This project focuses on solving various optimization problems including network flow and energy arbitrage. It demonstrates the application of different optimization algorithms to real-world scenarios in operations research.
Network flow problems are a central theme in operations research, where the goal is to optimize the movement or flow through a network in a way that minimizes or maximizes some quantity (like cost or flow amount).
- Ford-Fulkerson Method: Iteratively searches for augmenting paths to find maximum flow
- Edmonds-Karp Algorithm: Implements Ford-Fulkerson using BFS for shortest paths
- Dinic's Algorithm: Uses level graphs and blocking flows for efficient maximum flow computation
The flow value f in the network must satisfy:
- Capacity Constraint:
$f(u, v) \leq c(u, v)$ - Flow Conservation:
$$\displaystyle{\sum_{v \in V}} f(u, v) = 0 ),\forall u \neq s, t$$
The project includes an energy arbitrage optimization model that maximizes profit from battery storage operations while considering various constraints and costs.
- Battery charge/discharge optimization
- Time-of-use electricity pricing
- Battery degradation costs
- Round-trip efficiency considerations
- State of charge management
Results are changed each time iteration is run since I am manipulating data. The model achieves significant profit optimization while maintaining battery health:
- Net Profit: $53.35
- Energy Charged: 174.3 kWh
- Energy Discharged: 179.5 kWh
- Round-trip Efficiency: 103.0%
- Equivalent Cycles: 1.80
- Python: Primary programming language
- NetworkX: Graph operations
- Matplotlib: Visualization
- Pyomo: Mathematical optimization
- GLPK: Linear programming solver
- Traffic management
- Telecommunications
- Supply chain logistics
- Energy storage systems
- Resource allocation in cloud computing