Frontiers in Computing and Intelligent Systems 
ISSN: 2832-6024 | Vol. 2, No. 3, 2022 

 

16 

Compute offloading solution to maximize server 
rewards 

Xiaochen Zhu  

College of Automation and Electrical Engineering, Dalian Jiaotong University, Dalian 116028, China 

15506598522@163.com 

 

Abstract: With the development of the Internet of Things, cloud computing can no longer meet the demand, and edge 

computing emerges as the times require. As one of the most critical technologies in edge computing, computing offloading has 

been extensively studied. The research does not aim to minimize computing delay and energy consumption, but to maximize the 

reward of edge computing servers. Considering the scenario of one MEC server and multiple terminal devices, the target problem 

obtained is the two-dimensional 0-1 knapsack problem. In view of basic sine cosine algorithm is difficult to solve the discrete 

target offloading problem, the basic SCA is improved to obtain ISCA, and the offloading problems with 6, 15 and 50 terminal 

devices are solved respectively, compared with other algorithms, the simulation results show that ISCA has better performance, 

better solving ability, it is not easy to fall into local optimum, and the convergence speed is also greatly improved compared with 

SCA. 

Keywords: Edge computing; Compute offloading; Sine cosine algorithm(SCA); MEC server reward; Knapsack problem. 

 

1. Introduction 

With the development of the Internet of Things and 

wireless communication technologies, a large number of 

intelligent application devices have emerged. In many 

application scenarios, intelligent IoT terminal devices often 

need to run and process complex calculations and large 

amounts of data. However, most terminal devices are subject 

to physical constraints. Due to the limitations of size and 

appearance design, it only has limited computing, storage and 

energy resources. The traditional cloud computing solution is 

to offload tasks with intensive computing and high energy 

consumption from the terminal to the cloud for processing, 

but at the same time, the transmission of tasks brings high 

latency which makes it difficult to meet the requirements of 

certain tasks, and edge computing emerges as the times 

require. Edge computing is a supplement to cloud computing. 

Edge servers are closer to the terminal, and cloud services are 

"sinked" to the edge of the network, which can solve the 

problems of long delay in computing offloading and 

occupying too many network resources in cloud computing. 

Edge computing can be applied in Autonomous driving, 

Internet of Things and Industrial Internet, and many other 

fields. 

With the continuous increase of user equipment and the 

increasing amount of computing tasks, how to use edge server 

nodes with limited resources to ensure the quality of service 

for end users has become a hot issue in edge computing. It is 

impossible to place all the tasks of the terminal in the edge 

server for processing. Therefore, it is necessary to use a 

reasonable computing offloading strategy to offload some 

computing tasks to the edge or cloud, and computing 

offloading becomes a key problem. Authors of elaborates the 

research status of computing offloading technology according 

to the goals of offloading decision, coarse-grained and fine-

grained offloading methods, and offloading methods under 

the cooperation of MEC and Device-to-Device technology. 

The existing research results in this field are summarized. 

In order to meet the challenges, mobile edge computing 

deploys edge servers on the WLAN side and offloads some 

computing-intensive tasks to edge servers, thereby shortening 

the distance between computing services and mobile devices, 

and powerful computing capabilities localize computing tasks 

and reduce data transmission cost becomes possible. 

Literature proposes EUAGame, a game theory method that 

expresses the edge user allocation (EUA) problem as a 

potential game, and designs a novel decentralized algorithm 

to find Nash equilibrium in the game, as the EUA problem 

solution. The work proposed joint downlink and uplink edge 

computing offloading and communication and computing 

resource allocation, and then transformed the offload 

optimization problem into minimizing the total delay time of 

the task while saving the energy consumption of mobile 

devices. Authors of conducted research on the High-Altitude 

Balloons (HABs) network scenario in MEC, and proposed a 

federated learning algorithm based on Support Vector 

Machine (SVM) to determine user associations and optimize 

each user's Service sequence and task assignment. Most of the 

existing literature on compute offloading is discussed with the 

goal of minimizing the delay and energy consumption. This 

paper does not consider the delay and energy consumption, 

and focuses on the MEC server to study how to make 

decisions to maximize the rewards of the server. 

