Source-linked AI summary
Mycelial Search: A Graph-Structured Metaheuristic for Continuous Optimisation
Mohammad Mahdi Dehshibi
TL;DR
Continuous optimisation methods often lack an evolving spatial structure for local information exchange. Myco addresses this with an adaptive graph of active tips, communities, conductances, and anchors, achieving competitive results on selected benchmark functions while its ablations distinguish community- and edge-level roles.
Problem
Population methods often represent candidate relationships weakly, limiting explicit spatial interaction when useful information is local.
Method
Myco represents candidates as active tips in a reconstructed graph, uses Louvain communities to regulate information exchange, adapts flow-aligned cord conductances, and preserves strong anchors.
Results
On the CEC 2022 benchmark, Myco was compared with established methods, while ablations showed that cord plasticity controls edge-level persistence and community detection controls information-exchange range.
Takeaways & Limitations
Myco makes local organisation an explicit, analyzable component of continuous optimisation by incorporating community partitions and edge conductances into the search state.
Takeaways & Limitations
Performance weakens when useful information is distributed across disconnected or competing landscape regions, where community-weighted flow may restrict rapid redistribution of search effort.
Abstract
from arXiv · showhide
Continuous optimisation methods need to balance sharing information and maintaining alternative search directions. In this paper, we introduce Mycelial Search (Myco), a graph-structured metaheuristic designed around active tips, community-weighted flow, adaptive cord plasticity, and anchor-based injection. Candidate solutions form an evolving spatial graph in which a Louvain partition distinguishes within-community from cross-community information exchange. Adaptive cord plasticity subsequently modifies active tip-to-tip edges according to their alignment with the local flow. An anchor-based injection mechanism supplements the graph-driven tip dynamics. We evaluated Myco on the CEC 2022 single-objective bound-constrained benchmark suite at dimensions $D=10$ and $D=20$, using 30 independent runs per algorithm-function pair. The comparison includes eleven established optimisers from several search families. Myco reaches competitive results on selected functions across both dimensions. The ablation analysis further shows that community structure regulates the range of graph-based information exchange, whereas cord plasticity controls the persistence of local directional influence. These findings indicate that graph-structured local interaction can support continuous optimisation, while its effectiveness depends on landscape structure and information transfer across local search regions.
Highlights
Mycelial Search introduces an evolving graph structure for continuous optimisation, using community detection and adaptive cord plasticity to regulate information exchange and directional influence. It achieves competitive results on CEC 2022 functions across two dimensions, with sparse-graph per-iteration complexity of O(Nlog N+ ND).
- Mycelial Search introduces an evolving graph structure for continuous optimisation.
- Community detection regulates information exchange across local search regions.
- Adaptive cord plasticity reinforces flow-aligned links and attenuates others.
- O(Nlog N+ ND) per iteration under sparse graph connectivity.
- Myco achieves competitive results on CEC 2022 functions across two dimensions.
1. Introduction
The paper introduces Mycelial Search (Myco), a graph-structured metaheuristic that organizes candidate solutions through adaptive local interactions, community-weighted flow, and preserved high-quality anchors. It evaluates Myco on the CEC 2022 benchmark suite and studies the separate roles of adaptive conductance and community partitioning.
- Motivation: Many population methods weakly represent relationships among candidate solutions, limiting their ability to exploit useful local information that changes with the search state.Existing interactions are often mediated by global-best solutions, sampled exemplars, or temporary population differences rather than a persistent spatial structure.
- Method: Myco represents candidate solutions as active tips in a spatial graph reconstructed each iteration and retains a bounded set of historically favourable anchors.Tips receive locally weighted flow from neighbouring nodes, while anchors preserve accessible high-quality locations.
- Method: A Louvain partition distinguishes within-community from cross-community interactions, regulating the scope of information exchange across the evolving graph.The partition provides mesoscale organization for graph-based search.
- Method: Conductance updates reinforce tip-to-tip edges aligned with induced flow and attenuate unsupported edges, retaining directional influence according to local agreement.This adaptive edge-strength mechanism modifies the current graph during search.
- Evaluation: Myco is evaluated on the CEC 2022 single-objective bound-constrained benchmark suite across two dimensions and compared with established methods from several search families.The study also examines the separate contributions of adaptive conductance and community partitioning.
2. Related Work
Related work spans population-based, adaptive-operator, bio-inspired, and graph-structured optimisation methods. Myco extends graph-based connectivity and flow reinforcement from network-centred problems to interactions among candidate solutions in continuous optimisation.
- Population-based optimisation: Population-based methods coordinate concurrently updated candidates to balance exploration and exploitation through selection, variation, personal history, exemplars, or differential mutation.Examples include GA, PSO, and DE.
- Adaptive population methods: Later population methods refined learning sources, diversity maintenance, population sizing, archives, and success-history adaptation.Examples include CLPSO, SAP-DE, JADE, and SHADE.
- Bio-inspired optimisation: Bio-inspired optimisers recast population search using natural-process metaphors including foraging, leadership and hunting, oscillatory adaptation, and moss growth.Representative methods include ABC, GWO, WOA, and SMA.
