## 1 Introduction
The positions and velocities are evolved as Equations (1) and (2) [22]:  
\[v_{i}^{d}= v_{i}^{d}+\mathrm{c}_{1}\ r_{1}^{d}\Big{(}\ pbest_{i}^{d}-x_{i}^{d} \Big{)}+\mathrm{c}_{2}\ r_{2}^{d}\Big{(}gbest^{d}-x_{i}^{d}\Big{)}, \tag{1}\]  
\[x_{i}^{d}= x_{i}^{d}+v_{i}^{d}, \tag{2}\]  
where \(V_{i}=(v_{i}^{1},\ v_{i}^{2},\ v_{i}^{3},\ v_{i}^{4},\dots\dots,\ v_{i}^{D})\) is the \(i\)th particle velocity, \(X_{i}=(x_{i}^{1},\ x_{i}^{2},\ x_{i}^{3},\ x_{i}^{4},\dots\dots,\ x_{i}^{D})\) is the \(i\)th particle position, \(\mathrm{c}_{1}\), and \(\mathrm{c}_{2}\) are two coefficients of acceleration, \(r_{1}^{d}\) and \(r_{2}^{d}\) are two numbers selected randomly within the range of [0, 1], \(gbest=\Big{(}gbest^{1},\ gbest^{2},\dots,gbest^{d}\Big{)}\) is the greatest place found by swarm so far, \(pbest_{i}=(pbest_{i}^{1},\ pbest_{i}^{2},\ pbest_{i}^{3},\ pbest_{i}^{4},\dots,\ pbest_{i}^{D})\)  
Figure 1: Block diagram of energy requirements by a mobile robot. is the \"personal best position\" of ith particle achieved by itself, the dimension of an optimization problem is D, and \(d\in\{1,\ 2,\ \ldots\ldots,D\}\). In this paper, we develop the collection of information tasks for MRs in the form of multi-objective optimization under time and energy limitations. To be more specific, three goals are taken into consideration for surveillance: acquiring the greatest amount of data, going through the route with the least likelihood of hitting obstacles, and covering the shortest distance. In fact, numerous approaches are available to tackle multi-objective optimization problems, including genetic algorithms [23] and deep learning [24]. In comparison, the PSO algorithm is comparatively easy to understand and simple to implement in comparison to them. Thus, for addressing tasks involving multi-objective optimization, we switch toward the PSO algorithms technique. PSO was developed in part to address situations where the best answer is a location in a space with multiple dimensions of the variables, like the scenario with information flow and social interaction in schools of fish and flocks of birds. Differential objective functions and constraints are not required for PSO to achieve the global optimal solution with very high accuracy. In this work, we consider three goals and describe each objective as a multi-objective constraint optimization issue. Further, multi-objective optimization is analyzed for the navigation of MRs by keeping time and energy constraints in mind. Additionally, this paper provides an intelligent PSO technique for multi-objective problems in optimization, resulting in more rapid convergence and higher fitness. Listed below are some of the major significant contributions of this paper:  
1. We model the wireless data collecting operation as a multi-objective confined optimization challenge that optimizes civilian or military surveillance, reduces the likelihood of encountering obstacles, and shortens the route. The main goal of mobile surveillance is supposed to be to optimize the quantity of data gathered, considering the limits of MR energy and job completion time;
2. To reduce the overall length the MRs travel throughout their movements, as well as the energy and time required for MR to locate its optimal location, routes are developed using the lengths between the present MR locations and the probable ones in the coming generations;
3. We provide an intelligent PSO approach to address the given optimization issue. The simulation outcomes show that the presented advanced PSO method can attain faster convergence and greater accuracy compared to conventional PSO techniques;
4. The minimum-maximal normalization strategy is used to standardize numerous variables while evaluating the quality of the PSO technique, therefore eliminating the dimension discrepancy in multi-objective optimizations;
5.