Understanding fitness landscapes in morpho-evolution via local optima networks

TL;DR

This study applies Local Optima Network analysis to fitness landscapes arising from three morpho-evolution encodings (Direct, L-System, CPPN) in a 2D locomotion task, revealing encoding-dependent landscape navigability. The L-System encoding demonstrates superior landscape navigability, enabling escape from local optima and exploration of diverse designs, while CPPN encodings tend to trap searches in numerous low-quality optima; Direct encoding falls between them, with some good solutions but limited exploration. By linking encoding choices to the structure of local optima networks, the work explains observed performance differences and suggests landscape-aware algorithm design for morpho-evolution. The findings show LONs as a valuable tool for interpreting ME searches and guiding future encoding and operator design in evolutionary robotics, with broader implications for landscape-aware optimization strategies.

Abstract

Morpho-evolution (ME) refers to the simultaneous optimisation of a robot's design and controller to maximise performance given a task and environment. Many genetic encodings have been proposed which are capable of representing design and control. Previous research has provided empirical comparisons between encodings in terms of their performance with respect to an objective function and the diversity of designs that are evaluated, however there has been no attempt to explain the observed findings. We address this by applying Local Optima Network (LON) analysis to investigate the structure of the fitness landscapes induced by three different encodings when evolving a robot for a locomotion task, shedding new light on the ease by which different fitness landscapes can be traversed by a search process. This is the first time LON analysis has been applied in the field of ME despite its popularity in combinatorial optimisation domains; the findings will facilitate design of new algorithms or operators that are customised to ME landscapes in the future.

Figures (6)

• Figure 1: An example robot attempting to move horizontally through the virtual environment. Each shape is a module, and each module has its own controller.
• Figure 2: On the left: directed tree created by an L-System encoding after two iterations. The nodes labelled $C_1$ and $R_1$ show a circle and rectangle module, respectively. On the right: an example of a virtual 2D robot; its graph is visualised in the top right. Figure is from veenstra2022effects
• Figure 3: Diagram representing how an L-system works
• Figure 4: Diagram representing a CPPN network
• Figure 5: LONs for the three robot design encodings. larger size and darker colour of nodes indicate better fitness. Node size is proportional to fitness. For colour: nodes with fitness in the first quartile of the overall fitness distribution across the three LONs (this is a fitness of less than 9.59) are low-fitness and are coloured very pale purple. Nodes within the interquartile range are middle-fitness and are light purple in colour. Finally, nodes with fitness in the upper quartile --- which is 24.48 or above --- are high-fitness and are dark purple. Self-loops are represented with edges which curve out of and back into the right of a node.