Wireless Sensor Network Lifetime Maximization

This repository contains a Python + Gurobi optimization model that maximizes the network lifetime of a wireless sensor network (WSN) under energy constraints and limited outgoing links per node.

The model generates random sensor deployments in a disc-shaped area, builds a directed communication graph, and solves a mixed-integer optimization problem where the objective is to maximize the lifetime scalar T.

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What this code does

For each iteration (random topology seed):

1. Generates a disc-shaped topology

   • Node 0 is the base station (sink) at (0,0)
   • Nodes 1..n-1 are sensors uniformly distributed over a disk of radius Rnet

2. Builds directed links

   • Every sensor can transmit to every other node (including sink), excluding self-links
   • Link set: A = {(i,j) | i ∈ sensors, j ∈ all nodes, i ≠ j}

3. Computes energy per transmitted flow

   • Distance: D(i,j)
   • Transmission energy per unit flow: [ P_{tx}(i,j) = \rho + \epsilon \cdot D(i,j)^\alpha ]
   • Reception cost per unit flow: Prx

4. Solves an optimization model

   • Continuous flow variables f(i,j)
   • Binary link activation variables a(i,j)
   • Lifetime variable T (objective)

5. Logs results

   • Prints lifetime and solve time
   • Writes to results.txt in the format:

     iterNo; lifetime; runtime_ms
     

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Optimization model (summary)

Decision variables

• f(i,j) ≥ 0 : flow sent from node i to node j
• a(i,j) ∈ {0,1} : whether link (i,j) is used (activated)
• T ≥ 0 : network lifetime scaling factor

Constraints

1) Flow balance at each sensor node [ \sum_{j \in V, j\neq i} f(i,j) - \sum_{j \in W, j\neq i} f(j,i) = S_i \cdot T ] Each sensor generates S_i units of data per time, scaled by lifetime T.

2) Energy constraint at each sensor node [ \sum_{j \in V, j\neq i} P_{tx}(i,j),f(i,j) ;+; Prx\sum_{j \in W, j\neq i} f(j,i) \le e_i ]

3) Link activation coupling (Big-M) [ f(i,j) \le M \cdot a(i,j) ]

4) Outgoing link limit [ \sum_{j \in V, j\neq i} a(i,j) \le L_{out} ] Each sensor can use at most Lout outgoing links.

Objective

[ \max ; T ]

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Requirements

• Python 3.9+ recommended
• gurobipy
• numpy

You also need a working Gurobi installation + license.

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Installation

pip install numpy gurobipy