Over the last few years, an increasing number of publications has shown that living organisms are very effective in finding solutions to complex mathematical problems which usually demand large computation resources. The plasmodium of the slime mould Physarum polycephalum is a successful example that has been used to solve path-finding problems on graphs and combinatorial problems. Cellular automata (CAs) computational model can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally (emergent computation). We developed a CA that models exactly the Physarum's behavior and applied it in finding the minimum-length path between two points in a labyrinth, as well as in solving a path-planning problem by guiding the development of adaptive networks, as in the case of the actual rail network of Tokyo. The CA results are in very good agreement with the computation results produced by the living organism experiments in both cases. Moreover, our CA hardware implementation results in faster and more effective computation performance, because of its inherent parallel nature. Consequently, our CA, implemented both in software and hardware, can serve as a powerful and low-cost virtual laboratory that models the slime mould Physarum's computation behavior.

No abstract

Man-made transport networks and their design are closely related to the shortest path problem and considered amongst the most debated problems of computational intelligence. Apart from using conventional or bio-inspired computer algorithms, many researchers tried to solve this kind of problem using biological computing substrates, gas-discharge solvers, prototypes of a mobile droplet, and hot ice computers. In this aspect, another example of biological computer is the plasmodium of acellular slime mould Physarum polycephalum (P. polycephalum), which is a large single cell visible by an unaided eye and has been proven as a reliable living substrate for implementing biological computing devices for computational geometry, graph-theoretical problems, and optimization and imitation of transport networks. Although P. polycephalum is easy to experiment with, computing devices built with the living slime mould are extremely slow; it takes slime mould days to execute a computation. Consequently, mapping key computing mechanisms of the slime mould onto silicon would allow us to produce efficient bio-inspired computing devices to tackle with hard to solve computational intelligence problems like the aforementioned. Toward this direction, a cellular automaton (CA)-based, Physarum-inspired, network designing model is proposed. This novel CA-based model is inspired by the propagating strategy, the formation of tubular networks, and the computing abilities of the plasmodium of P. polycephalum. The results delivered by the CA model demonstrate a good match with several previously published results of experimental laboratory studies on imitation of man-made transport networks with P. polycephalum. Consequently, the proposed CA model can be used as a virtual, easy-to-access, and biomimicking laboratory emulator that will economize large time periods needed for biological experiments while producing networks almost identical to the tubular networks of the real-slime mould.

A network design problem is to select a subset of links in a transport network that satisfy passengers or cargo transportation demands while minimizing the overall costs of the transportation. We propose a mathematical model of the foraging behaviour of slime mould P. polycephalum to solve the network design problem and construct optimal transport networks. In our algorithm, a traffic flow between any two cities is estimated using a gravity model. The flow is imitated by the model of the slime mould. The algorithm model converges to a steady state, which represents a solution of the problem. We validate our approach on examples of major transport networks in Mexico and China. By comparing networks developed in our approach with the man-made highways, networks developed by the slime mould, and a cellular automata model inspired by slime mould, we demonstrate the flexibility and efficiency of our approach.

No abstract