pyswarms.handlers package¶
This package implements different handling strategies for the optimiziation.
The BoundaryHandler
and the
VelocityHandler
handlers help avoiding that particles
leave the defined search space.
The OptionsHandler
helps in varying the options with time/iterations.
pyswarms.handlers class¶
Handlers
This module provides Handler classes for the position, velocity and time varying acceleration coefficients
of particles. Particles that do not stay inside these boundary conditions have to
be handled by either adjusting their position after they left the bounded
search space or adjusting their velocity when it would position them outside
the search space. In particular, this approach is important if the optimium of
a function is near the boundaries.
For the following documentation let \(x_{i, t, d} \ \) be the \(d\) th
coordinate of the particle \(i\) ‘s position vector at the time \(t\),
\(lb\) the vector of the lower boundaries and \(ub\) the vector of the
upper boundaries.
The OptionsHandler
class provide methods which allow faster and better convergence by varying
the options \(w, c_{1}, c_{2}\) with various strategies.
The algorithms in the BoundaryHandler
and VelocityHandler
classes are adapted from [SH2010]
[SH2010] Sabine Helwig, “Particle Swarms for Constrained Optimization”, PhD thesis, FriedrichAlexander Universität ErlangenNürnberg, 2010.

class
pyswarms.backend.handlers.
BoundaryHandler
(strategy)[source]¶ Bases:
pyswarms.backend.handlers.HandlerMixin

__call__
(position, bounds, **kwargs)[source]¶ Apply the selected strategy to the positionmatrix given the bounds
Parameters:  position (numpy.ndarray) – The swarm position to be handled
 bounds (tuple of numpy.ndarray or list) – a tuple of size 2 where the first entry is the minimum bound while
the second entry is the maximum bound. Each array must be of shape
(dimensions,)
 kwargs (dict) –
Returns: the adjusted positions of the swarm
Return type:

__init__
(strategy)[source]¶ A BoundaryHandler class
This class offers a way to handle boundary conditions. It contains methods to repair particle positions outside of the defined boundaries. Following strategies are available for the handling:
 Nearest:
 Reposition the particle to the nearest bound.
 Random:
 Reposition the particle randomly in between the bounds.
 Shrink:
 Shrink the velocity of the particle such that it lands on the bounds.
 Reflective:
 Mirror the particle position from outside the bounds to inside the bounds.
 Intermediate:
 Reposition the particle to the midpoint between its current position on the bound surpassing axis and the bound itself. This only adjusts the axes that surpass the boundaries.
The BoundaryHandler can be called as a function to use the strategy that is passed at initialization to repair boundary issues. An example for the usage:
from pyswarms.backend import operators as op from pyswarms.backend.handlers import BoundaryHandler bh = BoundaryHandler(strategy="reflective") ops.compute_position(swarm, bounds, handler=bh)
By passing the handler, the
compute_position()
function now has the ability to reset the particles by calling theBoundaryHandler
inside.

intermediate
(position, bounds, **kwargs)[source]¶ Set the particle to an intermediate position
This method resets particles that exceed the bounds to an intermediate position between the boundary and their earlier position. Namely, it changes the coordinate of the outofbounds axis to the middle value between the previous position and the boundary of the axis. The following equation describes this strategy:
\[\begin{split}x_{i, t, d} = \begin{cases} \frac{1}{2} \left (x_{i, t1, d} + lb_d \right) & \quad \text{if }x_{i, t, d} < lb_d \\ \frac{1}{2} \left (x_{i, t1, d} + ub_d \right) & \quad \text{if }x_{i, t, d} > ub_d \\ x_{i, t, d} & \quad \text{otherwise} \end{cases}\end{split}\]

nearest
(position, bounds, **kwargs)[source]¶ Set position to nearest bound
This method resets particles that exceed the bounds to the nearest available boundary. For every axis on which the coordiantes of the particle surpasses the boundary conditions the coordinate is set to the respective bound that it surpasses. The following equation describes this strategy:
\[\begin{split}x_{i, t, d} = \begin{cases} lb_d & \quad \text{if }x_{i, t, d} < lb_d \\ ub_d & \quad \text{if }x_{i, t, d} > ub_d \\ x_{i, t, d} & \quad \text{otherwise} \end{cases}\end{split}\]

