T-DominO: Exploring Multiple Criteria with Quality-Diversity and the Tournament Dominance Objective

Real-world design problems are a messy combination of constraints, objectives, and features. Exploring these problem spaces can be defined as a Multi-Criteria Exploration (MCX) problem, whose goals are to produce a set of diverse solutions with high performance across many objectives, while avoiding low performance across any objectives. Quality-Diversity algorithms produce the needed design variation, but typically consider only a single objective. We present a new ranking, T-DominO, specifically designed to handle multiple objectives in MCX problems. T-DominO ranks individuals relative to other solutions in the archive, favoring individuals with balanced performance over those which excel at a few objectives at the cost of the others. Keeping only a single balanced solution in each MAP-Elites bin maintains the visual accessibility of the archive – a strong asset for design exploration. We illustrate our approach on a set of easily understood benchmarks, and showcase its potential in a many-objective real-world architecture case study

Evolution of linkages for prototyping of linkage based robots

Prototyping robotic systems is a time consuming process. Computer aided design, however, might speed up the process significantly. Quality-diversity evolutionary approaches optimise for novelty as well as performance, and can be used to generate a repertoire of diverse designs. This design repertoire could be used as a tool to guide a designer and kick-start the rapid prototyping process. This paper explores this idea in the context of mechanical linkage based robots. These robots can be a good test-bed for rapid prototyping, as they can be modified quickly for swift iterations in design. We compare three evolutionary algorithms for optimising 2D mechanical linkages: 1) a standard evolutionary algorithm, 2) the multi-objective algorithm NSGA-II, and 3) the quality-diversity algorithm MAP-Elites. Some of the found linkages are then realized on a physical hexapod robot through a prototyping process, and tested on two different floors. We find that all the tested approaches, except the standard evolutionary algorithm, are capable of finding mechanical linkages that creates a path similar to a specified desired path. However, the quality-diversity approaches that had the length of the linkage as a behaviour descriptor were the most useful when prototyping. This was due to the quality-diversity approaches having a larger variety of similar designs to choose from, and because the search could be constrained by the behaviour descriptors to make linkages that were viable for construction on our hexapod platform

Rigorous Runtime Analysis of Diversity Optimization with GSEMO on OneMinMax

The evolutionary diversity optimization aims at finding a diverse set of solutions which satisfy some constraint on their fitness. In the context of multi-objective optimization this constraint can require solutions to be Pareto-optimal. In this paper we study how the GSEMO algorithm with additional diversity-enhancing heuristic optimizes a diversity of its population on a bi-objective benchmark problem OneMinMax, for which all solutions are Pareto-optimal. We provide a rigorous runtime analysis of the last step of the optimization, when the algorithm starts with a population with a second-best diversity, and prove that it finds a population with optimal diversity in expected time $O(n^2)$, when the problem size $n$ is odd. For reaching our goal, we analyse the random walk of the population, which reflects the frequency of changes in the population and their outcomes.Comment: The full version of the paper accepted to FOGA 2023 conferenc

Bayesian optimisation for quality diversity search with coupled descriptor functions

Quality Diversity (QD) algorithms such as the Multi- Dimensional Archive of Phenotypic Elites (MAP-Elites) are a class of optimisation techniques that attempt to find many high performing points that all behave differently according to a userdefined behavioural metric. In this paper we propose the Bayesian Optimisation of Elites (BOP-Elites) algorithm. Designed for problems with expensive fitness functions and coupled behaviour descriptors, it is able to return a QD solution-set with excellent performance already after a relatively small number of samples. BOP-Elites models both fitness and behavioural descriptors with Gaussian Process surrogate models and uses Bayesian Optimisation strategies for choosing points to evaluate in order to solve the quality-diversity problem. In addition, BOP-Elites produces high quality surrogate models which can be used after convergence to predict solutions with any behaviour in a continuous range. An empirical comparison shows that BOP-Elites significantly outperforms other state-of-the-art algorithms without the need for problem-specific parameter tuning