Use of a genetic algorithm to find solutions to introductory physics problems

TL;DR

This paper demonstrates how a genetic algorithm can be employed to generate step-by-step solutions for introductory physics problems by optimizing equation sequences based on known and unknown quantities.

Contribution

It introduces a novel application of genetic algorithms to find physics problem solutions by modeling the sequence of equations as an optimization problem.

Findings

Successfully guided students to solutions in one-dimensional kinematics

The method effectively minimizes the difference between knowns and unknowns in equations

Discusses interpretability of the algorithm's solution process

Abstract

In this work, we show how a genetic algorithm (GA) can be used to find step-by-step solutions to introductory physics problems. Our perspective is that the underlying task for this is one of finding a sequence of equations that will lead to the needed answer. Here a GA is used to find an appropriate equation sequence by minimizing a fitness function that measures the difference between the number of unknowns versus knowns in a set of equations. Information about knowns comes from the GA posing questions to the student about what quantities exist in the text of their problem. The questions are generated from enumerations pulled from the chromosomes that drive the GA. Equations with smaller known vs. unknown differences are considered more fit and are used to produce intermediate results that feed less fit equations. We show that this technique can guide a student to an answer to any introductory physics problem involving one-dimensional kinematics. Interpretability findings are discussed.