Optimization-in-Cpp

Mathematical optimization project implementing derivative-free methods for minimization of the objective function.

Task:

Minimize Lennard-Jones potential function $E_{LJ}$ $$E_{LJ} = 4\epsilon\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}\Big[\big(\frac{\sigma}{r_{ij}}\big)^{12}-\big(\frac{\sigma}{r_{ij}}\big)^{6}\Big],$$ where $N$ is the number of the clusters, $\epsilon\ (=1)$ the pair well depth, $\sigma\ (=1)$ the equilibrium pair separation and $r_{ij}$ the Euclidean distance between $i$ and $j$ atom.

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Methods used:

1. Nelder-Mead Algorithm
2. Genetic Algorithm with binary representation
3. Genetic Algorithm with real representation
4. Particle Swarm Optimization

Compile & Run

make clean && make

./run <int>

(not complete)