Octopus Inspired Optimization (OIO): A Hierarchical Framework for Navigating Protein Fitness Landscapes

TL;DR

The paper tackles the challenge of optimizing protein sequences within rugged fitness landscapes by addressing the exploration–exploitation dilemma. It introduces Octopus Inspired Optimization (OIO), a hierarchical metaheuristic that fuses centralized global planning with decentralized semi-autonomous local search across three levels (brain, tentacles, and suckers), guided by a dynamic energy factor and PSO-like updates. Across GFP optimization, NK-Landscape, and CEC2022 benchmarks, OIO outperforms a broad suite of baselines, achieving top ranks on NK-Landscape and CEC2022 and strong performance on GFP, aided by a probabilistic matrix encoding that maps continuous search to discrete amino-acid sequences. The work positions OIO as a robust tool for protein engineering and a foundation for future hybrid optimization with deep learning surrogates and multi-objective extensions, enabling scalable, gradient-free design in drug discovery and personalized medicine.

Abstract

Navigating vast, rugged biological fitness landscapes to discover high-value functional patterns-such as optimal protein sequences-is a central challenge in health informatics. However, conventional algorithms often struggle with the exploration-exploitation dilemma, failing to synergize global search with deep local refinement, which leads to entrapment in suboptimal solutions. To overcome this barrier, we introduce Octopus Inspired Optimization (OIO), a novel hierarchical metaheuristic that mimics the octopus's unique neural architecture to intrinsically unify centralized global exploration and parallelized local exploitation. We validated OIO on a real-world protein engineering benchmark, where it surpassed 15 competing metaheuristics. This success is underpinned by OIO's architectural suitability for protein-like landscapes, confirmed by its top ranking on the NK-Landscape benchmark, and its powerful optimization engine, demonstrated by its first-place performance on the gold-standard CEC2022 benchmark. OIO thus provides a robust, nature-inspired computational tool for complex optimization problems in drug discovery and personalized medicine.

Figures (6)

• Figure 1: The octopus nervous system, illustrating the centralized brain and decentralized arm ganglia that inspire OIO's hierarchical architecture.
• Figure 2: The simplified framework of OIO, integrating signal generation, hierarchical mapping, and information interaction. Panel (a) illustrates how suckers perceive the environment, generate stimuli, and output signals as the initial source of information. Panel (b) presents the biological hierarchy of the octopus abstracted into the algorithm, where the octopus corresponds to the global individual, tentacles act as regional agents, and suckers serve as local units. Panel (c) demonstrates the bidirectional flow of information across the three levels, where suckers exchange information and report status upward, tentacles aggregate and transmit results to the octopus, and the octopus integrates feedback and issues control signals downward to guide the next iteration.
• Figure 3: Core dynamic mechanisms of OIO. Panel (a) illustrates the Group Co-evolution strategy, which balances exploration and exploitation using master and slave tentacles and includes an adaptive regeneration mechanism to escape local optima. Panel (b) shows the Iterative Optimization Process, a dynamic feedback loop where information flows from the suckers up to the individual, enabling adaptive resource allocation.
• Figure 4: Performance comparison of OIO and 15 baseline algorithms on the GFP optimization task. The boxplot illustrates the distribution of final fitness values across 10 independent runs. OIO (highlighted) demonstrates a superior median fitness and a consistently high-performing distribution, second only to the specialist Hill Climbing algorithm.
• Figure 5: Comprehensive performance comparison on the NK-Landscape benchmark. The boxplot shows the distribution of final fitness values from 10 independent runs across all five NK configurations. OIO (highlighted) exhibits a markedly superior distribution, with a higher median and less variance compared to the 15 baseline algorithms.