ReviewDoes being multi-headed make you better at solving problems? A survey of Physarum-based models and computations
Introduction
In the 1990s, computer scientists began to look to biological systems for inspiration when designing optimisation algorithms. For approximately 10 years, trail-laying ants were the paradigm, particularly with respect to shortest path problems [1], [2]. Ant colony optimisation algorithms (ACOs) worked well in static environments. However, most optimisation problems are dynamic and require the algorithms to constantly update their solutions. Later, ACOs became increasingly less based on real biological systems because of the (as it turned out incorrect [3], [4], [5]) assumption that trail-laying ants are incapable of adjusting rapidly to changes in their foraging environment. As a consequence, attention turned to another organism, the true slime mould Physarum polycephalum, because of its ability to solve mazes and to develop adaptive and fault-tolerant networks [6], [7].
Modelling has focused on two fundamental behaviours: expansion and contraction. The expansion behaviour is captured by models based on Physarum's morphology and taxis, while the contraction behaviour is characterised by positive feedback dynamics.
Similar to research on other nature-inspired computational methods (e.g., artificial immune systems [8], [9], ant colony systems [10], etc.), we will take two different perspectives, namely, Physarum-based modelling and Physarum-based computing. In the context of modelling, studies focus on Physarum's foraging behaviour to help better capture its core features and the underlying mechanisms [11], [12], [13]. These features and mechanisms are then exploited in the context of Physarum-based computing to solve complex computational problems (e.g., travelling salesman problems (TSPs) [14] and community detection [15]). Knowing the advantages and the limitations of the existing models is critical to designing novel and more effective Physarum-based solutions. Such solutions are now particularly sought after because of the technological advances that have led to, on the one hand, cheap sensing techniques, and on the other hand, ubiquitous real-time data streaming. A comprehensive survey that summarises the research on Physarum from both a modelling and a computing perspective is therefore badly needed. Now is also the time to explore if Physarum-based optimization methods are superior to the methods that are based on trail-laying ants or whether the field has simply moved on to the next charismatic model organism.
Here we will first survey the existing Physarum-based research in Section 2 by using the latest published literature in the Web of Science database. This survey classifies the achievements of Physarum-based research and lays emphasis on the two time-evolving foraging behaviours (i.e., expansion and contraction) and the three features of these behaviours (i.e., morphology, taxis, and the positive feedback loop). Then, Section 3 details the typical Physarum models in terms of the three characteristic features from both top-down and bottom-up perspectives and illustrates how the core features of Physarum's foraging process help solve the difficult problems that are encountered in complex systems research. The examples in this context include the design of man-made infrastructure networks [16], [17], network organisation [18], [19], path planning or finding [20], [21], and hybrid optimisation [14], [22]. Finally, Section 4 concludes with a list of unsolved problems in the field and a discussion of the potential to solve these problems by relying on Physarum as a source of inspiration.
Section snippets
Physarum's plasmodium
Physarum polycephalum (literally, multi-headed slime mould) is a unicellular organism in the class Myxomycetes. Physarum feeds on microorganisms but also on larger food items such as fungi, and, conveniently, oat flakes in the lab [23]. All behaviours studied concerning adaptive networks are exhibited in the active vegetative stage of its complex life cycle, called the ‘plasmodium’. In this stage the organism produces a large (up to in nature), multi-nucleated, but still unicellular,
Physarum-based modelling
Modelling inspired by Physarum's foraging behaviour has benefited from focusing on the above-mentioned characteristics, that is, Physarum's morphology, tactical behaviour, and feedback loop dynamics. A general aim for Physarum-based and similar bio-inspired models is to achieve self-organised computability [35]. The modelling techniques to achieve this general aim can be quite different and include cellular automata [36], [37], [38], [39], agent-based systems [13], [40], [41], [42], and
Conclusion and outlook
Is there a need for yet another organism to base bio-inspired optimisation algorithms on? And if so, is Physarum the best alternative? The initial choice of ants as inspiration for optimisation algorithms logically followed from studies on the organisation of ant colonies. By studying the behaviour of individual ants and translating that behaviour into colony-level behaviour, often with the use of mathematical models, we achieved a good understanding of how self-organisation leads to emergent
Acknowledgements
We would like to acknowledge the support from the National Natural Science Foundation of China (Nos. 61403315, 61402379) and the Fundamental Research Funds for the Central Universities (No. XDJK2016A008) to C.G. and Z.Z.; Ministry of Education, Culture, Sports, Science & Technology (MEXT) Scholarship (No. 152503) to D.S.; the Research Grant Program of Inamori Foundation to M.J.; the National 1000 Young Talent Plan (No. W099102), the Fundamental Research Funds for the Central Universities (No.
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