Table 1 Symbols and their descriptions.
Symbol | Description |
|---|---|
CPM parameters | |
G | Grid of CPM cells (edge nodes) |
\(s_i\) | State of cell (node) i |
\(s'_i\) | Proposed new state for cell i |
\(\Delta E\) | Change in energy: \(\Delta E = E(s'_i) - E(s_i)\) |
\(E(s_i)\) | Energy function capturing interactions and constraints |
\(J(s_i, s_j)\) | Interaction coefficient between neighboring cells i and j |
\(P(s_i)\) | Penalty function encoding resource constraints for cell i |
\(\lambda\) | Weighting factor for the penalty term in CPM |
T | Temperature parameter controlling probabilistic acceptance in CPM |
PSO parameters | |
M | Number of particles in the PSO swarm |
\(x_j(t)\) | Position (scheduling configuration) of particle j at iteration t |
\(v_j(t)\) | Velocity of particle j at iteration t |
\(pBest_j\) | Personal best position found by particle j |
gBest | Global best position found by the swarm |
\(\omega\) | Inertia weight balancing exploration/exploitation |
\(c_1, c_2\) | Acceleration coefficients guiding movement towards \(pBest_j\) and gBest |
\(r_1, r_2\) | Random scalars \(\in [0,1]\) for stochastic velocity updates |
Objective function terms | |
\(\alpha , \beta\) | Weights balancing energy vs. latency in the fitness function |
\(\text {Energy}(x)\) | Total energy consumption given scheduling configuration x |
\(\text {Latency}(x)\) | Total task latency under scheduling configuration x |
f(x) | Objective function: \(f(x) = \alpha \cdot \text {Energy}(x) + \beta \cdot \text {Latency}(x)\) |
Miscellaneous | |
N | Number of CPM cells (edge nodes) |
\(\text {maxIter}\) | Maximum iteration count for the hybrid algorithm |
