Alejandro Marrero

Generating new instances via evolutionary methods is commonly used to create new benchmarking data-sets, with a focus on attempting to cover an instance-space as completely as possible. Recent approaches have exploited Quality-Diversity methods to evolve sets of instances that are both diverse and discriminatory with respect to a portfolio of solvers, but these methods can be challenging when attempting to find diversity in a high-dimensional feature-space. We address this issue by training a model based on Principal Component Analysis on existing instances to create a low-dimension projection of the high-dimension feature-vectors, and then apply Novelty Search directly in the new low-dimension space. We conduct experiments to evolve diverse and discriminatory instances of Knapsack Problems, comparing the use of Novelty Search in the original feature-space to using Novelty Search in a low-dimensional projection, and repeat over a given set of dimensions. We find that the methods are complementary: if treated as an ensemble, they collectively provide increased coverage of the space. Specifically, searching for novelty in a low-dimension space contributes 56% of the filled regions of the space, while searching directly in the feature-space covers the remaining 44%.

To advance research in the development of optimisation algorithms, it is crucial to have access to large test-beds of diverse and discriminatory instances from a domain that can highlight strengths and weaknesses of different algorithms. The DIGNEA tool enables diverse instance suites to be generated for any domain, that are also discriminatory with respect to a set of solvers of the user choice. Written in C++, and delivered as a repository and as a Docker image, its modular and template-based design enables it to be easily adapted to multiple domains and types of solvers with minimal effort. This paper exemplifies how to generate instances for the Knapsack Problem domain.

The ability to generate example instances from a domain is important in order to benchmark algorithms and to generate data that covers an instance-space in order to train machine-learning models for algorithm selection. Quality-Diversity (QD) algorithms have recently been shown to be effective in generating diverse and discriminatory instances with respect to a portfolio of solvers in various combinatorial optimisation domains. However these methods all rely on defining a descriptor which defines the space in which the algorithm searches for diversity: this is usually done manually defining a vector of features relevant to the domain. As this is a limiting factor in the use of QD methods, we propose a meta-QD algorithm which uses an evolutionary algorithm to search for a nonlinear 2D projection of an original feature-space such that applying novelty-search method in this space to generate instances improves the coverage of the instance-space. We demonstrate the effectiveness of the approach by generating instances from the Knapsack domain, showing the meta-QD approach both generates instances in regions of an instance-space not covered by other methods, and also produces significantly more instances.

Gathering sufficient instance data to either train algorithm-selection models or understand algorithm footprints within an instance space can be challenging. We propose an approach to generating synthetic instances that are tailored to perform well with respect to a target algorithm belonging to a predefined portfolio but are also diverse with respect to their features. Our approach uses a novelty search algorithm with a linearly weighted fitness function that balances novelty and performance to generate a large set of diverse and discriminatory instances in a single run of the algorithm. We consider two definitions of novelty: (1) with respect to discriminatory performance within a portfolio of solvers; (2) with respect to the features of the evolved instances. We evaluate the proposed method with respect to its ability to generate diverse and discriminatory instances in two domains (knapsack and bin-packing), comparing to another well-known quality diversity method, Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) and an evolutionary algorithm that only evolves for discriminatory behaviour. The results demonstrate that the novelty search method outperforms its competitors in terms of coverage of the space and its ability to generate instances that are diverse regarding the relative size of the “performance gap” between the target solver and the remaining solvers in the portfolio. Moreover, for the Knapsack domain, we also show that we are able to generate novel instances in regions of an instance space not covered by existing benchmarks using a portfolio of state-of-the-art solvers. Finally, we demonstrate that the method is robust to different portfolios of solvers (stochastic approaches, deterministic heuristics, and state-of-the-art methods), thereby providing further evidence of its generality.

The present thesis has been partially supported by Agencia Canaria de Investigación Innovación y Sociedad de la Información de la Consejería de Economía, Conocimiento y Empleo y por el Fondo Social Europeo (FSE) Programa Operativo Integrado de Canarias 2014-2020, Eje 3 Tema Prioritario 74 (85%) - under grant TESIS2020010005.