A Physarum-inspired approach to the Euclidean Steiner tree problem

Abstract

This paper presents a novel biologically-inspired explore-and-fuse approach to solving a large array of problems. The inspiration comes from Physarum, a unicellular slime mold capable of solving the traveling salesman and Steiner tree problems. Besides exhibiting individual intelligence, Physarum can also share information with other Physarum organisms through fusion. These characteristics of Physarum imply that spawning many such organisms we can explore the problem space in parallel, each individual gathering information and forming partial solutions pertaining to a local region of the problem space. When the organisms meet, they fuse and share information, eventually forming one organism which has a global view of the problem and can apply its intelligence to find an overall solution to the problem. This approach can be seen as a “softer” method of divide and conquer. We demonstrate this novel approach, developing the Physarum Steiner Algorithm which is capable of finding feasible solutions to the Euclidean Steiner tree problem. This algorithm is of particular interest due to its resemblance to Physarum polycephalum, ability to leverage parallel processing, avoid obstacles, and operate on various shapes and topological surfaces including the rectilinear grid.