2. System Model 

In this paper, we consider an edge computing scenario 

consisting of an MEC server and multiple terminals. The 

computing resources and communication resources of the 

server are limited, and each terminal has different 

requirements for computing resources and communication 

resources. The size of computing resources is measured by the 

number of cpu cycles, and the number of communication 

resources is measured by the number of sub-channels. (C , B) 

represents the computing resources and communication 

resources of the MEC server. Tasks are indivisible, either 

executed locally or fully offloaded to the MEC server for 

execution. (pi , qi) represent the computing resource and 



 

17 

communication resource requirements of the i-th terminal 

task, respectively. When the terminal wants to offload the task 

to the server, it needs to pay a certain reward to the server. 

Due to the preference of the terminal to the server and other 

factors, the reward that each terminal is willing to pay is 

different. Si represents the reward that the i-th terminal is 

willing to pay to the MEC server. In this offloading scenario, 

the constraint of delay is not considered, and it is assumed that 

all terminals meet the general offloading conditions, that is, 

the offloading delay is smaller than the local execution delay. 

Use the variable yi to indicate whether the i-th task is 

offloaded, yi=1 indicates offloading, and yi=0 indicates not. 

 
Figure 1. system architecture 

3. Problem Formulation 

The goal is to let the server reasonably select some 

terminals to obtain the maximum reward under the condition 

of limited resources. The total reward of the server is: 

1

L

i i

i

R y S
=

=                (1) 

The target problem is described as:  

1

max( )
L

i i

i

R y S
=

=              (2) 

s.t. 
1

L

i i

i

y p C
=

              (3) 

1

L

i i

i

y q B
=

                (4) 

The analysis shows that the objective optimization problem 

is a two-dimensional 0-1 knapsack problem. The method to 

solve the problem is discussed below. 

4. Algorithm to Solve the Target 
Problem 

4.1. Dynamic Programming 

Dynamic programming is a more classical method for 

solving the knapsack problem. The implementation is as 

follows: V(L, mL, nL) indicates that the MEC server has 

selected the maximum value obtained by the first L mobile 

terminals, mL indicates the remaining communication 

resources of the MEC server at this time, and nL indicates the 

remaining computing resources of the server. Supposing a 

choice is to be made on the L-th terminal, there are two cases 

for the L-th terminal: 

(1) When the resources required by the terminal are greater 

than the current remaining resources of the server, it is 

impossible for the server to select it for offloading. The total 

reward is the same as that of the options for the first L-1 

terminals, i.e.V(L-1,mL,nL). 

(2) When the remaining resources of the server meet the 

needs of the terminal, assuming that offload is selected, the 

total reward is SL+V (L-1, mL-qL,nL-pL). If you choose not 

to offload, the reward is V (L-1, mL,nL). The final plan is 

determined according to the total reward of the two options. 

So, the state transition equation is: 
( , , ) max{ ( 1, , ), ( 1, , )}j j j j j j j j jV j m n V j m n S V j m q n p= − + − − −

 
The dynamic programming method can obtain the exact 

solution of the problem, but the time and space complexity of 

the algorithm is exponential, and the recursive algorithm will 

lead to solving the common sub-problem more than once, 

which can be achieved when the amount of data is small, but 

when the amount of problem data is large, the solution 

efficiency is very low and it takes a long time to calculate. 

Although the heuristic algorithm cannot guarantee that the 

optimal solution can be obtained, the algorithm has low 

complexity and can obtain the sub-optimal or optimal solution 

of the problem with high efficiency, which meets the 

requirements of the offloading system for algorithm 

efficiency. 

