Fast Shortest Path Optimization Inspired by Shuttle Streaming of Physarum Polycephalum Jayantha Siriwardana Department of Mechanical Engineering School of Engineering The University of Melbourne Parkville, Victoria, Australia Email: jsat@pgrad.unimelb.edu.au Saman K. Halgamuge Department of Mechanical Engineering School of Engineering The University of Melbourne Parkville, Victoria, Australia Email: saman@unimelb.edu.au Abstract—The plasmodium of the slime mold Physarum poly- cephalum, a large amoeboid organism, displays remarkable intelligent behaviors such as solving mazes, shuttle streaming and event anticipation. These amoeboid behaviors are results of the dynamics of the viscoelastic protoplasm and its biochemical rhythms. Having inspired by the intelligence shown by this primitive organism without a nerve system to solve mazes, we proposed mathematical models to mimic the intelligent foraging behavior that can be used to find the shortest path between two points of a graph. In result, we found that the convergence of the proposed two versions, Physarum Optimization with Shuttle Streaming (POSS) and POSS with mutation, are 40-11650 times faster when compared with the currently available Physarum Solver (PS) method and the results obtained are comparable. I. I NTRODUCTION The true slime mold Physarum polycephalum is a large amoeboid organism that inhabits shady, cool and moist areas. The vegetative phase of the life cycle of Physarum poly- cephalum is the plasmodium, which consists of protoplasmic tube-like plasmodial veins and many nuclei. Usually during the search of food, plasmodium spreads out its network of tubes to fill the total available area that permits it to grow. It sometimes grows to a size of several square meters, while separated segments as small as 1mm 2 can survive as individuals. On the other hand, two plasmodia can coalesce spontaneously to form one larger plasmodium when they encounter each other. While being a unicellular organism, it has been reported that the plasmodium can display remarkable smart behavior: solving mazes [1], [2], [3], periodic event anticipation [4], maintaining an effective communication system within the cell [5] and moving towards nutrients and humidity [6]. These intriguing behaviors are considered as a result of information processing at intracellular level [7] although there is no widely accepted mechanism to explain it. The intelligent foraging be- havior that gives rise to solving mazes has inspired researchers to suggest a new model to solve shortest path problems [8]. The intelligent behaviors of the plasmodium also inspired researchers to exploit and utilize them in achieving variety of non-classical computational schemes. Adamatzky demon- strated realization of Kolmogorov-Uspensky machines [9] and computation of spanning trees [10] on an appropri- ately cultured substrate of plasmodium. Tsuda, Aono and colleagues implemented Boolean gates that are fundamental to digital computing on the plasmodium to mark possibility of biological computing devices [11], [12], [13]. Aono and colleagues demonstrated a solution to the traveling salesman problem by inducing plasmodium’s photosensitive branches to grow or degenerate [14]. In another occasion, Tsuda and colleagues experimented controlling a hexapod robot using a biological control circuit made of plasmodium of Physarum polycephalum [15]. In this paper, we focus on the back and forth movement of protoplasmic flow in the tubular network of the plasmodium and propose a model that mimic the shortest path finding behavior. We also propose a modification to a previously proposed model called ‘Physarum Solver’ in order to achieve fast and sustained convergence. We incorporate all the variants of models to find the shortest path of graphs with various complexities and compare their performance with Ant Colony Optimization (ACO) [16], [17]. II. I NTELLIGENT BEHAVIOR OF Physarum polycephalum The plasmodium of Physarum polycephalum is essentially a unicellular organism with many nuclei. Hence, it does not possess a central information processing mechanism such as a brain to process information intelligently nor a sophisticated information communication system such as a nerve system to communicate information throughout its body structure. Therefore, it is indeed remarkable to witness aforementioned intelligent behavior. There has been numerous research work that attempt to answer the question: where does this intelli- gence originate? In the plasmodium, streaming of the protoplasm through its tubular veins plays an important role in chemical signal generation. This protoplasmic streaming is known as shuttle streaming because the direction of flow changes back and forth periodically [7], [18]. Shuttle streaming is a result of hydro- static pressure produced by the active rhythmic contraction throughout the cell [7]. The protoplasm stream flows through the tubular veins with speed circa 1 − 3 mm/sec [19] and changes the direction of flow every 1 − 3 minutes [9]. The rhythmic contractions occur synchronously throughout the organism also plays a key role in forming the cell shape. U.S. Government work not protected by U.S. copyright WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia IEEE CEC