An adaptive bio-inspired optimisation model based on the foraging behaviour of a social spider

Figures & data

Figure 1. Vibrations generated by prey and spider at source positions

Figure 2. Model Test Functions

Figure 3. Model Test Functions Cont’d

Figure 4. Model Test Functions Cont’d

Figure 5. Parameter test results on f₂, f₁₁, f₁₃ and f_15.

Figure 6. Minimisation curves for ASSCO model vs. SSO model tested on f₂, f₁₂, f₁₀, f_14, f₁₁ and f_15.

Table

Input {population of spiders and prey, iteration number) Output local_best_fitness, global_best_fitness, local_best_position, global_best_solution} 1. Initialize spiders, prey, spiderfitnessValues, preyfitnessValue, spiderFrequency and preyFrequency to zero 2. Generate the population of spiders S at random for i = 1:totspidn Si = lowerbound(i)+rand(upperbound(i)-lowerbound(i)) end for 3. Evaluate the fitness of spiders and prey positions using the fitness functions While not maximum iteration for i = 1:totspidn sfit(i) =$f\left(x_{i,t}\right)$ end for for i = 1:pn pfit(i)=$f\left(p_t\right)$ end for 4. Calculate the frequency of the spiders S for i = 1:totspidn$f_{i,t}=\frac{f\left(x_{i,t}\right)-f_{min}}{f_{max}-f_{min}}+C$end for check the frequency and update Ftar and Fbest 5. Perform spider search 5.1 Calculate distance R between spider $x_i$and $x_j$, and prey P for i = 1:totspidn for j = 1:totspidn$R_{i.j}=x_i-x_j$end for end for for k = 1:totspidn$R_{k.p}=x_k-p$end for 5.2 Prey generates vibration with respect to its frequency $f_p$ at time t as $A\ast \mathrm{s}\mathrm{i}\mathrm{n}{f}_{p,t}\alpha$ 5.3 Spiders receive the vibration with spider position $i$ being the closest to prey $V_{p,i}=V_p.e^{-R_{p,i}^2}$ 5.3 Spider generates vibration with respect to their frequencies $f_i$ at time t$A\ast \mathrm{s}\mathrm{i}\mathrm{n}{f}_{i,t}\alpha$ 5.4 Neighbouring spiders receive this vibration with spider at position $i$ closest to $j$, with $i$ having a higher frequency $Fbest$ than $j$ as $V_{i.j}=V_j.e^{-R_{i,j}^2}$ 5.5 Spider S performs random walk towards prey p as$x_{i+1}=x_i+v_{i,j}\ast \left(x_j-x_i\right).\ast {\theta }_1+v_{p,i}\ast \left(x_j-x_i\right).\ast {\theta }_1+v_{p,i}\ast \left(x_p-x_i\right).\ast {\theta }_1$ end while 6. Stop if maximum iteration is reached and output best solution else goto step3

Table 1. Simulation Settings for ASSCO and SSO Model

ASSCO		SSO
Parameters	Values	Parameters	Values
Number of Spiders	50	Number of spiders (NS)	50
Number of Prey	1	Female spiders (NF)	65–90% of NS
Maximum Iterations	2000	Male spiders (NM)	NS-NF
Dimensions (d)	30	Dimensions (d)	30
Amplitude (A)	5,4	Maximum Iterations	2000
Unit time (α)	1 s	PF	0.7
a	0.5
b	0.1

Table 2. Minimisation Results of Validated Functions on ASSCO model vs. SSO model

Functions	Best fitness values (ASSCO)	Best fitnessvalues (SSO)
f1	4.9459e-56	4.7879e-04
f2	2.8197e-18	0.9825e+00
f3	0.0000e+00	6.0892e-10
f4	0.0000e+00	1.9207e-08
f5	0.0000e+00	1.1398e-10
f6	0.1800e+00	0.1800e+00
f7	0.0000e+00	33.4802e+00
f8	0.6681e+00	1.9666e+00
f9	3.6000e-03	1.4756e+00
f10	3.2000e-03	7.9234e+00
f11	1.9456e-24	0.8250e+00
f12	3.8337e-05	2.0804e-04
f13	4.4409e-16	1.1400e-02
f14	1.4998e-32	5.1040e-01
f15	4.1093e-07	0.2959e+00
f16	1.0000e+00	1.0000e+00
f17	0.0000e+00	9.0250e-12
f18	4.8325e-06	1.9000e-03
f19	−3.8708e+03	−3.8708e+03
f20	1.6400e-02	8.5100e-02
f21	2.3888e-295	2.7724e-11
f22	0.0000e+00	NAN
f23	−2.9996e+00	−2.2990e+00
f24	4.0000e-03	4.0634e-04
f25	1.6569e-10	1.8194e-10

Key: NAN = Not a Number.

Table 3. P-values Obtained from Wilcoxon Rank Sum Test for ASSCO model vs. SSO model

Functions	P-values (ASSCO vs. SSO)
f1	2.1837e-50
f2	0.0000e+00
f3	1.2931e-19
f4	1.5772e-13
f5	2.6692e-56
f6	3.5929e-07
f7	4.1001e-159
f8	0.0000e+00
f9	0.0000 + 00
^f10	0.0000 + 00
^f11	1.0736e-217
^f12	6.0810e-01
^f13	9.2218e-190
^f14	0.0000e+00
^f15	0.0000e+00
^f16	5.3335e-73
^f17	1.7661e-09
^f18	6.9473e-15
^f20	0.0000e+00
^f21	1.4309e-11
^f23	0.0000e+00
^f24	9.9970e-01
^f25	1.2723e-243