Advantages of Task-Specific Multi-Objective Optimisation in Evolutionary Robotics

RESEARCH ARTICLE Advantages of Task-Specific Multi-Objective Optimisation in Evolutionary Robotics Vito Trianni1*, Manuel López-Ibáñez2 1 Institute of Cognitive Sciences and Technologies (ISTC), National Research Council (CNR), Rome, Italy, 2 IRIDIA, CoDE, Université Libre de Bruxelles (ULB), Brussels, Belgium * Abstract a11111 OPEN ACCESS Citation: Trianni V, López-Ibáñez M (2015) Advantages of Task-Specific Multi-Objective Optimisation in Evolutionary Robotics. PLoS ONE 10(8): e0136406. doi:10.1371/journal.pone.0136406 Editor: Long Wang, Peking University, CHINA Received: October 16, 2014 Accepted: August 4, 2015 Published: August 21, 2015 Copyright: © 2015 Trianni, López-Ibáñez. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. The software for replicating the experiments presented is available on GitHub at the following address: https://github.com/vito-trianni/more. Funding: The authors have no support or funding to report. Competing Interests: The authors have declared that no competing interests exist. The application of multi-objective optimisation to evolutionary robotics is receiving increasing attention. A survey of the literature reveals the different possibilities it offers to improve the automatic design of efficient and adaptive robotic systems, and points to the successful demonstrations available for both task-specific and task-agnostic approaches (i.e., with or without reference to the specific design problem to be tackled). However, the advantages of multi-objective approaches over single-objective ones have not been clearly spelled out and experimentally demonstrated. This paper fills this gap for task-specific approaches: starting from well-known results in multi-objective optimisation, we discuss how to tackle commonly recognised problems in evolutionary robotics. In particular, we show that multiobjective optimisation (i) allows evolving a more varied set of behaviours by exploring multiple trade-offs of the objectives to optimise, (ii) supports the evolution of the desired behaviour through the introduction of objectives as proxies, (iii) avoids the premature convergence to local optima possibly introduced by multi-component fitness functions, and (iv) solves the bootstrap problem exploiting ancillary objectives to guide evolution in the early phases. We present an experimental demonstration of these benefits in three different case studies: maze navigation in a single robot domain, flocking in a swarm robotics context, and a strictly collaborative task in collective robotics. 1 Introduction Artificial evolution is a powerful optimisation tool, and has been successfully applied to the synthesis of behaviours for autonomous robots, as demonstrated in the evolutionary robotics literature [1–4]. The advantages of the evolutionary robotics approach reside in the possibility of exploiting the sensorimotor coordination resulting from the interactions between the robot’s brain (i.e., the control software), its body (i.e., the embodiment including sensors and actuators) and the environment [5]. Through evolutionary approaches, the designer is exempted from a detailed modelling of the brain-body-environment interactions, and solutions can be obtained that match the specificities and statistical regularities of the problem at hand. However, a suitable engineering methodology to support the fundamental design choices in PLOS ONE | DOI:10.1371/journal.pone.0136406 August 21, 2015 1 / 27 Task-Specific Multi-Objective Optimisation in Evolutionary Robotics evolutionary robotics is currently missing. Indeed, most of the studies in evolutionary robotics strongly rely on the expertise of the designer, who assembles the evolutionary system following his personal intuition. Only few attempts have been made to propose an engineering methodology for the evolutionary design of robotic controllers [6, 7]. Among the several design choices required to devise an evolutionary robotics experiment, the fitness function is particularly important because it determines task-specific selective pressures to drive the evolutionary search (although task-agnostic approaches have been proposed as well [3, 8, 9]). However, the definition of a suitable fitness function is not always straightforward in evolutionary robotics [10, 11]. First of all, the features of the desired behaviour must be encoded in a measurable form, but often there is no definite and measurable way of expressing either the dynamical aspects of the robots’ behaviour or the desired outcome. Hence, it is common to find in the literature fitness functions composed of multiple behavioural terms that contribute to the one or the other feature (e.g., move fast, avoid obstacles, approach target) [11]. That is, the design problem in evolutionary robotics is intrinsically characterised by multiple objectives, but often tackled as a single-objective problem by means of an a priori aggregation (i.e., scalarization) of the various objectives. However, finding the correct trade-off between possibly conflicting terms is not easy. In this case, a multi-objective approach may provide a set of solutions that explore different trade-offs, so that a principled choice can be made a posteriori. Secondly, the fitness function must support the evolvability of the system [12], that is, the possibility to progressively synthesise better solutions through random exploration and avoid premature convergence [3]. Even when a single-objective (fitness) function—or a scalarization of multiple objectives—is available for the desired behaviour, this function might be difficult to optimise by evolution, because it may present many local optima or suffer from the bootstrap problem, which is defined as the absence of selective pressures among randomly initialised individuals at the beginning of the evolutionary optimisation [11, 13, 14]. Hence, it may be preferable to adopt a multi-objective formulation and approximate the corresponding Pareto front (finding the actual Pareto front is typically infeasible in evolutionary robotics). In this case, the original objective function can be exploited for choosing a posteriori the best solution from the obtained Pareto set. In the last two decades, evolutionary multi-objective approaches have shown their ability to explore multiple trade-offs in the objective space and to avoid premature convergence to poor solutions [15, 16]. As a result, the application of multi-objective optimisation (MOO) in evolutionary robotics is receiving increasing attention. However, evolutionary robotics goes beyond pure black-box optimisation, because there are multiple ways of introducing selective pressures other than the definit (...truncated)