4.2. Sine Cosine Algorithm 

The sine-cosine algorithm is a meta-heuristic algorithm 

based on the characteristics of the sine function and cosine 

function in mathematics. It uses the periodic oscillation of the 

trigonometric function to explore the optimal solution. By 

embedding random parameters and adaptive amplitude 

adjustment, it achieves a balance between global exploration 

and local exploitation. 

In SCA, it is assumed that the population size is N, D-

dimensional solution space, and a set of random initial 

solutions is generated first. Each iteration, the individual 

updates its position according to the following formula: 

1 2 3 4

1 2 3 4

( ) sin( ) | ( ) ( ) |    0.5
( 1)

( ) cos( ) | ( ) ( ) |    0.5

d d d

i id

i d d d

i i

X t r r r P t X t r
X t

X t r r r P t X t r

 +   − 
+ = 

+   − 
(5) 

( )d

iX t
 is the position of the d-th dimension of the i-th 

individual in the t-th generation; 
( )dP t

is the position of the 

d-th dimension of the optimal individual of the t-th generation; 

r2, r3, r4 are random numbers subject to different uniform 

distributions, r2∈[0, 2π], r3∈[0,2], r4∈[0,1]; r1 is a control 

parameter that balances the exploration and exploitation of 

SCA by controlling the amplitude of the sine and cosine 

functions, it is adaptively adjusted by formula (6) 

1

a
r a t

T
= −                   (6) 

a is a constant, T is the maximum number of iterations, and 

t is the current number of iterations. 

4.3. Improved Sine Cosine Algorithm 

Like other intelligent optimization algorithms, the basic 

sine and cosine algorithm has shortcomings such as slow 

convergence speed and poor local exploitation ability. This 

paper adopts the improved sine and cosine algorithm to solve 

the target problem. 

···

MEC server



 

18 

4.3.1. The nonlinear decreasing function adaptively 

adjusts the parameter r1 

Change r1 in a non-linear manner, and r1 is decremented 

using formula (7). The parameter r1 controls the search 

process of the algorithm. In SCA, r1 decreases linearly in the 

entire algorithm iteration cycle. This reduction method is not 

flexible enough, which leads to a relatively rigid process from 

exploration to exploitation of the algorithm, and is out of 

balance in the face of many target problems. The algorithm 

will show the disadvantages of premature or too slow 

convergence. By changing the original linear decreasing 

strategy of r1, the improved SCA algorithm has the stronger 

global exploration ability in the early stage of the iteration, 

and the reduction of r1 is relatively slow to ensure the full 

exploration of the algorithm; in the middle of the iteration, the 

algorithm transitions from exploration to exploitation at a 

relatively fast speed; By the end of the iteration, the 

descending curve of r1 will not be too steep, which better 

takes into account the exploitation of the algorithm. r1 adopts 

such a parameter adjustment scheme to better balance the 

global exploration and local exploitation of SCA. 

1 exp( 10 ( ) )bt
r a

T
=  −              (7) 

 
Figure 2. R1 reduction curve 

Figure 2 is the reduction curve of r1 when a=2, b=5. 

4.3.2. Modify the Location Update Formula 

The sine function sin(r2) and cosine function cos(r2) have 

the same probability of obtaining a positive value as that of 

obtaining a negative value, so the removal of the absolute 

value sign in formula (5) will not affect the overall position 

update, and it can be reduced the complexity of the algorithm, 

so the position update formula is rewritten as: 

1 2 3 4

1 2 3 4

( ) sin( ) ( ) ( )   0.5
( 1)

( ) cos( ) ( ) ( )   0.5

d d d

i id

i d d d

i i

X t r r r P t X t r
X t

X t r r r P t X t r

 +   − 
+ = 

+   − 
(8) 

4.3.3. Crossover Strategy 

Inspired by the chromosomal crossover in genetic 

algorithm, the crossover operation is introduced into ISCA. In 

each iteration, two individuals are randomly selected, and the 

selected two individuals are crossed according to the 

crossover ratio pc. Crossover realizes the exchange of 

information between individuals and improves the diversity 

of the population. 

