)$ | Current search agent, i.e., subset of wild dogs being attacked |

$\overrightarrow{{x}_{*}}\left(t\right)$ | Iteration of the best subset of dingoes so far |

$\overrightarrow{{x}_{{r}_{1}}}\left(t\right),\overrightarrow{{x}_{{r}_{2}}}\left(t\right)$ | Randomly selected ${r}_{1}$, ${r}_{2}$ search agent, i.e., subset of dingoes, where ${r}_{1}\ne i$ |

$\mathrm{SizePop}$ | Total size of the dingo population |

$\sigma $ | Randomly generated binary numbers, $\sigma \u03f5\left\{0,1\right\}$ |

${\beta}_{1},{\beta}_{2}$ | Randomly generated scale factor |

${r}_{1},{r}_{2}$ | Random numbers generated from [1, maximum search agent size] with ${r}_{1}\ne {r}_{2}$; $\overrightarrow{{x}_{{r}_{1}}}\left(t\right)$ |

Parameter | Value |
---|---|

Number of Mobile Users u | {12,20,32,40,52,60,72,80,92,100} |

Number of Micro-BSs n | {3,5,8,10,13,15,18,20,23,25} |

The fixed bandwidth B | 20 (MHz) |

The fixed height of BSs H | 10 (m) |

Workload of request wq | 600–1000 (MHz) |

Input data of request lq | 300–1500 (KB) |

Ideal delay of request q Tgq | 0.5 ± 0.1 (s) |

Tolerable delay of request q Tbq | Tgq + [0.1,0.15] (s) |

Maximum transmission power for mobile users Pmax | 5 (w) |

Background Gaussian noise power Sig | −100 (dBm) |

Average power consumption of microbase station Pmi | 7500 (w) |

Average power consumption of macrobase station Pma | 15,000 (w) |

The computing power of edge servers Rmi | 70 (GHz) |

Computing power of the cloud server Rma | 140 (GHz) |

Algorithm | Number of Mobile Users | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

12 | 20 | 32 | 40 | 52 | 60 | 72 | 80 | 92 | 100 | |

DOA | 166 | 75 | 62 | 91 | 94 | 119 | 95 | 159 | 165 | 127 |

ADOA | 125 | 69 | 97 | 69 | 76 | 111 | 90 | 110 | 142 | 142 |

GDOA | 71 | 66 | 78 | 77 | 82 | 80 | 125 | 99 | 102 | 146 |

AGDOA | 57 | 53 | 51 | 66 | 34 | 66 | 71 | 89 | 80 | 74 |

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## Share and Cite

**MDPI and ACS Style**

Cai, W.; Duan, F.
Task Scheduling for Federated Learning in Edge Cloud Computing Environments by Using Adaptive-Greedy Dingo Optimization Algorithm and Binary Salp Swarm Algorithm. *Future Internet* **2023**, *15*, 357.
https://doi.org/10.3390/fi15110357

**AMA Style**

Cai W, Duan F.
Task Scheduling for Federated Learning in Edge Cloud Computing Environments by Using Adaptive-Greedy Dingo Optimization Algorithm and Binary Salp Swarm Algorithm. *Future Internet*. 2023; 15(11):357.
https://doi.org/10.3390/fi15110357

**Chicago/Turabian Style**

Cai, Weihong, and Fengxi Duan.
2023. "Task Scheduling for Federated Learning in Edge Cloud Computing Environments by Using Adaptive-Greedy Dingo Optimization Algorithm and Binary Salp Swarm Algorithm" *Future Internet* 15, no. 11: 357.
https://doi.org/10.3390/fi15110357