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Multi-objective optimization problems (MOPs) often require a trade-off between conflicting objectives, maximizing diversity and convergence in the objective space. This study presents an approach to improve the quality of MOP solutions by…

Optimization and Control · Mathematics 2026-02-02 Gladston Moreira , Ivan Meneghini , Elizabeth Wanner

The majority of standard approaches to financial portfolio optimization (PO) are based on the mean-variance (MV) framework. Given a risk aversion coefficient, the MV procedure yields a single portfolio that represents the optimal trade-off…

Portfolio Management · Quantitative Finance 2024-02-27 Bruno Gašperov , Marko Đurasević , Domagoj Jakobovic

While standard approaches to optimisation focus on producing a single high-performing solution, Quality-Diversity (QD) algorithms allow large diverse collections of such solutions to be found. If QD has proven promising across a large…

Neural and Evolutionary Computing · Computer Science 2023-04-27 Manon Flageat , Luca Grillotti , Antoine Cully

Consider the problem of training robustly capable agents. One approach is to generate a diverse collection of agent polices. Training can then be viewed as a quality diversity (QD) optimization problem, where we search for a collection of…

Machine Learning · Computer Science 2022-04-18 Bryon Tjanaka , Matthew C. Fontaine , Julian Togelius , Stefanos Nikolaidis

Multi-objective optimization (MOO) arises in many real-world applications where trade-offs between competing objectives must be carefully balanced. In the offline setting, where only a static dataset is available, the main challenge is…

Machine Learning · Computer Science 2026-02-16 Jatan Shrestha , Santeri Heiskanen , Kari Hepola , Severi Rissanen , Pekka Jääskeläinen , Joni Pajarinen

Choices in scientific research and management require balancing multiple, often competing objectives.Multiple-objective optimization (MOO) provides a unifying framework for solving multiple objective problems. Model selection is a critical…

Applications · Statistics 2018-10-26 Perry Williams , William Kendall , Mevin Hooten

The estimation and improvement of quality attributes in software architectures is a challenging and time-consuming activity. On modern software applications, a model-based representation is crucial to face the complexity of such activity.…

Software Engineering · Computer Science 2024-01-31 Daniele Di Pompeo , Michele Tucci

Single-objective optimization algorithms search for the single highest-quality solution with respect to an objective. Quality diversity (QD) optimization algorithms, such as Covariance Matrix Adaptation MAP-Elites (CMA-ME), search for a…

Machine Learning · Computer Science 2023-06-07 Matthew C. Fontaine , Stefanos Nikolaidis

Quality Diversity (QD) algorithms such as MAP-Elites are a class of optimisation techniques that attempt to find many high performing points that all behave differently according to a user-defined behavioural metric. In this paper we…

Optimization and Control · Mathematics 2023-07-20 Paul Kent , Adam Gaier , Jean-Baptiste Mouret , Juergen Branke

An iterative computer-aided ideation procedure is introduced, building on recent quality-diversity algorithms, which search for diverse as well as high-performing solutions. Dimensionality reduction is used to define a similarity space, in…

Neural and Evolutionary Computing · Computer Science 2018-07-26 Alexander Hagg , Alexander Asteroth , Thomas Bäck

Quality-Diversity (QD) has demonstrated potential in discovering collections of diverse solutions to optimisation problems. Originally designed for deterministic environments, QD has been extended to noisy, stochastic, or uncertain domains…

Neural and Evolutionary Computing · Computer Science 2025-02-11 Manon Flageat , Johann Huber , François Helenon , Stephane Doncieux , Antoine Cully

Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…

Quantum Physics · Physics 2022-10-13 Edric Matwiejew , Jason Pye , Jingbo B. Wang

Quality diversity (QD) algorithms have shown to provide sets of high quality solutions for challenging problems in robotics, games, and combinatorial optimisation. So far, theoretical foundational explaining their good behaviour in practice…

Artificial Intelligence · Computer Science 2024-12-17 Duc-Cuong Dang , Aneta Neumann , Frank Neumann , Andre Opris , Dirk Sudholt

Quality diversity (QD) is a branch of evolutionary computation that seeks high-quality and behaviorally diverse solutions to a problem. While adversarial problems are common, classical QD cannot be easily applied to them, as both the…

Neural and Evolutionary Computing · Computer Science 2026-05-18 Timothée Anne , Noah Syrkis , Meriem Elhosni , Florian Turati , Alexandre Manai , Franck Legendre , Alain Jaquier , Sebastian Risi

Quantum and quantum-inspired optimisation algorithms are designed to solve problems represented in binary, quadratic and unconstrained form. Combinatorial optimisation problems are therefore often formulated as Quadratic Unconstrained…

Artificial Intelligence · Computer Science 2022-05-27 Mayowa Ayodele , Richard Allmendinger , Manuel López-Ibáñez , Matthieu Parizy

Multi-objective optimization (MOO) is a well-studied problem for several important recommendation problems. While multiple approaches have been proposed, in this work, we focus on using constrained optimization formulations (e.g., quadratic…

Applications · Statistics 2016-02-16 Kinjal Basu , Ankan Saha , Shaunak Chatterjee

Improving open-ended learning capabilities is a promising approach to enable robots to face the unbounded complexity of the real-world. Among existing methods, the ability of Quality-Diversity algorithms to generate large collections of…

Machine Learning · Computer Science 2022-11-29 Luca Grillotti , Antoine Cully

More and more, optimization methods are used to find diverse solution sets. We compare solution diversity in multi-objective optimization, multimodal optimization, and quality diversity in a simple domain. We show that multiobjective…

Neural and Evolutionary Computing · Computer Science 2021-05-11 Alexander Hagg , Mike Preuss , Alexander Asteroth , Thomas Bäck

Multi-objective optimization (MOO) aims at finding a set of optimal configurations for a given set of objectives. A recent line of work applies MOO methods to the typical Machine Learning (ML) setting, which becomes multi-objective if a…

Machine Learning · Computer Science 2021-10-15 Michael Ruchte , Josif Grabocka

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without…