- Adaptive-graph optimisation: Adaptive-graph optimisation uses connectivity, flow balance, and path reinforcement to influence search, with Physarum-inspired methods representing this computational direction.These methods have mainly targeted network-centred problems such as routing and transmission-path reconstruction.
- Research gap: Myco addresses the gap between network-oriented graph methods and continuous optimisation by organising candidate-solution interactions through adaptive connectivity and flow-based reinforcement.Earlier graph-oriented methods generally assumed that solutions were paths, routes, or transport networks.
3. Proposed Method
Myco models continuous search as an evolving weighted spatial graph of active tips and retained anchors, combining community-weighted flow with adaptive tip-to-tip cord conductance. Anchors preserve strong locations and guide neighbourhood structure, while the method updates tips, anchors, and graph interactions iteratively.
- Biological motivation: Myco is motivated by distributed mycelial exploration and transport, representing candidate solutions as local explorers interacting through connections, directional flow, and adaptive edge strength.Tips provide concurrent exploration, while anchors preserve historically strong locations and keep promising regions accessible to the network.
- Cord plasticity: Cord plasticity provides short-term memory by reinforcing tip-to-tip edges aligned with induced flow and decaying unsupported conductances within bounded limits.Anchor edges contribute to flow but are not adapted; shared undirected conductances can be revised from both endpoints in one iteration.
- Graph construction: The search state is an undirected, weighted spatial graph whose nodes are active tips and retained anchors, with at most K_max anchors retained by lowest objective value.New tip-to-tip edges start with conductance g_pq = 1; anchor-incident conductances are fixed and excluded from plasticity.
- Community-driven flow: Community-weighted flow uses Louvain partitions to distinguish within-community and cross-community interactions when computing weighted displacement flows toward neighbouring tips and anchors.The sigmoid gate is annealed over the evaluation budget, becoming less selective as κ decreases toward κ_min.
- Tip and anchor updates: Each iteration evaluates tips, updates the incumbent best position, and inserts it as an anchor only when its distance from every retained anchor exceeds ε = 10^-6.The retained-anchor set is subsequently capped by retaining only the K_max anchors with the lowest objective values.
4. Experiments
Experiments evaluate Myco on CEC 2022 functions across two dimensions using repeated, equal-budget comparisons with eleven established optimisers. Results show competitive but landscape-dependent performance, while ablations separate community-scale communication from local directional persistence.
- Experimental protocol: Myco was evaluated on CEC 2022 functions F1–F11 at D=10 and D=20, using 30 independent runs per algorithm–function pair.Myco used 30 tips under an equal function-evaluation budget, while comparators used configured populations of 50.
- Experimental protocol: Final-error comparisons report means and standard deviations, with results organized by search family and lowest means identified globally and within non-differential-evolution families.Tables 3 and 4 cover D=10 and D=20, respectively.
- Main comparative results: Myco reaches exact convergence on F1 at both dimensions and performs strongly on F2 at D=20, consistent with graph construction, anchor retention, and flow-driven tip motion.These mechanisms provide locally weighted displacement and preserve previously favourable locations through a local structural memory.
- Main comparative results: Myco remains competitive on hybrid and composition functions when local flow identifies productive directions, but performance weakens when useful information is distributed across disconnected or competing regions.This reflects a trade-off between community-weighted local-flow support and maintaining alternative search directions.
- Ablation analysis: At D=20, Plasticity reduces mean error on F1, F3, F4, F5, F7, F8, F9, and F11, whereas Louvain remains preferable on F2, F6, and F10.Plasticity also substantially lowers standard deviations on F4 and F7, but its benefit is not universal.
- Ablation analysis: Greedy Modularity produces one community, losing intra- versus inter-community distinctions and yielding extreme mean-to-median divergence on selected functions.Louvain restores partitioned flow with weaker cross-community messaging, while Plasticity controls persistence of directions within the local graph.
5. Conclusion
The conclusion presents Mycelial Search (Myco) as continuous optimisation over an evolving local interaction graph, with anchors, community detection, and cord plasticity shaping information exchange. Evaluations and ablations show that community structure and edge-level plasticity regulate different aspects of search behaviour.
- Method: Myco represents candidate solutions as active tips in an evolving graph, while bounded anchors preserve historically favourable positions.The graph is reconstructed at each iteration.
- Mechanisms: Louvain community detection controls the strength and range of information exchange within and across communities.The community detection backend operates at the partition level.
- Mechanisms: Cord plasticity reinforces or decays individual tip-to-tip connections according to their alignment with the local flow.It operates at the edge level, affecting the persistence of local directional influence.
- Evaluation: Myco was evaluated on the CEC 2022 single-objective bound-constrained benchmark suite and compared with established metaheuristic methods, alongside ablations of cord plasticity and community detection.The ablation results demonstrated that these mechanisms control different aspects of the search.
- Significance: Myco makes community partitions and tip-to-tip edge conductances explicit components of the search state that affect information flow between candidate solutions.This formulation makes local organisation a component of continuous optimisation that can be defined, examined, and modified.