Metaheuristics for the Template Design Problem: Encoding, Symmetry and Hybridisation

TL;DR

This paper evaluates various metaheuristics for the complex Template Design Problem, considering problem encoding, symmetry, and hybridisation, and introduces a novel slot-based formulation to improve solution quality.

Contribution

It provides a comprehensive analysis of metaheuristics for TDP, including a new slot-based formulation and insights into their effectiveness and efficiency.

Findings

Some metaheuristics achieve state-of-the-art results on specific instances.

Hybrid and symmetry-breaking approaches improve solution quality.

The slot-based formulation offers an alternative to classical methods.

Abstract

The template design problem (TDP) is a hard combinatorial problem with a high number of symmetries which makes solving it more complicated. A number of techniques have been proposed in the literature to optimise its resolution, ranging from complete methods to stochastic ones. However, although metaheuristics are considered efficient methods that can find enough-quality solutions at a reasonable computational cost, these techniques have not proven to be truly efficient enough to deal with this problem. This paper explores and analyses a wide range of metaheuristics to tackle the problem with the aim of assessing their suitability for finding template designs. We tackle the problem using a wide set of metaheuristics whose implementation is guided by a number of issues such as problem formulation, solution encoding, the symmetrical nature of the problem, and distinct forms of hybridisation. For the TDP, we also propose a slot-based alternative problem formulation (distinct to other slot-based proposals), which represents another option other than the classical variation-based formulation of the problem. An empirical analysis, assessing the performance of all the metaheuristics (i.e., basic, integrative and collaborative algorithms working on different search spaces and with/without symmetry breaking) shows that some of our proposals can be considered the state-of-the-art when they are applied to specific problem instances.