## 2 Literature Survey
### Sc-Mopso-Dg
#### 3.3.1 Mathematical Model of Objective Space  
For conducting optimization, we need to mathematically model each of the objectives, namely, trust, energy, cost, and time using the decision variables. The decision variables are defined using Equation (3):  
\[x=\left(Nms,N^{i}_{Rv},NH^{ij}\right) \tag{3}\]  
where \(Nms\) denotes the number of mobile sinks; \(N^{i}_{Rv}\) denotes the number of rendezvous points for mobile sink \(i\); \(NH^{ij}\) denotes the number of hops for mobile sink \(i\) at rendezvous point \(j\). ```
1-NumOfParticles
2-NumOfIterations
3-Boundary
4-DimensionsRange
5-ObjectiveFunctions
6-Inertia,C1,C2
7-adaptiveTimeOut
8-classMinThreshold
Output
1-ParetoFront
2-ParetoSet

Start Algorithm
1: initSwarm(NumOfParticles)
2: numOfClass = DimensionsRange.Max - DimensionsRange.Min + 1;
3: for i = 1 until NumOfParticles
4: Dimension = genRan(DimensionsRange)
5: particle = genRan(Dimension,Boundary)
6: add particle to swarm
7: end
8: Classes = Distribute(swarm)
9: for iteration = 1 until NumOfIterations
10: for classIndex = 1 until length(Classes)
11: for each particle of Classes(classIndex)
12: exemplar = selectExemplar(Classes(classIndex)//-1-
13: newParticle = moveParticle(particle,exemplar,Inertia,C1,C2)
14: if(NoImprove(newParticle,particle))
15: particle.counter = particle.counter + 1;
16: else
17: particle.counter = 0;
18: particle = newParticle;
19: end
20: end
21: end
22: for classIndex = 1 until length(Classes)
23: for each particle of Classes(classIndex)
24: adaptiveTimeOut = timeoutUpdate(particle.nonImpWindow, maxTimeOut)
25: if(particle.counter > adaptiveTimeOut and length(particle. Class) > classMinThreshold)
26: Class = selectNewClass(particle)
27: particle = moveToNewClass(particle, Class)
28: end
29: end
30: end
31: end
32: end
33: End
34 End
35
```  
**Algorithm 1** Pseudocode of SC-MOSPO for the V-length problem [42]  
(1) Trust  
In a wireless sensor network, the trust of a sensor can be defined as the degree of confidence that can be placed in the accuracy, reliability, and security of the data generated by that sensor. A high degree of trust in a sensor implies that the data it generates are accurate, reliable, and secure, while a low degree of trust implies the opposite. The trust of a sensor can be quantified as an integer value between 1 and 10 based on a number of factors: 1, sensor calibration: a sensor that is properly calibrated and periodically maintained is more trustworthy than one that is not; 2, sensor accuracy: a sensor that consistently generates accurate data is more trustworthy than one that generates inaccurate data; 3, sensor reliability: a sensor that consistently operates without interruption is more trustworthy than one that frequently fails; 4, security: a sensor that is secure and protected against tampering is more trustworthy than one that is not; 5, data integrity: a sensor that generates data that are consistent with other sources of information is more trustworthy than one that generates inconsistent data; 6, age and usage: a new sensor that has not been extensively used is generally more trustworthy than an older sensor that has been in use for a long time. Based on these and other factors, the trust of a sensor can be quantified as an integer value between 1 and 10, with a value of 1 indicating very low trust and a value of 10 indicating very high trust. This quantification provides a simple, intuitive way to express the degree of trust in a sensor and can be used to inform decisions about how to use and rely on the data generated by that sensor within the wireless sensor network. Trust is calculated based on the number of mobile sinks, the set of a rendezvous points for each one, and the number of assumed hops for each rendezvous point. We also assume that increasing the number of hops implies obtaining trust, which is the minimum among all hops, as provided in Equation (4).