Slime Mold Algorithm (SMA)

1. Algorithm inspiration
2. Algorithm introduction
3. Experimental results
4. References

1. Algorithm inspiration

The Slime Mold Algorithm (SMA) is an optimization algorithm based on the foraging behavior of slime molds. During foraging, slime molds undergo oscillatory contractions when they find food. In addition, a vein network of varying thicknesses will be formed between multiple food sources. The thickness of the vein network is related to the quality of the food source. When slime molds obtain food, they may still search unknown areas.

2. Algorithm introduction

2.1 Initialization phase

In SMA, the initial slime mold population position update formula is as shown in (1):
${X_i} = rand \bullet (UB - LB) + LB \tag {1}$ In formula $($ $1$ $)$ $X_{i}$ is the position of the i-th individual, $U B$ and $L B$ is the upper and lower bounds of the search range, $r and d$ are random numbers between 0 and 1.

2.2 Exploration stage

Even though slime molds find better food sources, they will separate individuals and explore other areas in an attempt to find higher quality food sources. According to the above analysis, the update of the slime mold position can be expressed as
$\tag{2}$ Among them, $z = 0.03$ ， $r an d$ is $0$ toA random number between $1 .$

2.3 Development stage

When the slime mold finds food, it will shrink. Its contraction pattern can be described as
${X_B}(t)),r < p,} \cr &{vc \times X(t)\qquad\qquad\qquad\qquad\qquad\quad,r \ge p,} \cr \end{aligned}} \right. \tag{3}$ Among them, $v b$ is $[- a, a]$ random number, $v c$ is at $[-1, 1]$ parameter that oscillates within and eventually approaches zero, $X_{b}(t)$ represents the current individual position with optimal fitness, $X (t)$ represents the current position of the slime mold individual, $X_{A}(t)$ and $X_{B}(t)$ represents the position of two random individuals, $t$ represents the current iteration number, $W$ represents the weight coefficient of slime mold.
Control parameter $p$ , parameter $a$ and weight coefficient $The update formulas of W$ are
$\tanh |S(i) - DF|,(i = 1,\;2,\; \cdots ,\;N), \tag{4}$ ${\mathop{ arctanh}\nolimits} ( - {t \over T} + 1), \tag{5}$ $\left\{ {\begin{aligned} {1 + {r_1}\log ({ {bF - S(i)} \over {bF - wF}} + 1),i < {N \over 2},} \cr {1 - {r_1}\log ({ {bF - S(i)} \over {bF - wF}} + 1),i \ge {N \over 2},} \cr \end{aligned} } \right. \tag{6}$ $\tag{7}$ Among them, $N$ is the population size, $S (i)$ display No.Fitness of $i$ $D F$ represents the current optimal fitness, $r_{1}$ Represents $[0, 1]$ random number, $T$ represents the maximum number of iterations, $\over 2}$ represents $S (i)$ The top half of slime mold individuals, $b F$ represents the best fitness obtained in the current iteration, $wF$ represents the worst fitness obtained in the current iteration, $S m e ll I n d ex represents the$ fitness sequence.

2.4 Algorithm pseudocode

Initialize the number of slime molds $N$ and the maximum number of iterations $T$ , etc.
Initialize the population $X_i(i=1,2,...,n)$
While $t < T$ do
Check if any slime mold individuals exceed the search space and modify them
Calculate the hunger value of each slime mold
Sort the slime molds by hunger value and find the slime mold that eats the most $X_{b}$ and its location $b es tF i t n ess$
Use formula (6) to update parameter $W$
For $i = 1$ to $N$ do
If $R an d < z$ then
Use formula (2) to update the slime mold position
Else
Use formula (4) to update parameter $p$
Use formula (3) to update the slime mold position
End If
End For
$t = t + 1$
End While
Return the most eaten slime mold $X_{b}$ and its location $b es tF i t n ess$

3. Experimental results

SMA on 23 classic test functions (set dimension $d im = 30$ ) The convergence curves in F1, F5, and F8, the test function formula is as follows:

function	official	Theoretical value
F1	${F_1}(x) = \sum\nolimits_{i = 1}^d {x_i^2}$	$0.00$
F5	${F_5}(x) = \sum\nolimits_{i = 1}^{n - 1} {[100{ {({x_{i + 1}} - x_i^2)}^2} + { {({x_i} - 1)}^2}]}$	$0.00$
F8	${F_8}(x) = \sum\nolimits_{i = 1}^d { - {x_i}\sin (\sqrt {\|{x_i}\|})}$	$- 418.9829 \times d im$

3.1 F1 convergence curve

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3.2 F5 convergence curve

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3.3 F8 convergence curve

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4. References

[1] LI S M, CHEN H L, WANG M J, et al. Slime mould algorithm: a new method for stochastic optimization[J]. Future generation computer systems, 2020, 111, 300-323.