Setting Parameters by Example

TL;DR

This paper introduces inverse parametric optimization, where the goal is to find parameters that produce a specific optimal solution, with algorithms for various problems and applications in routing, planning, and resource management.

Contribution

It presents new algorithms for inverse parametric optimization problems across multiple combinatorial optimization tasks and discusses practical applications.

Findings

Algorithms successfully determine parameters for given solutions.

Applicable to minimum spanning trees, shortest paths, and other subgraph problems.

Demonstrates relevance in routing, planning, and resource allocation.

Abstract

We introduce a class of "inverse parametric optimization" problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We describe algorithms for solving such problems for minimum spanning trees, shortest paths, and other "optimal subgraph" problems, and discuss applications in multicast routing, vehicle path planning, resource allocation, and board game programming.