PAMSO

This package provides code to implement Parametric Autotuning Multi-time Scale Optimization Algorithm (PAMSO), an algorithm to solve multi-time scale optimization models.

Table of Contents

1. Overview
2. Installation
3. Example
4. Running Cases
5. Citation

Overview

Multi-time scale optimization models involving decision variables in multiple time scales have been used in different fields. To address scalability challenges in existing algorithms, we present the Parametric Autotuning Multi-time Scale Optimization algorithm (PAMSO) as a solution. PAMSO involves tuning parameters in a low-fidelity optimization model to help solve a higher-fidelity multi-time scale optimization model. The tunable parameters represent the mismatch between the low-fidelity and high-fidelity models and are tuned by forming a black box with these models which is optimized using Derivative-Free Optimization methods.

Installation

To intall the package and its dependencies run the following in julia

using Pkg
Pkg.add(url = "https://github.com/li-group/PAMSO.jl.git")

In addition, follow the instructions on Gurobi.jl to install the solver Gurobi.

Example

As an example, we try to solve a generator planning problem. The problem is based on example 6.5 in the Introduction to Linear Programming book by Dimitris Bertsimas and John N. Tsitsiklis. The data we use for the problem is in the Generator_expansion subfolder in the examples folder. The following steps are followed:

1. A high-level model and low-level model are formulated based on the full-space model and coded into separate files as functions. The high-level model is an aggregated version of model where we aggregate the system for entire time period. The low-level model involves fixing the capacity of the generators in the full-space model. The high-level model is parametrized based on the physics of the model. The high-level model is coded as a function which takes the tunable parameters as a parameters to the function and gives the high-level decisions (like the capacity of the gnerators) as an output. In this example, we store the high-level decision as a dictionary. The low-level model takes in the high-level decisions as parameters and outputs the objective function
2. We create a block of parameters and intitialize it with the initial set of parameters (init), lower bounds of parameters (lb),upper bounds of parameters ub and input_types (can be integer ("I") or real ("R")). In this example, the code is as follows:

  PAMSO_toy_params = PAMSO.PAMSO_params([1.0,1.0,0.0],[0.0,0.0,0.0],[10.0,10.0,1000.0], ["R","R","R"])

4. We create a PAMSO_block and initialize it with the function to generate the high-level model (gen_highlevel),the function to generate the low-level model (gen_lowlevel), the full-space model, number of parameters (dimmensions) and the parameters block. The code is as follows:

  PAMSO_toy = PAMSO.PAMSO_block(gen_highlevel, gen_lowlevel, fs_model, 3, params)

3. We then run one of the DFO agorithms ("MADS","Bayesopt" or "PSO") on the associated MBBF for a given number of function evaluations (approximate) like the following code:

  PAMSO.run(PAMSO_toy,"MADS",300)

PAMSO_toy.Param_best holds the best set of parameters after training the parameters using the DFO solvers.

The solution can be compared to the solution from the full-space model. The full-space model is coded in the file full_space_model.jl. Camerin Lee constributed to coding the full space model and data for the example.

Running Cases

We have a few examples of cases in the examples folder. They are listed in documentation sections. The associated PAMSO block can be accessed using the gen_problem(case) function. For example, to access the generator expansion case, we can use the following code:

  PAMSO_toy = PAMSO.gen_problem("Generator expansion")

Citation

Cite us

@misc{ramanujam2024pamsoparametricautotuningmultitime,
     title={PAMSO: Parametric Autotuning Multi-time Scale Optimization Algorithm}, 
     author={Asha Ramanujam and Can Li},
     year={2024},
     eprint={2407.16570},
     archivePrefix={arXiv},
     primaryClass={math.OC},
     url={https://arxiv.org/abs/2407.16570}, 
}