Optimization

This document describes the TG Planner optimization workflow and algorithms. It begins with a high-level overview of optimization approach and then dives into the specifics of the mathematical formulation.

Table of Contents

1. Overview
   1. Problem Modeling
   2. High-Level Formulation
   3. Optimization Workflow
   4. Network Analysis
2. Notation
3. Cost Minimization
   1. Objective Function
   2. Constraints
      1. Minimum Coverage
      2. Flow Balance
      3. Flow Capacity
      4. Flow Site
      5. Time Division Multiplexing
      6. Polarity
      7. Co-Located Sites
4. Coverage Maximization
   1. Objective Function
   2. Constraints
      1. Budget
      2. Adversarial Links
5. Cost Minimization with Redundancy
   1. Objective Function
   2. Decision Variables
   3. Redundancy Constraints
      1. Flow Site
      2. Flow Balance
      3. Polarity
   4. Two Phase Solution
      1. Flow Balance with Shortage
      2. Relaxed Redundancy Objective Function
   5. Heuristic Acceleration
      1. Delaunay Acceleration
6. Interference Minimization
   1. Objective Function
   2. Constraints
      1. Time Division Multiplexing
      2. Polarity
      3. Sector
      4. Symmetric Link
      5. Point-to-Multipoint
      6. CN Link
      7. Deployment Guidelines
      8. Interference
   3. Multi-Channel Constraints
      1. Multi-Channel Sector
      2. Multi-Channel Deployment Guidelines
      3. Multi-Channel Time Division Multiplexing
      4. Multi-Channel Interference
7. Connected Demand Site Optimization
   1. Objective Function
   2. Decision Variables
   3. Cost Minimization and Coverage Maximization Constraints
      1. Flow Balance
      2. Flow Capacity
      3. Flow Site
      4. Polarity
      5. Adversarial Links
      6. Flow Demand
   4. Interference Minimization Constraints
      1. Flow Link
8. Flow Optimization
   1. Objective Function
   2. Constraints
      1. Flow Balance
9. Future Directions
   1. P2MP Constraints in Site Selection
   2. Multi-Channel Link Capacity and Interference
   3. Sector Orientation
   4. POP Placement
   5. Variable POP Capacity
   6. Uplink Modeling
   7. Channel Bonding
   8. A Note on Run-to-Run Reproducibility