4.3.4. Discretization and Greedy Repair 

The optimization space of most intelligent optimization 

algorithms is continuous, which is suitable for solving 

numerical continuous optimization problems. The target 

problem of this research is a two-dimensional 0-1KP problem, 

which is a discrete problem. Each dimension of the feasible 

solution can only take 1 or 0, so the continuous solution in the 

original algorithm needs to be converted into a discrete 

solution, that is, the individual should use binary coding. 

The continuous solution is transformed into a discrete 

solution in the following way: a candidate solution in the 

solution space is represented by an ordered vector pair (X, Y), 

where X=(x1,x2,...,xd) is a D-dimensional real vector, 

represents a continuous solution, and Y=(y1,y2,…,yd) is the 

corresponding binary vector, which is the candidate solution 

of the target problem. Taking X∈[-s,s] as the continuous 

solution space of the problem to be sought, we take s=5; Y∈
{0, 1} is the binary solution space corresponding to the target 

problem, and the encoding method of converting the 

continuous solution into the discrete solution is as follows : 

1     sig( )

0    sig( )

i

i

i

if x rand
y

if x rand


= 


         (9) 

Sig () is the sigmoid function, the expression is:  

1
sig( )

1 i
i x

x
e−

=
+

          (10) 

rand∈(0,1) is a random number. 

When the intelligent optimization algorithm solves 0-1KP, 

there will be individuals that do not meet the constraints in the 

iterative process, and methods need to be used to repair these 

individuals. The abnormal individuals are transformed by the 

greedy repair method: the mobile terminals are arranged in 

ascending order of value density, and then the mobile 

terminals that request the MEC server to be offloaded are 

discarded in order, that is, the abnormal individuals are 

checked in order, and the corresponding dimension 0 becomes 

1 until the individual satisfies the constraints. 

4.3.5. Scout bee mutation strategy 

The scout bee strategy in the artificial bee colony algorithm, 

when the individual's continuous stay times n to a certain 

threshold G, still cannot find a better position, it indicates that 

they are trapped in a local optimum. The role of the observer 

bee will transform into a scout bee and a new location will be 

generated randomly. Inspired by this, a mutation strategy of 

scout bees is proposed. When the number of consecutive 

times n that the individual position does not become better 

reaches G, the algorithm mutates it, that is, the original 0 in 

each dimension becomes 1, and 1 becomes 0. The mutation 

ratio is pb. 

4.4. Algorithm Flow 

Step1: Initialization parameters, including population size 

N, space dimension D, number of consecutive stays n, 

threshold G, maximum number of iterations T, and constant a, 

b. 

Step 2: Randomly generate a binary population, and repair 

the individuals that do not meet the constraints. 

Step 3: Calculate the value density of each mobile terminal, 

and sort the mobile terminals according to the calculated 

value density. 

Step4: Calculate the target function value of each 

individual and record the global optimal solution. 

Step5: Calculate r1 according to formula (7). 

Step6: Update the position of the individual according to 

formula (8). 

Step7: Execute the crossover strategy. 

Step8: Execute the scout bee mutation strategy. 

Step9: Greedy Repair. 

Step10: Update the global optimal solution. 

Step11: Is the termination condition met? If satisfied, 

0 20 40 60 80 100

Iteration

0

0.5

1

1.5

2

r1

linear

nonlinear



 

19 

output the optimal solution; otherwise, turn to Step5. 

5. Simulation Results and Discussions 

5.1. Simulation Environment 

The simulation was performed on a laptop with 64bit 

windows10 operating system, Intel(R) Core (TM) i7-6700HQ 

CPU @ 2.6GHz processor, and 8G memory configuration. 

The simulation code was written and run with MATLAB 

R2020b. 

