Dwarf Sperm Whale Optimization (DSWO) Algorithm

inspired by the behavior or characteristics of the dwarf sperm whale.

Algorithm Steps

1. Initialization:Randomly initialize a population of candidate solutions (called "whales").
2. Deep Dive (Exploration):Update positions based on deep, long-range movements, possibly using Levy flights:Xit+1=Xit+α⋅Levy(β)X_i^{t+1} = X_i^t + \alpha \cdot \text{Levy}(\beta)Xit+1​=Xit​+α⋅Levy(β)
3. Prey Detection (Exploitation):Refine search around promising solutions using small adaptive steps:Xit+1=Xit+γ⋅(Xbest−Xit)⋅rX_i^{t+1} = X_i^t + \gamma \cdot (X_{\text{best}} - X_i^t) \cdot rXit+1​=Xit​+γ⋅(Xbest​−Xit​)⋅rwhere rrr is a random number in [0, 1].
4. Escape Mechanism (Avoiding Local Minima):With a small probability ppp, apply an "ink escape":Xit+1=Xit+δ⋅randn()X_i^{t+1} = X_i^t + \delta \cdot \text{randn}()Xit+1​=Xit​+δ⋅randn()where randn()\text{randn}()randn() adds noise to escape a local optimum.
5. Evaluation:Evaluate fitness of each solution.
6. Update Best:Keep track of the best solution found so far.
7. Termination:Repeat until a maximum number of iterations or convergence.

🔢 Parameters

• α\alphaα: step size for deep dive
• β\betaβ: shape parameter for Levy flight
• γ\gammaγ: step size for exploitation
• δ\deltaδ: escape strength
• ppp: escape probability

✅ Advantages

• Balances exploration and exploitation
• Can avoid premature convergence with its "ink" defense strategy
• Suitable for high-dimensional or noisy optimization problems

🔧 Applications

• Engineering design
• Neural network training
• Renewable energy optimization (e.g., solar/wind systems)
• Economic dispatch in power systems