A biologically inspired network design model

Physarum-Inspired Bicycle Lane Network Design in a Congested Megacity

Improvement of mobility, especially environment-friendly green mobility, is challenging in existing megacities due to road network complexity and space constraints. Endorsing the bicycle lane network (BLN) in congested megacities is a promising option to foster green mobility. This research presents a novel bioinspired network design method that considers various constraints and preferences related to the megacity for designing an optimal BLN. The proposed method is inspired by natural Physarum polycephalum, a brainless, multi-headed single-celled organism, which is capable of developing a reticulated network of complex foraging behaviors in pursuit of food. The mathematical model of Physarum foraging behavior is adapted to maneuver various BLN constraints in megacity contexts in designing the optimal BLN. The Physarum-inspired BLN method is applied to two case studies on the megacity Dhaka for designing BLNs: the first one covers congested central city area, and the second one covers a broader area that includes major locations of the city. The obtained BLNs were evaluated comparing their available routes between different locations with the existing vehicle routes of the city in terms of distance and required travel times in different time periods, and the BLN routes were found to be suitable alternatives for avoiding congested main roads. The expected travel time using BLNs is shorter than other transport (e.g., car and public bus); additionally, at glance, the average travel speed on BLNs is almost double that of public buses in peak hours. Finally, the designed BLNs are promising for environment-friendly and healthy mobility.

An Accelerated Physarum Solver for Network Optimization

As a novel computational paradigm, Physarum solver has received increasing attention from the researchers in tackling a plethora of network optimization problems. However, the convergence of Physarum solver is grounded by solving a system of linear equations iteratively, which often leads to low computational performance. Two factors have been highlighted along the process: 1) high time complexity in solving the system of linear equations and 2) extensive iterations required for convergence. Thus, Physarum solver has been largely restricted by its unsatisfactory computational performance. In this paper, we aim to address these two issues by developing two enhancement strategies: 1) pruning inactive nodes and 2) terminating Physarum solver in advance. First, extensive nodes and edges become and stay inactive after a few iterations in identifying the shortest path. Removing these inactive nodes and edges significantly decreases the graph size, thereby reducing computational complexity. Second, we define a transition phase for edges. All of the paths experiencing such a transition phase are dynamically aggregated to form a set of near-optimal paths among which the optimal path is included. Depth-first search is then leveraged to identify the optimal path from the near-optimal paths set. Earlier termination of Physarum solver saves considerable iterations while guaranteeing the optimality of the found solution. Empirically, 20 randomly generated sparse and complete graphs with network sizes ranging from 50 to 2000 as well as two real-world traffic networks are used to compare the performance of accelerated Physarum solver to the other two state-of-the-art algorithms.

Optimizing biologically inspired transport networks by control

Transportation networks with intrinsic flow dynamics governed by the Kirchhoff's current law are ubiquitous in natural and engineering systems. There has been recent work on designing optimal transportation networks based on biological principles with the goal to minimize the total dissipation associated with the flow. Despite being biologically inspired, e.g., adaptive network design based on slime mold Physarum polycephalum, such methods generally lead to suboptimal networks due to the difficulty in finding a global or nearly global optimum of the nonconvex optimization function. Here we articulate a design paradigm that combines engineering control and biological principles to realize optimal transportation networks. In particular, we show how small control signals applied only to a fraction of edges in an adaptive network can lead to solutions that are far more optimal than those based solely on biological principles. We also demonstrate that control signals, if not properly designed, can lead to networks that are less optimal. Incorporating control principle into biology-based optimal network design has broad applications not only in biomedical science and engineering but also in other disciplines such as civil engineering for designing resilient infrastructure systems.

A Bio-Inspired Approach to Traffic Network Equilibrium Assignment Problem

Finding an equilibrium state of the traffic assignment plays a significant role in the design of transportation networks. We adapt the path finding mathematical model of slime mold Physarum polycephalum to solve the traffic equilibrium assignment problem. We make three contributions in this paper. First, we propose a generalized Physarum model to solve the shortest path problem in directed and asymmetric graphs. Second, we extend it further to resolve the network design problem with multiple source nodes and sink nodes. At last, we demonstrate that the Physarum solver converges to the user-optimized (Wardrop) equilibrium by dynamically updating the costs of links in the network. In addition, convergence of the developed algorithm is proved. Numerical examples are used to demonstrate the efficiency of the proposed algorithm. The superiority of the proposed algorithm is demonstrated in comparison with several other algorithms, including the Frank-Wolfe algorithm, conjugate Frank-Wolfe algorithm, biconjugate Frank-Wolfe algorithm, and gradient projection algorithm.

An outer approximation method for the road network design problem

Best investment in the road infrastructure or the network design is perceived as a fundamental and benchmark problem in transportation. Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as a bilevel Discrete Network Design Problem (DNDP) of NP-hard computationally complexity. We engage with the complexity with a hybrid exact-heuristic methodology based on a two-stage relaxation as follows: (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the user equilibrium traffic assignment problem (UE-TAP) in the lower level as a constraint. It results in a mixed-integer nonlinear programming (MINLP) problem which is then solved using the Outer Approximation (OA) algorithm (ii) we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, that is, the multiple OD pairs are aggregated to a single OD pair. This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for a large-sized network of Winnipeg, Canada. The results suggest that within a limited number of iterations (as termination criterion), global optimum solutions are quickly reached in most of the cases; otherwise, good solutions (close to global optimum solutions) are found in early iterations. Comparative analysis of the networks of Gao and Sioux-Falls shows that for such a non-exact method the global optimum solutions are found in fewer iterations than those found in some analytically exact algorithms in the literature. (ii) Integration of the objective function among the constraints provides a commensurate capability to tackle the multi-objective (or multi-criteria) DNDP as well.

From Cellular Attractor Selection to Adaptive Signal Control for Traffic Networks

The management of varying traffic flows essentially depends on signal controls at intersections. However, design an optimal control that considers the dynamic nature of a traffic network and coordinates all intersections simultaneously in a centralized manner is computationally challenging. Inspired by the stable gene expressions of Escherichia coli in response to environmental changes, we explore the robustness and adaptability performance of signalized intersections by incorporating a biological mechanism in their control policies, specifically, the evolution of each intersection is induced by the dynamics governing an adaptive attractor selection in cells. We employ a mathematical model to capture such biological attractor selection and derive a generic, adaptive and distributed control algorithm which is capable of dynamically adapting signal operations for the entire dynamical traffic network. We show that the proposed scheme based on attractor selection can not only promote the balance of traffic loads on each link of the network but also allows the global network to accommodate dynamical traffic demands. Our work demonstrates the potential of bio-inspired intelligence emerging from cells and provides a deep understanding of adaptive attractor selection-based control formation that is useful to support the designs of adaptive optimization and control in other domains.