Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions

TL;DR

This paper introduces a practical evolutionary heuristic for the minimum tile set problem in algorithmic self-assembly, aiming to minimize supply diversity while ensuring proper assembly of simple objects in 2D and 3D.

Contribution

It presents the first practical approach to MTSP using a multi-objective evolutionary heuristic tailored for self-assembly systems.

Findings

Heuristic effectively reduces tile set size in experiments.

Demonstrates applicability to 2D and 3D object assembly.

Provides insights into optimizing self-assembly processes.

Abstract

The field of algorithmic self-assembly is concerned with the design and analysis of self-assembly systems from a computational perspective, that is, from the perspective of mathematical problems whose study may give insight into the natural processes through which elementary objects self-assemble into more complex ones. One of the main problems of algorithmic self-assembly is the minimum tile set problem (MTSP), which asks for a collection of types of elementary objects (called tiles) to be found for the self-assembly of an object having a pre-established shape. Such a collection is to be as concise as possible, thus minimizing supply diversity, while satisfying a set of stringent constraints having to do with the termination and other properties of the self-assembly process from its tile types. We present a study of what we think is the first practical approach to MTSP. Our study starts with the introduction of an evolutionary heuristic to tackle MTSP and includes results from extensive experimentation with the heuristic on the self-assembly of simple objects in two and three dimensions. The heuristic we introduce combines classic elements from the field of evolutionary computation with a problem-specific variant of Pareto dominance into a multi-objective approach to MTSP.