Table 1.

Suggested parameters for the RZOA.

Parameter Type	Parameter Name	Symbol	Recommended Range / Value	Description
DZOA Core	Population size	N	100	Number of agents (Zebra tours)
	Maximum iterations	Tmax	1000	Number of main iterations (depends on problem size)
	Initial Zebra weight	Wi	0.5	Determines the initial balance between exploration and exploitation
	Migration rate	β1	0.5	Controls the strength of migration effect
	Alignment rate	β2	0.5	Controls the strength of alignment effect
	Metropolis acceptance probability	p = exp(-∆L/T)	-	Allows acceptance of slightly worse tours to avoid local minim
DQN Parameters	Learning rate	α	0.003	Controls learning speed of the Q-network
	Discount factor	γ	0.95	Balances importance of future vs. immediate rewards
	Replay buffer size	C	25,000	Number of experience samples stored for replay
	Mini-batch size	B	32–128	Number of samples per training step
	Initial epsilon	ε0	1.0	Starts with full exploration
	Minimum epsilon	εmin	0.1	Minimum exploration rate
	Epsilon decay schedule	decay	Linear or exponential	Governs transition from exploration to exploitation
	Target network update frequency	τ or freq	τ = 0.01 or every 100 steps	Controls stability of DQN training
	Hidden layer neurons	-	[64, 32, 16]	Three-layer fully connected Q-network
	Activation function	-	ReLU	Ensures stable and nonlinear learning
General and Hybrid Parameters	Temperature coefficient (Metropolis	T0	1.0	Initial temperature in Metropolis rule
	Reward normalization	rt		Scaled reward proportional to improvement ratio
	Weight update mechanism		Adaptive based on success	Adjusts exploration/exploitation dynamically
	Stopping criterion	-	No improvement in 200 iterations	Early stopping to prevent unnecessary computation