Minimum cost polygon overlay with rectangular shape stock panels

TL;DR

This paper formulates the Minimum Cost Polygon Overlay problem, involving covering a polygon with rectangular panels, and compares the effectiveness of greedy, Monte Carlo, and genetic algorithms for solving it.

Contribution

It introduces a model for the MCPO problem and evaluates three different optimization algorithms to determine their effectiveness.

Findings

Genetic Algorithm outperforms other methods in cost minimization.

Monte Carlo method provides a good balance between solution quality and computational effort.

Greedy search is the fastest but less optimal.

Abstract

Minimum Cost Polygon Overlay (MCPO) is a unique two-dimensional optimization problem that involves the task of covering a polygon shaped area with a series of rectangular shaped panels. This has a number of applications in the construction industry. This work examines the MCPO problem in order to construct a model that captures essential parameters of the problem to be solved automatically using numerical optimization algorithms. Three algorithms have been implemented of the actual optimization task: the greedy search, the Monte Carlo (MC) method, and the Genetic Algorithm (GA). Results are presented to show the relative effectiveness of the algorithms. This is followed by critical analysis of various findings of this research.