periodic
(position, bounds, **kwargs)[source]¶ Sets the particles a periodic fashion
This method resets the particles that exeed the bounds by using the modulo function to cut down the position. This creates a virtual, periodic plane which is tiled with the search space. The following equation describtes this strategy:
\begin{gather*} x_{i, t, d} = \begin{cases} ub_d  (lb_d  x_{i, t, d}) \mod s_d & \quad \text{if }x_{i, t, d} < lb_d \\ lb_d + (x_{i, t, d}  ub_d) \mod s_d & \quad \text{if }x_{i, t, d} > ub_d \\ x_{i, t, d} & \quad \text{otherwise} \end{cases}\\ \\ \text{with}\\ \\ s_d = ub_d  lb_d \end{gather*}

random
(position, bounds, **kwargs)[source]¶ Set position to random location
This method resets particles that exeed the bounds to a random position inside the boundary conditions.

reflective
(position, bounds, **kwargs)[source]¶ Reflect the particle at the boundary
This method reflects the particles that exceed the bounds at the respective boundary. This means that the amount that the component which is orthogonal to the exceeds the boundary is mirrored at the boundary. The reflection is repeated until the position of the particle is within the boundaries. The following algorithm describes the behaviour of this strategy:
\begin{gather*} \text{while } x_{i, t, d} \not\in \left[lb_d,\,ub_d\right] \\ \text{ do the following:}\\ \\ x_{i, t, d} = \begin{cases} 2\cdot lb_d  x_{i, t, d} & \quad \text{if } x_{i, t, d} < lb_d \\ 2\cdot ub_d  x_{i, t, d} & \quad \text{if } x_{i, t, d} > ub_d \\ x_{i, t, d} & \quad \text{otherwise} \end{cases} \end{gather*}

shrink
(position, bounds, **kwargs)[source]¶ Set the particle to the boundary
This method resets particles that exceed the bounds to the intersection of its previous velocity and the boundary. This can be imagined as shrinking the previous velocity until the particle is back in the valid search space. Let \(\sigma_{i, t, d}\) be the \(d\) th shrinking value of the \(i\) th particle at the time \(t\) and \(v_{i, t}\) the velocity of the \(i\) th particle at the time \(t\). Then the new position is computed by the following equation:
\begin{gather*} \mathbf{x}_{i, t} = \mathbf{x}_{i, t1} + \sigma_{i, t} \mathbf{v}_{i, t} \\ \\ \text{with} \\ \\ \sigma_{i, t, d} = \begin{cases} \frac{lb_dx_{i, t1, d}}{v_{i, t, d}} & \quad \text{if } x_{i, t, d} < lb_d \\ \frac{ub_dx_{i, t1, d}}{v_{i, t, d}} & \quad \text{if } x_{i, t, d} > ub_d \\ 1 & \quad \text{otherwise} \end{cases} \\ \\ \text{and} \\ \\ \sigma_{i, t} = \min_{d=1...n} \sigma_{i, t, d} \\ \end{gather*}


class
pyswarms.backend.handlers.
HandlerMixin
[source]¶ Bases:
object
A HandlerMixing class
This class offers some basic functionality for the Handlers.

class
pyswarms.backend.handlers.
OptionsHandler
(strategy)[source]¶ Bases:
pyswarms.backend.handlers.HandlerMixin

__init__
(strategy)[source]¶ An OptionsHandler class
This class offers a way to handle options. It contains methods to vary the options at runtime. Following strategies are available for the handling:
 exp_decay:
 Decreases the parameter exponentially between limits.
 lin_variation:
 Decreases/increases the parameter linearly between limits.
 random:
 takes a uniform random value between limits
 nonlin_mod:
 Decreases/increases the parameter between limits according to a nonlinear modulation index .
The OptionsHandler can be called as a function to use the strategy that is passed at initialization to account for timevarying coefficients. An example for the usage:
from pyswarms.backend import operators as op from pyswarms.backend.handlers import OptionsHandler oh = OptionsHandler(strategy={ "w":"exp_decay", "c1":"nonlin_mod","c2":"lin_variation"}) for i in range(iters): # initial operations for global and local best positions new_options = oh(default_options, iternow=i, itermax=iters, end_opts={"c1":0.5, "c2":2.5, "w":0.4}) # more updates using new_options
Note
As of pyswarms v1.3.0, you will need to create your own optimization loop to change the default ending options and other arguments for each strategy in all of the handlers on this page.
A more comprehensive tutorial is also present here for interested users.

