Juhi Optimization Algorithm (JOA)

The main inspiration of this algorithm comes from the juhi (Jasminum auriculatum)plant.

Mathematical Model

Let:

• NNN = number of plants (population)
• XiX_iXi​ = position of plant iii in the search space
• f(Xi)f(X_i)f(Xi​) = fitness (objective function)
• XbestX_{best}Xbest​ = best position found so far
• ttt = current iteration, TmaxT_{max}Tmax​ = maximum iterations

Mathematical Model

Let:

• NNN = number of plants (population)
• XiX_iXi​ = position of plant iii in the search space
• f(Xi)f(X_i)f(Xi​) = fitness (objective function)
• XbestX_{best}Xbest​ = best position found so far
• ttt = current iteration, TmaxT_{max}Tmax​ = maximum iterations

1. Root Expansion Phase (Exploration)

Plants spread roots randomly to explore nutrients:

Xinew=Xi+α⋅rand(1,D)⋅(Xrand−Xi)X_i^{new} = X_i + \alpha \cdot rand(1, D) \cdot (X_{rand} - X_i)Xinew​=Xi​+α⋅rand(1,D)⋅(Xrand​−Xi​)

where

• α\alphaα = root expansion rate (0.5–1.0),
• XrandX_{rand}Xrand​ = random plant position.

2. Stem Growth Phase (Transition)

Plants grow toward light and resources:

Xinew=Xi+β⋅rand(1,D)⋅(Xbest−∣Xi∣)X_i^{new} = X_i + \beta \cdot rand(1, D) \cdot (X_{best} - |X_i|)Xinew​=Xi​+β⋅rand(1,D)⋅(Xbest​−∣Xi​∣)

where

• β\betaβ = growth factor (0.3–0.7).

3. Flower Blooming Phase (Exploitation)

Flowers bloom around the best nutrient/light zone:

Xinew=Xbest+γ⋅(randn(1,D))X_i^{new} = X_{best} + \gamma \cdot (randn(1, D))Xinew​=Xbest​+γ⋅(randn(1,D))

where

• γ=γ0(1−tTmax)\gamma = \gamma_0 (1 - \frac{t}{T_{max}})γ=γ0​(1−Tmax​t​), decreasing over time to refine the search.

🌸 Algorithm Steps

1. Initialize population XiX_iXi​ randomly within bounds [lb,ub][lb, ub][lb,ub].
2. Evaluate fitness f(Xi)f(X_i)f(Xi​).
3. Identify XbestX_{best}Xbest​.
4. Repeat until maximum iterations:

• Perform Root Expansion for a fraction of plants.
• Perform Stem Growth for middle-range plants.
• Perform Flower Blooming for top-performing plants.
• Update XbestX_{best}Xbest​.

1. Return XbestX_{best}Xbest​ as optimal solution.

1. Root Expansion Phase (Exploration)

Plants spread roots randomly to explore nutrients:

Xinew=Xi+α⋅rand(1,D)⋅(Xrand−Xi)X_i^{new} = X_i + \alpha \cdot rand(1, D) \cdot (X_{rand} - X_i)Xinew​=Xi​+α⋅rand(1,D)⋅(Xrand​−Xi​)

where

• α\alphaα = root expansion rate (0.5–1.0),
• XrandX_{rand}Xrand​ = random plant position.

2. Stem Growth Phase (Transition)

Plants grow toward light and resources:

Xinew=Xi+β⋅rand(1,D)⋅(Xbest−∣Xi∣)X_i^{new} = X_i + \beta \cdot rand(1, D) \cdot (X_{best} - |X_i|)Xinew​=Xi​+β⋅rand(1,D)⋅(Xbest​−∣Xi​∣)

where

• β\betaβ = growth factor (0.3–0.7).

3. Flower Blooming Phase (Exploitation)

Flowers bloom around the best nutrient/light zone:

Xinew=Xbest+γ⋅(randn(1,D))X_i^{new} = X_{best} + \gamma \cdot (randn(1, D))Xinew​=Xbest​+γ⋅(randn(1,D))

where

• γ=γ0(1−tTmax)\gamma = \gamma_0 (1 - \frac{t}{T_{max}})γ=γ0​(1−Tmax​t​), decreasing over time to refine the search.