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Abstract-Particle swarm optimization (PSO) is known to suffer from stagnation once particles have prematurely converged to any particular region of the search space. The proposed regrouping PSO (RegPSO) avoids the stagnation problem by automatically triggering swarm regrouping when premature convergence is detected. This mechanism liberates particles from sub-optimal solutions and enables continued progress toward the true global minimum. Particles are regrouped within a range on each dimension proportional to the degree of uncertainty implied by the maximum deviation of any particle from the globally best position. This is a computationally simple yet effective addition to the computationally simple PSO algorithm. Experimental results show that the proposed RegPSO successfully reduces each popular benchmark tested to its approximate global minimum.

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This paper proposes improvements to PSO with velocity clamping to overcome its known disadvantage of allowing particle to move outside the search space. The new proposed PSO algorithm actively penalizes the particle velocities to ensure particles are confined within the search space. The algorithm is called PSO with Active Velocity Penalty (PSO-AVP). The paper also presents some simulation results to give insights into the correlation between swarm particle explosion control and its effects on the exploration-exploitation dynamics of a swarm while it is still in motion. The advantages of PSO-AVP reside in algorithm simplicity, consistency, and better balance between exploration and exploitation.Computational models of swarm intelligence have been developed as a result of studies that aimed at understanding and modeling the collective behavior of biological swarm systems including bird flocks, ants, and fish schools [1]. Even though the model representing an individual within a swarm is relatively simple, the collective behavior of all swarm individuals is usually very complex. This complex emergent swarm model behavior has been exploited to solve complex computational problems, such as optimization problems. Particle swarm optimization (PSO), a paradigm of computational swarm intelligence, was developed by Kennedy and Eberhart [2]-[3] while attempting to simulate the collective behavior that emerges during the motion of swarms of birds. Individuals in a PSO model are called particles and are represented by position points in a multidimensional search space. Each particle position is a candidate solution to the optimization problem being solved by the PSO algorithm.A large body of research has been conducted to study the performance of PSO, and several approaches have been proposed to improve its performance. Some of these studies concentrated on the sensitivity of PSO to control parameters, such as inertia weight, acceleration coefficients, and swarm size [4]- [5].One of the crucial criterion that can determine the performance of population-based stochastic optimization algorithms, such as PSO, is how to maintain a balance between exploration and exploitation [6]- [7]. Exploration is the ability of the search algorithm to explore various regions of the search space in order to locate promising good solutions. Exploitation is the ability to conduct a thorough search within a smaller area recognized as promising in finding the optimal solution.Any PSO approach that aims at improving the balance between exploration and exploitation has to focus on how particle velocities should be updated. In fact, what drives a swarm particle in a search space is the velocity vector which determines the direction and the speed of the particle motion. Moreover, without a proper control of particle velocities, the PSO algorithm may suffer from the explosion phenomenon characterized by large speed values which in turn may result in particles having large position updates [3]. This explosion phenomenon affects the exploration and the e...