exp_decay
(start_opts, opt, **kwargs)[source]¶ Exponentially decreasing between \(w_{start}\) and \(w_{end}\) The velocity is adjusted such that the following equation holds:
Defaults: \(d_{1}=2, d_{2}=7, w^{end} = 0.4, c^{end}_{1} = 0.8 * c^{start}_{1}, c^{end}_{2} = c^{start}_{2}\)
\[w = (w^{start}w^{end}d_{1})exp(\frac{1}{1+ \frac{d_{2}.iter}{iter^{max}}})\]Ref: Li, H.R., & Gao, Y.L. (2009). Particle Swarm Optimization Algorithm with Exponent Decreasing Inertia Weight and Stochastic Mutation. 2009 Second International Conference on Information and Computing Science. doi:10.1109/icic.2009.24

lin_variation
(start_opts, opt, **kwargs)[source]¶ Linearly decreasing/increasing between \(w_{start}\) and \(w_{end}\)
Defaults: \(w^{end} = 0.4, c^{end}_{1} = 0.8 * c^{start}_{1}, c^{end}_{2} = c^{start}_{2}\)
\[w = w^{end}+(w^{start}w^{end}) \frac{iter^{max}iter}{iter^{max}}\]Ref: Xin, Jianbin, Guimin Chen, and Yubao Hai. “A particle swarm optimizer with multistage linearlydecreasing inertia weight.” 2009 International joint conference on computational sciences and optimization. Vol. 1. IEEE, 2009.

nonlin_mod
(start_opts, opt, **kwargs)[source]¶ Non linear decreasing/increasing with modulation index(n). The linear strategy can be made to converge faster without compromising on exploration with the use of this index which makes the equation nonlinear.
Defaults: \(n=1.2\)
\[w = w^{end}+(w^{start}w^{end}) \frac{(iter^{max}iter)^{n}}{(iter^{max})^{n}}\]Ref: A. Chatterjee, P. Siarry, Nonlinear inertia weight variation for dynamic adaption in particle swarm optimization, Computer and Operations Research 33 (2006) 859–871, March 2006


class
pyswarms.backend.handlers.
VelocityHandler
(strategy)[source]¶ Bases:
pyswarms.backend.handlers.HandlerMixin

__call__
(velocity, clamp, **kwargs)[source]¶ Apply the selected strategy to the velocitymatrix given the bounds
Parameters:  velocity (numpy.ndarray) – The swarm position to be handled
 clamp (tuple of numpy.ndarray or list) – a tuple of size 2 where the first entry is the minimum clamp while
the second entry is the maximum clamp. Each array must be of shape
(dimensions,)
 kwargs (dict) –
Returns: the adjusted positions of the swarm
Return type:

__init__
(strategy)[source]¶ A VelocityHandler class
This class offers a way to handle velocities. It contains methods to repair the velocities of particles that exceeded the defined boundaries. Following strategies are available for the handling:
 Unmodified:
 Returns the unmodified velocites.
 Adjust
 Returns the velocity that is adjusted to be the distance between the current and the previous position.
 Invert
 Inverts and shrinks the velocity by the factor
z
.
 Zero
 Sets the velocity of outofbounds particles to zero.

adjust
(velocity, clamp=None, **kwargs)[source]¶ Adjust the velocity to the new position
The velocity is adjusted such that the following equation holds:
\[\mathbf{v_{i,t}} = \mathbf{x_{i,t}}  \mathbf{x_{i,t1}}\]Note
This method should only be used in combination with a position handling operation.

invert
(velocity, clamp=None, **kwargs)[source]¶ Invert the velocity if the particle is out of bounds
The velocity is inverted and shrinked. The shrinking is determined by the kwarg
z
. The default shrinking factor is0.5
. For all velocities whose particles are out of bounds the following equation is applied:\[\mathbf{v_{i,t}} = z\mathbf{v_{i,t}}\]
