Bullfrog Optimization Algorithm(BOA)

This program implements BOA a new bio inspired evolutionary algorithm based on bullfrog

Enhanced E-BOA Algorithm Steps

Input:

• N — Population size
• MaxIter — Maximum iterations
• nVar — Number of variables (dimensions)
• VarMin, VarMax — Variable bounds
• fobj — Objective function
• params — Algorithm parameters (elite ratio, mutation probability, use of Levy flights, etc.)

Output:

• BestSol — Best solution found
• BestFit — Best fitness value
• ConvergenceCurve — Fitness progression over iterations
• Stats — Algorithm statistics (diversity, stagnation count, restarts, function evaluations)

Step 1: Initialization

1. Initialize population X randomly within bounds [VarMin, VarMax].
2. If opposition-based initialization is enabled, initialize half of the population using opposition-based strategy:Xi=VarMin+VarMax−XiX_i = VarMin + VarMax - X_iXi​=VarMin+VarMax−Xi​
3. Evaluate fitness Fitness(i) = fobj(X(i,:)) for all individuals.
4. Set PersonalBest(i,:) = X(i,:) and PersonalBestFit(i) = Fitness(i).
5. Identify BestSol and BestFit from the initial population.
6. Initialize velocity, stagnation counters, and statistics.

Step 2: Main Optimization Loop (Iterations t = 1 to MaxIter)Step 2.1: Adaptive Parameter Update

• Step size:

s=smax−(smax−smin)⋅t/MaxIters = s_{max} - (s_{max} - s_{min}) \cdot t / MaxIters=smax​−(smax​−smin​)⋅t/MaxIter

• Inertia weight for velocity:

w=0.9−0.5⋅t/MaxIterw = 0.9 - 0.5 \cdot t / MaxIterw=0.9−0.5⋅t/MaxIter

• Number of neighbors for social learning: decreases over time.

Step 2.2: Population Diversity Check

• Compute population diversity using pairwise distances.
• If diversity < diversity_threshold and iteration > MaxIter/4, restart part of the population while retaining elite individuals.

Step 2.3: Update Each Individual

For each individual i:

1. Elite Solutions Perturbation:

• If i is elite, apply small Gaussian perturbation.

1. Enhanced Ambush Hunting:

• Multi-step update toward BestSol:

Xi←Xi+hunt_factor⋅(BestSol−Xi)X_i \leftarrow X_i + hunt\_factor \cdot (BestSol - X_i)Xi​←Xi​+hunt_factor⋅(BestSol−Xi​)

• With probability, apply Levy flight for long jumps.

1. Social Learning with Neighbors:

• Select neighbors_idx based on fitness.
• Update position using one of three strategies:
• Direct learning: move toward neighbor
• Personal best learning: move toward neighbor’s personal best
• Hybrid learning: weighted combination

1. Predator Avoidance:

• Move away from worst solutions to avoid local traps:

Xi←Xi+avoidance_strength⋅(Xi−Xworst)X_i \leftarrow X_i + avoidance\_strength \cdot (X_i - X_{worst})Xi​←Xi​+avoidance_strength⋅(Xi​−Xworst​)

1. Velocity-based Update (PSO inspired):Velocity(i,:)=w⋅Velocity(i,:)+c1⋅(PersonalBest−Xi)+c2⋅(BestSol−Xi)Velocity(i,:) = w \cdot Velocity(i,:) + c1 \cdot (PersonalBest - X_i) + c2 \cdot (BestSol - X_i)Velocity(i,:)=w⋅Velocity(i,:)+c1⋅(PersonalBest−Xi​)+c2⋅(BestSol−Xi​)Xi←Xi+Velocity(i,:)X_i \leftarrow X_i + Velocity(i,:)Xi​←Xi​+Velocity(i,:)
2. Gaussian Mutation:

• With probability mutation_prob, perturb solution using Gaussian noise.

1. Crossover with Random Partner:

• Swap variables with another random individual with probability crossover_prob.

1. Escape for Stagnant Solutions:

• If Stagnant(i) >= k_stagnant, apply one of:
• Random restart
• Opposition-based restart
• Elite-guided restart

1. Boundary Control:

• Reflect variables that exceed bounds back into feasible range.

1. Evaluate New Solution

• Update fitness and personal best.
• Update global best if improvement occurs.
• Update stagnation counters.

Step 2.4: Global Stagnation Tracking

• Track number of iterations without improvement in BestFit.

Step 3: Convergence Recording

• Save BestFit for current iteration in ConvergenceCurve(t)
• Save population diversity and other statistics.

Step 4: Termination

• Stop after MaxIter iterations.
• Return BestSol, BestFit, ConvergenceCurve, and Stats.