A Biologically Inspired Network Design Model

Abstract

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.

A modified Physarum-inspired model for the user equilibrium traffic assignment problem

“…According to the feature of Physarum foraging behavior system, the optimum problem and the user equilibrium problem in directed traffic networks are solved by modified Physarum models [49,50] . There are mainly two points different from from the original Physarum model in Zhang's method [50].…”

“…Recently, quite a few researchers try to apply the Physarum model to solve the traffic assignment problem [49,50]. These Physarum-inspired models can affect well in specific conditions where networks are unilaterally connecting.…”

Physarum solver: a bio-inspired method for sustainable supply chain network design problem

“…The fact that Physarum optimises its protoplasmic network inspired researchers to interpret the slime mould's behaviour in terms of computation and to develop experimental laboratory prototypes and computer and mathematical models of Physarum-based algorithms and computing devices. In laboratory experiments and theoretical studies, it is shown that the slime mould can solve many graph theoretical problems, such as finding the shortest path (Nakagaki et al 2000;Zhang et al 2013b, c), connecting different arrays of food sources in an efficient manner (Adamatzky 2014;Jones and Adamatzky 2014;Nakagaki et al 2007), and network design (Adamatzky and Martinez 2013;Masi and Vasile 2014;Tero et al 2010;Zhang et al 2015a).…”

An Improved Genetic Algorithm with Initial Population Strategy for Symmetric TSP

“…But, because of exponential complexity [3], they are always infeasible if the scale of TSP becomes large, for example, 100 cities with approximately 10 155 different solutions. In contrast, the approximate algorithms, especially many bioinspired algorithms [4][5][6][7][8][9], can obtain accepted solutions for many NPhard problems with (relatively) short running time. These approaches are usually very simple, like Lin-Kernigan [10], colony optimization (ACO) [11], and so on [12,13].…”