Algorithm 1: The AHALA

Initialize parameters: Population size ($N$), Maximum iterations ($T_{max}$), Dimensions ($Dim$), Upper and lower bounds ($ub, lb$) Initialize exploration parameters: Frequency of Hill Climbing ($k$), Maximum Hill Climbing Iterations ($M$) Set step size parameters: Initial Step Size ($\alpha$), Step size decay factor ($\beta$) Initialize a population of agents ($Z$) with random positions within the search space Evaluate the fitness of each agent Calculate the Current Optimal Solution $Z_{best}$ For ($t$ = 1 to $T_{max}$) Calculate the value of E by Equation (14) For each search agents $Z$ If E > 1 then If rand < 0.3 then Update the current Position by Equation (3) else Update the current Position by Equation (7) else If rand < 0.5 then Update the current Position by Equation (9) else Update the current Position by Equation (12) End Evaluate the fitness of all modified population If the current iteration is divisible by $k$: Perform Hill Climbing on top-performing agents: For each selected agent (based on fitness ranking): Initialize step size = α For t = 1 to M: Update agent position using Hill Climbing mechanism by Equation (15) Evaluate the new fitness If new fitness is better, accept the solution Decay the step size by factor β by Equation (16) End Update population with new agent positions Store and track the best global solution $Z_{best}$ End Return: Best global solution $Z_{best}$, and it’s fitnes value ${fitness}_{best}$