Adaptive Particle Swarm Optimization

Abstract

Abstract-An adaptive particle swarm optimization (APSO) that features better search efficiency than classical particle swarm optimization (PSO) is presented. More importantly, it can perform a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and particle fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, including exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist learning strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best particle to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist learning will be studied. Results show that APSO substantially enhances the performance of the PSO paradigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity. Index Terms-Adaptive particle swarm optimization (APSO), evolutionary computation, global optimization, particle swarm optimization (PSO).

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“…Initially, the nPSO algorithm operates as a standard PSO algorithm using an increased local search (c 1 ) parameter. After a set number of iterations, the algorithm detects if individuals in the population have stagnated, which occurs when an individual's best solution has remained unchanged over a number of iterations [32,33]. The best individual is identified and removed from the population to form a niche seed.…”

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“…The second PSO variant is Advanced PSO (hereafter referred to as AdPSO) [24]. AdPSO has been reported to be more effective than sPSO over a set of standard test functions [24].…”

“…AdPSO has been reported to be more effective than sPSO over a set of standard test functions [24]. The AdPSO algorithm has been reimplemented from scratch for the research reported here, adhering to Zhan et al [24]. In AdPSO, four different states of search for solutions are defined.…”

“…The values of parameters φ 1 and φ 2 are algorithmically varied during run-time, depending on the current search state, enabling the swarm to switch between exploration and exploitation as appropriate. According to Zhan et al [24], AdPSO does not require a local search component, in contrast to sPSO. Elitism is an integral part of AdPSO, and is coupled with a perturbation algorithm that exploits the search space around the best solution P g (t), to find better local solutions.…”

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“…The experimental results using the OR-Library have shown that the proposed algorithm is better than both: the GA based version and the original PSO. Zhan, Zhang and Chung [10] proposes another modification of the PSO algorithm, that speeds up the processing by considering only the promising solutions (particles) for fitness evaluation. Besides GA and PSO, other searching techniques have been used to solve the STP such as the Tabu Search [11] [12] .…”