# A Particle Swarm and Smell Agent-Based Hybrid Algorithm for Enhanced Optimization  
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1 Department of Computer Engineering, Ahmadu Bello University Zaria, Zaria 810107, Nigeria; [EMAIL_ADDRESS] (A.T.S. ); bellosala@abu.edu.ung (H.B.-S.); [EMAIL_ADDRESS] (M.B.M. ); [EMAIL_ADDRESS] (E.A.A. ); [EMAIL_ADDRESS] (A.D.A.) [PERSON]  
1 Department of Computer Engineering, Ahmadu Bello University Zaria, Zaria 810107, Nigeria; [EMAIL_ADDRESS] (A.T.S. ); bellosala@abu.edu.ung (H.B.-S.); [EMAIL_ADDRESS] (M.B.M. ); [EMAIL_ADDRESS] (E.A.A. ); [EMAIL_ADDRESS] (A.D.A.) [PERSON]  
2 Nest Generation Enterprises and Institutions, Council for Scientific and Industrial Research (CSIR), Pretoria 0001, South Africa 2 Nest Generation Enterprises and Institutions,vehicle navigation amid numerous possibilities from source to destination [7; 8; 9]. Furthermore, during the development of optimization algorithms, the initial evaluation of such algorithms typically involves applying them to standard mathematical test functions to gauge their performance [10]. Other examples include the use of optimization techniques in solving the traveling salesman problem [7; 8; 9; 11; 12] and in path planning areas [13; 14]. These examples illustrate the many application areas in which optimization algorithms, like PSO, can be effectively utilized to yield societal benefits. The PSO algorithm operates by guiding a population of particles through the search space iteratively, with the objective of locating the optimal solution [15]. In this case, the search space refers to the population of all possible solutions to the problem under consideration. Specifically, each particle represents a potential solution to the problem, with its position in the search space representing a candidate solution. The PSO algorithm then updates each particle's position iteratively, guided by both its own best position (referred to as personal best or pbest) and the best position among its neighboring particles [15]. Initially, each particle is assigned a random velocity, propelling it into the optimization hyperspace. Consequently, every particle maintains a record of its hyperspace coordinates, which are tied to its best solution found so far (pbest). Simultaneously, the entire swarm of particles collectively monitors the optimal solution and its location in hyperspace, referred to as the global best (gbest) [16]. In an n-dimensional search space, the position and velocity of a particle indexed by \(i\) at some present iteration cycle \(t\) are determined by the following equations [17]:  
\[x_{i}^{t}=[x_{i1},\ldots,x_{in}] \tag{1}\]  
\[v_{i}^{t}=[v_{i1},\ldots,v_{in}] \tag{2}\]  
\[v_{i}^{(t+1)}=v_{i}^{t}+c_{1}r_{1}\cdot(pbest_{i}^{t}-x_{i}^{t})+c_{2}r_{2} \cdot(gbest_{i}^{t}-x_{i}^{t}) \tag{3}\]  
where \(c_{1}\) and \(c_{2}\) are the velocity control parameters, and \(r_{1}\) and \(r_{2}\) are random numbers generated differently. Therefore, the position of the particles is updated as expressed in Equation (4):  
\[x_{i}^{(t+1)}=x_{i}^{t}+v_{i}^{(t+1)} \tag{4}\]  
Many variants of the PSO algorithm exist in the literature, designed to enhance its performance. Noteworthy among these is the constriction factor PSO (CFPSO) [18; 19], developed to mitigate premature convergence, a common issue in conventional PSO. CFPSO uses a constriction factor to regulate the particle velocity, thereby curbing excessive growth. This mechanism aids in preserving population diversity and safeguards against premature convergence to sub-optimal solutions. Similarly, a popular variant of the PSO algorithm is the hybrid PSO, which amalgamates PSO with other optimization techniques to enhance its performance. Some studies advocate for the fusion of PSO with differential evolution (DE) to create a hybrid PSO-DE algorithm [20; 21]. This hybrid approach combines PSO's global search capabilities with DE's local search abilities, resulting in an improved convergence speed and solution quality.