A physarum-inspired approach to supply chain network design

A supply chain is a system which moves products from a supplier to customers, which plays a very important role in all economic activities. This paper proposes a novel algorithm for a supply chain network design inspired by biological principles of nutrients’ distribution in protoplasmic networks of slime mould Physarum polycephalum. The algorithm handles supply networks where capacity investments and product flows are decision variables, and the networks are required to satisfy product demands. Two features of the slime mould are adopted in our algorithm. The first is the continuity of flux during the iterative process, which is used in real-time updating of the costs associated with the supply links. The second feature is adaptivity. The supply chain can converge to an equilibrium state when costs are changed. Numerical examples are provided to illustrate the practicality and flexibility of the proposed method algorithm

A Hexagonal Cell Automaton Model to Imitate Physarum Polycephalum Competitive Behaviour

Abubakr Awad research is supported by Elphinstone PhD Scholarship (University of Aberdeen). Wei Pang, George Coghill, and David Lusseau are supported by the Royal Society International Exchange program (Grant Ref IE160806).Publisher PD

A physarum-inspired approach to supply chain network design

A supply chain is a system which moves products from a supplier to customers, which plays a very important role in all economic activities. This paper proposes a novel algorithm for a supply chain network design inspired by biological principles of nutrients’ distribution in protoplasmic networks of slime mould Physarum polycephalum. The algorithm handles supply networks where capacity investments and product flows are decision variables, and the networks are required to satisfy product demands. Two features of the slime mould are adopted in our algorithm. The first is the continuity of flux during the iterative process, which is used in real-time updating of the costs associated with the supply links. The second feature is adaptivity. The supply chain can converge to an equilibrium state when costs are changed. Numerical examples are provided to illustrate the practicality and flexibility of the proposed method algorithm

CAMELOT - computational-analytical multi-fidelity low-thrust optimisation toolbox

CAMELOT (Computational-Analytical Multi-fidelity Low-thrust Optimisation Toolbox) is a toolbox for the fast preliminary design and optimisation of low-thrust trajectories. It solves highly complex combinatorial problems to plan multi-target missions characterised by long spirals including different perturbations. In order to do so, CAMELOT implements a novel multi-fidelity approach combining analytical surrogate modelling and accurate computational estimations of the mission cost. Decisions are then made by using two pptimisation engines included in the toolbox, a single objective global optimiser and a combinatorial optimisation algorithm. CAMELOT has been applied to a variety of applications: from the design of interplanetary trajectories to the optimal deorbiting of space debris, from the deployment of constellations to on-orbit servicing. In this paper the main elements of CAMELOT are described and two space mission design problems solved using the toolbox are described

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most sophisticated tasks involving decision making, can be reduced to solving certain optimization problems. These advances however, bring several new challenges to the field of algorithm design. The first of them is related to the ever-growing size of instances, these optimization problems need to be solved for. In practice, this forces the algorithms for these problems to run in time linear or nearly linear in their input size. The second challenge is related to the emergence of new, harder and harder problems which need to be dealt with. These problems are in most cases considered computationally intractable because of complexity barriers such as NP completeness, or because of non-convexity. Therefore, efficiently computable relaxations for these problems are typically desired. The material of this thesis is divided into two parts. In the first part we attempt to address the first challenge. The recent tremendous progress in developing fast algorithm for such fundamental problems as maximum flow or linear programming, demonstrate the power of continuous techniques and tools such as electrical flows, fast Laplacian solvers and interior point methods. In this thesis we study new algorithms of this type based on continuous dynamical systems inspired by the study of a slime mold Physarum polycephalum. We perform a rigorous mathematical analysis of these dynamical systems and extract from them new, fast algorithms for problems such as minimum cost flow, linear programming and basis pursuit. In the second part of the thesis we develop new tools to approach the second challenge. Towards this, we study a very general form of discrete optimization problems and its extension to sampling and counting, capturing a host of important problems such as counting matchings in graphs, computing permanents of matrices or sampling from constrained determinantal point processes. We present a very general framework, based on polynomials, for dealing with these problems computationally. It is based, roughly, on encoding the problem structure in a multivariate polynomial and then recovering the solution by means of certain continuous relaxations. This leads to several questions on how to reason about such relaxations and how to compute them. We resolve them by relating certain analytic properties of the arising polynomials, such as the location of their roots or convexity, to the combinatorial structure of the underlying problem. We believe that the ideas and mathematical techniques developed in this thesis are only a beginning and they will inspire more work on the use of dynamical systems and polynomials in the design of fast algorithms

A hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system for the travelling salesman problem

open access articleThe ant colony optimization (ACO) is one efficient approach for solving the travelling salesman problem (TSP). Here, we propose a hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system (SSMFAS) to address the TSP. The state-adaptive slime mold (SM) model with two targeted auxiliary strategies emphasizes some critical connections and balances the exploration and exploitation ability of SSMFAS. The consideration of fractional-order calculus in the ant system (AS) takes full advantage of the neighboring information. The pheromone update rule of AS is modified to dynamically integrate the flux information of SM. To understand the search behavior of the proposed algorithm, some mathematical proofs of convergence analysis are given. The experimental results validate the efficiency of the hybridization and demonstrate that the proposed algorithm has the competitive ability of finding the better solutions on TSP instances compared with some state-of-the-art algorithms