5.2. Problems and Parameter Settings 

Table 1. Parameters of each algorithm 

algorithm parameters 

SCA a=2 

ISCA a=2,b=5,G=4,pc=0.3,pb=0.1 

PSO W=0.9,c1=c2=1,Vmax=6 

GA cp=0.5,mp=0.1 

The population size is N=90, the maximum number of 

iterations is T=100, and each algorithm runs independently 

for 50 times. Particle Swarm Optimization (PSO) prososed in 

and Genetic Algorithm (GA) are used as comparison 

algorithms. 

Table 2. Problem 1: 6 mobile terminals 

(The total amount of computing and communication 

resources of the MEC server are respectively 80,20) 

terminal pay 

computing 

resource 

requirements 

wireless 

resource 

requirements 

1 100 8 3 

2 600 12 6 

3 1200 13 4 

4 2400 64 18 

5 500 22 6 

6 2000 41 4 

5.3. Results 

In Table 6, the evaluation indicators include the average 

optimal value, standard deviation, worst value, best value and 

success rate obtained by running several algorithms 

independently for 50 times. Among them, the average optimal 

value can reflect the solution accuracy and convergence speed 

of the algorithm, the standard deviation is an index to evaluate 

the stability and robustness of the algorithm, and the best 

value and the worst value represent the upper and lower limits 

of the algorithm’s ability to solve problems to a certain extent, 

the success rate reflects the execution efficiency of the 

algorithm to achieve the target result. 

According to Table 6, from the average optimal value 

obtained by several algorithms, on the offloading problem 

with different numbers of terminals, ISCA obtains the largest 

average optimal value. Compared with basic SCA, ISCA has 

a significant convergence speed and solution accuracy. In 

terms of standard deviation, the standard deviation obtained 

by ISCA is the smallest among the three target problems. In 

contrast, the standard deviation of basic SCA has a 

considerable gap, which greatly improves the stability of the 

algorithm; All of them have the ability to solve the problem 

and get the theoretical optimal value. From the worst value 

obtained by each algorithm solving 3 offloading problems 

independently for 50 times, the performance of basic SCA is 

the worst, it’s worst value is the smallest, and the worst value 

of ISCA is the largest. ISCA is more capable of obtaining 

higher quality feasible solutions. 

For simple problems, that is, when the number of mobile 

terminals is small, several algorithms can obtain the optimal 

solution with a success rate higher than 90%, and the success 

rate of ISCA and GA directly reaches 100%. When the 

number of mobile terminals increases to 15, the success rate 

of each algorithm decreases, and when the number of mobile 

terminals is 50, the success rate further decreases, and the 

complexity of the target problem has a significant impact on 

the success rate of the algorithm. The success rate of ISCA is 

always the highest among several algorithms, and the 

reliability of solving the target problem is much better than 

that of SCA. The success rate is not 0, and each algorithm has 

a certain ability to obtain the theoretical optimal solution. 

 

Figure 3. Convergence curves of problem 1 

 

Figure 4. Convergence curves of problem 2 

 

Figure 5. Convergence curves of problem 3 

0 20 40 60 80 100
1000

1500

2000

2500

3000

3500

4000

R
ew

ar
d

Iteration

SCA

ISCA

0 20 40 60 80 100
1500

2000

2500

3000

3500

4000

R
ew

ar
d

Iteration

SCA

ISCA

0 20 40 60 80 100
6000

8000

10000

12000

14000

16000

18000

R
ew

ar
d

Iteration

SCA

ISCA



 

20 

In the above convergence curve, the abscissa is the number 

of iterations, and the ordinate is the server reward. From the 

convergence curve of SCA and ISCA, the convergence speed 

of ISCA is faster than that of SCA. The ability of the 

algorithm to jump out of local optimum in late iterations is 

improved. 

