SLIDE 1
Graph-Based Modeling and Optimization using Plasmo.jl
Jordan Jalving & Victor M. Zavala Department of Chemical and Biological Engineering University of Wisconsin-Madison
1
Motivation: Cyber-Physical Systems
2
Optimization using Plasmo.jl Jordan Jalving & Victor M. Zavala - - PowerPoint PPT Presentation
Optimization using Plasmo.jl Jordan Jalving & Victor M. Zavala - - PowerPoint PPT Presentation
Graph-Based Modeling and Optimization using Plasmo.jl Jordan Jalving & Victor M. Zavala Department of Chemical and Biological Engineering University of Wisconsin-Madison Third Annual JuMP Development Workshop March 14 th , 2019 1
SLIDE 2
SLIDE 3
Algebraic Graphs (Model Graphs)
3
Model Graph Formulation Connectivity Matrix JuMP Model JuMP Model JuMP Model Link JuMP Models
SLIDE 4
4
Algebraic Graph Example
Create a Model-Graph (Algebraic Graph) Solve and Query Results JuMP Models Load Packages
SLIDE 5
Hierarchical Algebraic Graphs
5
Link Systems Gas Infrastructure Graph Power Infrastructure Graph
SLIDE 6
Hierarchical Modeling Example
6
SLIDE 7
Decomposition Algorithms
7
Braulio Brunaud
SLIDE 8
Graph Decomposition
8
Linear Algebra Decomposition (e.g., PIPS-NLP) Lagrangean Decomposition Modeled System Graph Partitions
SLIDE 9
Model Graph Partitioning
9
➢ 1 million variable nonlinear programming problem ➢ Solves with PIPS-NLP ~40 minutes
SLIDE 10
Model Graph Community Detection
10
SLIDE 11
Graph-Based Modeling Abstractions
11
Algebraic Graphs Computing Graphs
- Exploit physical topology
- Nodes=Models, Edges=Static Connections
- Exploit topology to decompose
large-scale optimization problems
- Exploit communication topology
- Nodes=Tasks, Edges=Dynamic Connections
- Exploit topology to simulate behavior of
algorithms and computing architectures
SLIDE 12
Computing Graphs
Challenge: Capture computing aspects (e.g., Asynchronicity, Delays, Latency) of a real-time system
12
Key Elements
Nodes: Tasks and Attributes (data) Tasks: Computing time Edges: Communication Clock: Scheduling & Management State-Space Description
SLIDE 13
Computing Graphs
13
➢ Compute tasks and communication each require time ➢ A discrete-event queue coordinates simulation timings (the clock)
SLIDE 14
Simulation of Distributed Optimization Algorithms
14
Master solution (and scenarios) Sub-problem solution
Idea: Predict Effects of Computing/Communication Delays and Failures Example: Benders Decomposition
Simulate parallel algorithm variants (synchronous & asynchronous) Sub-problem solution
SLIDE 15
Plasmo.jl Implementation
15
- 1. Create Computing Graph
- 2. Add Master Node with Attributes (Data) and Tasks
- 3. Initialize Graph
- 4. Add Sub-nodes and Connections
- 5. Execute Computing Graph
SLIDE 16
Synchronous Benders Algorithm
16
CPU
- Simulation Predicts Poor Parallel Efficiency (Idle Processors)
Idle CPU time
SLIDE 17
Asynchronous Benders Algorithm
CPU
- Simulation predicts much higher parallel efficiency (but longer solution time)
17
SLIDE 18
Thank You
18