Draft:Atomic Energy Optimization

Atomic Energy Optimization (AEO) is a metaheuristic optimization algorithm introduced in 2024. The method is inspired by physical processes of atomic energy, in particular the accumulation, transfer, and dissipation of energy. AEO treats candidate solutions as "atoms" whose energy states evolve during the search process. The algorithm has been applied to benchmark test functions, wireless sensor networks, and feature selection problems.

History

The development of AEO was motivated by research into physics-inspired metaheuristics. While earlier approaches drew inspiration from biological or social processes, AEO was designed to incorporate analogies from atomic energy dynamics. Specifically, it models how electrons accumulate energy, exchange it with neighboring systems, and dissipate energy through processes such as static discharge.

The first formal presentation of AEO appeared in 2024 in a peer-reviewed article, which introduced the mathematical formulation and validated the method on benchmark functions.

In 2025, AEO was adapted for wireless sensor network clustering, where the AEOWSNC protocol demonstrated its use in managing the energy consumption of sensor nodes.

Design Principles

AEO is built around analogies with atomic processes:

• Accumulation: atoms with higher stability store energy in a way similar to favorable candidate solutions.
• Transfer: energy is exchanged between atoms through interactions, modeling how information passes between solutions.
• Dissipation: excess or unstable energy is released, preventing unproductive search directions.

Algorithm

Each candidate solution is represented as an atom with a position vector and energy state. At every iteration, atoms undergo accumulation, transfer, and dissipation according to their fitness and interactions.

Mathematical Formulation

Let:

• $N$ – number of atoms (population size)
• $x_{i}^{t}$ – position of atom $i$ at iteration $t$
• $f(x_{i}^{t})$ – fitness value of solution $x_{i}^{t}$
• $E_{i}^{t}$ – energy of atom $i$ at iteration $t$

Equations:

$E_{acc,i}^{t}=g(f(x_{i}^{t})),\quad E_{diss,i}^{t}=\delta \cdot E_{i}^{t}$

$T_{ij}^{t}=\kappa (E_{j}^{t}-E_{i}^{t}){\frac {x_{j}^{t}-x_{i}^{t}}{\|x_{j}^{t}-x_{i}^{t}\|+\epsilon }},\quad j\neq i$

$x_{i}^{t+1}=x_{i}^{t}+\alpha (E_{acc,i}^{t}-E_{diss,i}^{t})u_{i}^{t}+\beta \sum _{j\neq i}T_{ij}^{t}$

where:

• $\alpha ,\beta ,\delta ,\kappa$ are control parameters
• $u_{i}^{t}$ is a perturbation vector
• $\epsilon$ prevents division by zero

Pseudocode

Initialize population of N atoms randomly
Assign initial energies based on fitness
for t = 1 to T_max:
    for each atom i:
        Compute accumulation and dissipation
        Compute transfer from other atoms
        Update position using energy dynamics
        Evaluate new fitness and update energy
    end for
    Retain the best solutions (elitism)
end for
Return the best atom as solution

Applications

AEO has been investigated in several areas:

• Wireless Sensor Networks: applied to clustering and energy balancing in WSNs.
• Benchmark Functions: tested on unimodal and multimodal functions including Sphere, Rosenbrock, Rastrigin, and Schwefel.
• Combinatorial Optimization: adapted for discrete problems such as the Traveling Salesman Problem.
• Feature Selection: applied in machine learning to select subsets of features for classification tasks.
• Engineering Design: used in optimization of structural and design parameters.

Research Context

Since its introduction, AEO has been studied as part of physics-inspired optimization research. Ongoing and potential research directions include:

• Adaptive parameter adjustment for accumulation, transfer, and dissipation.
• Variants for constrained, multi-objective, and large-scale optimization.
• Hybrid methods combining AEO with local search.
• Applications in communication networks, scheduling, and energy systems.

Limitations

• Computationally demanding for large populations.
• Sensitive to parameter choices, requiring calibration.
• Theoretical convergence analysis is limited.
• Independent replication and application to real-world problems are still emerging.

See also

• Metaheuristic
• Swarm intelligence
• Evolutionary computation
• Genetic algorithm
• Particle swarm optimization
• Simulated annealing
• Differential evolution
• Artificial bee colony algorithm