Self-Adaptive Brain-Eating Amoeba Optimization(SABEO)

this program ilutrates working of Self-Adaptive Brain-Eating Amoeba Optimization

Algorithm: SA-BEAO

Step 1. Initialization

1.1. Define the objective function f(x)f(x)f(x), decision variables dimension DDD, population size NNN, and maximum iterations Tmax⁡T_{\max}Tmax​.

1.2. Initialize amoeba population X={x1,x2,…,xN}X = \{x_1, x_2, …, x_N\}X={x1​,x2​,…,xN​} randomly within bounds [lb,ub][lb, ub][lb,ub].

1.3. Evaluate fitness f(xi)f(x_i)f(xi​) for each amoeba.

1.4. Set the best solution xbestx_{best}xbest​ and record the best fitness.

1.5. Initialize operator probabilities pj=1/Mp_j = 1/Mpj​=1/M, where MMM is the number of operators. Initialize operator success counters sj=1s_j = 1sj​=1.

Step 2. Adaptive Evolution (for each iteration t=1→Tmax⁡t = 1 \to T_{\max}t=1→Tmax​)

2.1. Update adaptive parameters

• Reduce exploration factor α=α0(1−t/Tmax⁡)0.5\alpha = \alpha_0 (1 - t/T_{\max})^{0.5}α=α0​(1−t/Tmax​)0.5.
• Adjust local search radius rloc=0.1+0.9(1−t/Tmax⁡)r_{loc} = 0.1 + 0.9(1 - t/T_{\max})rloc​=0.1+0.9(1−t/Tmax​).

2.2. For each amoeba xix_ixi​:

• Select an operator OjO_jOj​ using roulette wheel selection based on probabilities pjp_jpj​.
• Apply the chosen operator to generate a candidate solution xnewx_{new}xnew​.

Operators:

• Flagellate Motion: Directed movement toward the global best.
• Phagocytosis: Local Gaussian perturbation (exploit).
• Encystment: Random reinitialization (diversify).
• Swarm Interaction: Attraction toward neighbor mean.
• Shapeshifting: Scaling mutation of current vector.
• Binary Splitting: Create child solution via Gaussian offspring.
• Lévy Flight: Large jump with heavy-tailed step.

2.3. Boundary control

• Ensure xnewx_{new}xnew​ lies within [lb,ub][lb, ub][lb,ub].

2.4. Selection

• If f(xnew)<f(xi)f(x_{new}) < f(x_i)f(xnew​)<f(xi​), replace xi←xnewx_i \leftarrow x_{new}xi​←xnew​.
• Update operator success counter sj=sj+1s_j = s_j + 1sj​=sj​+1 if improvement occurred.

2.5. Update global best

• If f(xnew)<f(xbest)f(x_{new}) < f(x_{best})f(xnew​)<f(xbest​), update xbest=xnewx_{best} = x_{new}xbest​=xnew​.

Step 3. Adaptive Operator Probability Update

• Every Δt\Delta tΔt iterations (e.g., 20):

pj=max⁡(sj∑k=1Msk,  pmin⁡)p_j = \max\left(\frac{s_j}{\sum_{k=1}^M s_k}, \; p_{\min}\right)pj​=max(∑k=1M​sk​sj​​,pmin​)

• Normalize probabilities so that ∑jpj=1\sum_j p_j = 1∑j​pj​=1.
• This favors operators with higher success while ensuring exploration.

Step 4. Stopping Condition

• Repeat Steps 2–3 until Tmax⁡T_{\max}Tmax​ is reached or convergence is satisfied.

Step 5. Output

• Return best solution xbestx_{best}xbest​ and its fitness f(xbest)f(x_{best})f(xbest​).