Table 1.
Characteristics of the existing one-stage niching methods.
Fig 1.
Comparison of the characteristics (computational complexity and number of tuning parameters, #parameters) of our proposed GPSA and existing one-stage niching methods.
Fig 2.
A two-particle GPSA solving a one-dimensional UMO function.
(A) Particle positions (0 ≤ t ≤ 45). (B) Particle positions (35 ≤ t ≤ 200). (C) Personal bests.
Fig 3.
Different gravity-induced behaviors of two nearby particles.
(A) Swap. (B) Attractive flip. (C) Repulsive flip.
Fig 4.
A six-particle GPSA solving a one-dimensional MMO function with three global optima.
(A) Particle positions. (B) Personal bests.
Fig 5.
Snapshots of a GPSA run that found all four global optima of the Himmelblau function.
xj denotes the jth axis of position vector x, and the black and red circles indicate the positions and personal bests of particles, respectively. (A) t = 0. (B) t = 10. (C) t = 30. (D) t = 60.
Fig 6.
Snapshots of a GPSA run that found only three global optima of the Himmelblau function.
(A) t = 0. (B) t = 10. (C)t = 60.
Table 2.
Benchmark functions.
Table 3.
PR results of our GPSA with different parameters (c2 = 10−2, 10−4, and 10−6).
Table 4.
SR results of our GPSA with c2 = 10−2, 10−4, and 10−6, RPSO, and FERPSO.
Fig 7.
Dynamic c2 as a function of iteration t, for , n = 20, and tmax = 1000.
Table 5.
PR results of our DGPSA, RPSO, and FERPSO.
Table 6.
SR results of our DGPSA for all benchmark functions and all accuracy levels.
Table 7.
Resulting numbers of functions in ,
, and
.
Fig 8.
Comparison of runtime of our DGPSA and existing one-stage methods, where **** indicates significantly difference between the runtime of our DGPSA and that of the compered method with p-value <10−4.
Table 8.
PR results of our DGPSA and the existing two-stage methods with ϵ = 10−5.