Genetic Algorithm for Network Optimization

Optimization of traffic flow in a road network using MATLAB’s Genetic Algorithm, applied to a nonlinear objective function with flow conservation and capacity constraints.

Developed as part of the course Optimization Techniques at the Aristotle University of Thessaloniki (AUTH), School of Electrical & Computer Engineering.

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Problem Overview

A traffic network with 9 intersections (nodes) and 17 roads (edges) is modeled. Each road has a specific capacity and a congestion-sensitive travel time. The objective is to minimize the total travel time per vehicle by distributing traffic optimally, while satisfying:

• Flow conservation at all internal nodes
• Inflow = outflow condition
• Per-road capacity limits

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Network Diagram

Red numbers indicate road capacity ( c_i ) (vehicles/min). Each arrow represents a one-way traffic path between intersections.

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Travel Time Function

The delay for road (i) is modeled by the nonlinear function:

Where:

• ( t_i ): base (uncongested) travel time
• ( a_i ): congestion factor
• ( x_i ): flow on road (i)
• ( c_i ): road capacity

The total network cost is:

f(x) = ∑ᵢ xᵢ · Tᵢ(xᵢ)

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Methodology

We solve the nonlinear constrained optimization problem using MATLAB’s built-in Genetic Algorithm (ga). This choice is robust to local minima and does not require gradient information.

Constraints

• Linear equality constraints: Aₑq · x = bₑq
• Bound constraints: 0 ≤ xᵢ ≤ cᵢ
• Flow conservation is built into Aeq, beq

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Experiments

Baseline Optimization

• File: optimize_flow_baseline.m
• Traffic inflow: ( V = 100 ) vehicles/min

Robustness Analysis

• File: optimize_flow_variable_V.m
• Tested inflows: ( V = 85, 95, 105, 115 )
• For each V, the GA is run and convergence plots are generated.

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Repository Structure

genetic-algorithm-for-network-optimization
├── src/
│ ├── travel_time_objective.m # Objective function f(x)
│ ├── optimize_flow_baseline.m # GA run for V = 100
│ └── optimize_flow_variable_V.m # GA runs for V ∈ {85, 95, 105, 115}
├── images/
│ ├── network_diagram.png # Network structure
│ └── Ti(xi).png # Travel time function 
├── report.pdf # Project report with equations and results
└── README.md

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Tools Used

• MATLAB
• Optimization Toolbox
• Global Optimization Toolbox

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Author

Panagiotis Koutris
Undergraduate at AUTH – School of Electrical & Computer Engineering

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License

Licensed under the Apache 2.0 License.