 

Table 3. Problem 2: 15 mobile terminals 

(The total amount of computing and communication resources of the MEC server are respectively 500,110) 

terminal pay 
computing resource 

requirements 

wireless resource requirements 

1 100 8 3 

2 220 24 6 

3 90 13 4 

4 400 80 20 

5 300 70 20 

6 400 80 30 

7 205 45 8 

8 120 15 3 

9 160 28 12 

10 580 90 14 

11 400 130 40 

12 140 32 6 

13 100 20 3 

14 1300 120 20 

15 650 40 5 

Table 4. Problem 3: 50 mobile terminals 

(The total amount of computing and communication resources of the MEC server are respectively 800,650) 

terminal pay 
computing 

resource  

Wireless 

resource  
terminal pay 

computing 

resource  

Wireless 

resource  

1 560 40 16 26 103 5 5 

2 1125 91 92 27 215 10 10 

3 300 10 41 28 81 8 6 

4 620 30 16 29 91 2 4 

5 2100 160 150 30 26 1 7 

6 431 20 23 31 49 3 4 

7 68 3 4 32 420 10 12 

8 328 12 18 33 316 42 8 

9 47 3 6 34 72 6 4 

10 122 18 2 35 71 4 3 

11 322 9 12 36 49 8 8 

12 196 25 8 37 108 5 10 

13 41 1 2 38 116 10 6 

14 25 1 1 39 90 1 6 

15 425 10 3 40 738 40 28 

16 4260 280 200 41 1811 86 93 

17 416 10 20 42 430 11 9 

18 115 8 6 43 3060 120 30 

19 82 1 2 44 215 8 22 

20 22 1 1 45 58 3 33 

21 631 49 70 46 296 32 36 

22 132 8 9 47 620 28 45 

23 420 21 22 48 418 13 13 

24 86 6 4 49 47 2 2 

25 42 1 1 50 81 4 2 

In short, the optimization capability of ISCA has been greatly improved compared with the basic SCA. When SCA solves 

discrete computational offloading problems, it lacks the ability to jump out of the local optimum, and it is easy to stagnate, 

making it difficult to achieve the goal of finding a better solution. ISCA overcomes this deficiency very well. When solving the 

corresponding offloading problem, it can always jump out of the local optimum, the convergence speed is also improved, and it 

can approach the optimal solution at a faster speed. When the number of mobile terminals is small, the solution results of various 

algorithms are less different, they can solve the problem with a high success rate, while when the number of mobile terminals is 

large, the superior performance of ISCA can be more clearly reflected. 

Table 5. computational results of deterministic algorithms 

problem dynamic programming greedy algorithm 

problem 1 3900 3800 

problem 2 3965 3925 

problem 3 16761 16590 



 

21 

Table 6. Comparison of heuristic algorithm results 

problem algorithm 
average 

optimum 

standard 

deviation 
best worst 

Success rate 

/% 

problem1 

SCA 3886 85.738 3900 3300 96 

ISCA 3900 0 3900 3900 100 

PSO 3898 14.142 3900 3800 98 

GA 3900 0 3900 3900 100 

problem 2 

SCA 3814.6 328.403 3965 2665 80 

ISCA 3963.4 7.918 3965 3925 96 

PSO 3899 157.529 3965 3315 84 

GA 3931.8 109.739 3965 3465 90 

problem 3 

SCA 15595.5 1779.677 16761 12070 60 

ISCA 16695.96 223.828 16761 15873 92 

PSO 16465.48 439.7 16761 15710 68 

GA 16625.68 296.967 16761 15770 82 

6. Conclusion 

In this paper, we consider a computing offloading scenario 

of a MEC server and multiple terminal devices, aiming at the 

maximum reward of the server, modeling the target problem 

as a knapsack problem, and improving the sine cosine 

algorithm to solve it without using the traditional solution 

method with high complexity. The computational offloading 

problem is solved with an improved sine cosine algorithm and 

compared with two classical heuristics. The simulation results 

show that when solving discrete offloading problems, the 

improved sine cosine algorithm has the best performance. In 

the results, the average optimal value and standard deviation 

of ISCA rank first among all algorithms. Stability, solution 

speed, and solution success rate of ISCA are greatly improved 

over the basic sine SCA. We’ll consider applying the ISCA 

other compute offloading scenarios in future work. 

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