A Novel Graphical Method to Globally Solve Mixed-Integer Nonlinear Programs

Abstract

Optimization solvers play a crucial role in the advancement of the field of mathematical optimization as they bridge theoretical breakthroughs and computational power to solve real-world problems. While mixed-integer linear programming and convex solvers have matured greatly over the past several decades, the solution technology for general mixed-integer nonlinear programs (MINLPs) has not nearly reached that level of maturity. There are still various problem structures that cannot be modeled properly through state-of-the-art global solvers due to the lack of an efficient parser for their algebraic representation. Even for problems that are admissible within the modeling boundaries of modern solvers, there are several classes with complex structures that suffer from weak relaxations and poor solution performances. An example of such structures is the trigonometric constraints that appear in trajectory optimization problems in aerospace engineering, which also have applications in Air Force where unmanned aerial vehicles need to reconstruct optimal trajectories when encountering an obstacle in their original proposed paths. Therefore, there is a critical need to design novel global solution algorithms that mitigate the limitations posed by traditional techniques. This project seeks to address the need for more effectively solve general MINLPs via a graphical framework. If successful, this project will open new pathways for globally solving MINLPs that are poorly handled by modern solvers and existing solution methods.

Document Details

Document Type
DoD Grant Award
Publication Date
Feb 29, 2024
Source ID
FA95502310183

Entities

People

  • Danial Davarnia

Organizations

  • Air Force Office of Scientific Research
  • Iowa State University
  • United States Air Force

Tags

Readers

  • Military Science and Technology Research and Modernization.
  • Operations Research
  • Systems Analysis and Design

Technology Areas

  • Autonomy
  • Space