Salp Swarm Algorithm (SSA)¶

A module for the Salp Swarm Algorithm with parallel computing support.

Original paper: Mirjalili, S., Gandomi, A. H., Mirjalili, S. Z., Saremi, S., Faris, H., & Mirjalili, S. M. (2017). Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163-191.

What can you use?¶

Multi processing: ✔️
Discrete spaces: ✔️
Continuous spaces: ✔️
Mixed Discrete/Continuous spaces: ✔️

Parameters¶

class neorl.evolu.ssa.SSA(mode, bounds, fit, nsalps=5, int_transform='nearest_int', ncores=1, seed=None)[source]¶

Salp Swarm Algorithm

Parameters

mode – (str) problem type, either min for minimization problem or max for maximization
bounds – (dict) input parameter type and lower/upper bounds in dictionary form. Example: bounds={'x1': ['int', 1, 4], 'x2': ['float', 0.1, 0.8], 'x3': ['float', 2.2, 6.2]}
fit – (function) the fitness function
nsalps – (int): number of salps in the swarm
int_transform – (str): method of handling int/discrete variables, choose from: nearest_int, sigmoid, minmax.
ncores – (int) number of parallel processors (must be <= nsalps)
seed – (int) random seed for sampling

evolute(ngen, x0=None, c1=None, verbose=False)[source]¶

This function evolutes the SSA algorithm for number of generations.

Parameters

ngen – (int) number of generations to evolute
x0 – (list of lists) initial position of the salps (must be of same size as nsalps)
c1 – (float/list): a scalar value or a list of values with size ngen for the coefficient that controls exploration/exploitation. If None, default annealing formula for c1 is used (see Notes below for more info).
verbose – (bool) print statistics to screen

Returns

(tuple) (best individual, best fitness, and dictionary containing major search results)

Example¶

from neorl import SSA

#Define the fitness function
def FIT(individual):
    """Sphere test objective function.
                    F(x) = sum_{i=1}^d xi^2
                    d=1,2,3,...
                    Range: [-100,100]
                    Minima: 0
    """
    y=sum(x**2 for x in individual)
    return y

#Setup the parameter space (d=5)
nx=5
BOUNDS={}
for i in range(1,nx+1):
    BOUNDS['x'+str(i)]=['float', -100, 100]

nsalps=20
#setup and evolute SSA
ssa=SSA(mode='min', bounds=BOUNDS, fit=FIT, nsalps=nsalps, ncores=1, seed=1)
x_best, y_best, ssa_hist=ssa.evolute(ngen=100, c1=None, verbose=1)

Notes¶

SSA mimics the swarming behavior of salps when navigating and foraging in oceans. SSA cares mostly about the leading salp, where its position is optimized to achieve better food source (i.e. fitness).
Salp leader is mostly controlled by the coefficient c1, which balances SSA exploration and exploitation. The default formula for \(c_1 = 2e^{-(4g/ngen)^2}\), where \(g\) is the current generation (goes from 1 to ngen), and \(ngen\) is the total number of generations to evolute (ngen). Therefore, c1 is typically annealed from a large value at the beginning to increase exploration, to a very small value toward the end of evolution to prioritize exploitation.
The user can also provide a scalar/fixed value for c1 to overwrite the default annealing formula described above. Also, the user can provide a schedule for c1 generated by another formula in a list form. The size of the list MUST equal to ngen. For example, for ngen=5, the user can provide c1=[5, 0.5, 0.05, 0.005, 0.0005], where for every generation, the corresponding c1 value is used.
Therefore, if c1=None, the user should notice that ngen value used within the .evolute function has an impact on the c1 value and hence on SSA overall performance.
ncores argument evaluates the fitness of all salps in the swarm in parallel. Therefore, set ncores <= nsalps for most optimal resource allocation.
Look for an optimal balance between nsalps and ngen, it is recommended to minimize the number of nsalps to allow for more updates and more generations.
Total number of cost evaluations for SSA is nsalps * (ngen + 1).