PSO with Mixed Strategy for Global Optimization

Algorithm 1

Nelder–Mead variant.

	Input: population P with three individuals.
(1)	Sort the three points in the order: f(x1) ≤ f(x2) ≤ f(x3).
(2)	Calculate xo as follows:
(3)	[Reflection] Compute the reflected point xr = xo + α(xo − x3). Where α is a reflection coefficient. Its standard value is α = 1.
(4)	if f(x1) ≤ f(xr) < f(x3), then
(5)	= the reflected point xr.
(6)	else if f(xr) < f(x1) then
(7)	[Expansion] Compute the expanded point xe = xo + γ(xr −  xo). Where γ is an expansion coefficient. Its standard value is γ = 2.
(8)	if f(xe) < f(xr) then
(9)	= the expanded point xe
(10)	else
(11)	= the reflected point xr
(12)	end if
(13)	else
(14)	[Contraction] Compute the contracted point xc = xo + ρ(x3 − xo). Where ρ is a contraction coefficient. Its standard values is ρ = .
(15)	if f(xc) < f(x3) then
(16)	= the contracted point xc
(17)	else
(18)	for i = 2, 3 do
(19)	[Shrink]  = x1 + σ(xi − x1). Where σ is a shrink coefficient. Its standard value is σ = .
(20)	end for
(21)	end if
(22)	end if
	Output: population P = {}.