Physica A 398 (2014) 179–186 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa An amoeboid algorithm for solving linear transportation problem Cai Gao a , Chao Yan b,c , Zili Zhang a,d , Yong Hu e , Sankaran Mahadevan f , Yong Deng a,∗ a School of Computer and Information Science, Southwest University, Chongqing 400715, China b University of Chinese Academy of Sciences, Beijing 100190, China c Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China d School of Information Technology, Deakin University, VIC 3271, Australia e Institute of Business Intelligence and Knowledge Discovery, Guangdong University of Foreign Studies, Guangzhou 510006, China f School of Engineering, Vanderbilt University, TN 37235, USA highlights • The directed amoeba algorithm is developed to solve multi-source multi-sink minimum cost flow problem in directed networks. • The proposed method can solve the Linear Transportation Problem effectively. • Experimental results indicate that the proposed method can well solve minimum cost flow problem. article info Article history: Received 15 July 2013 Received in revised form 10 October 2013 Available online 25 December 2013 Keywords: Transportation problem Physarum solver Network optimization Physarum polycephalum abstract Transportation Problem (TP) is one of the basic operational research problems, which plays an important role in many practical applications. In this paper, a bio-inspired mathematical model is proposed to handle the Linear Transportation Problem (LTP) in directed networks by modifying the original amoeba model Physarum Solver. Several examples are used to prove that the provided model can effectively solve Balanced Transportation Problem (BTP), Unbalanced Transportation Problem (UTP), especially the Generalized Transportation Problem (GTP), in a nondiscrete way. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Transportation problem (TP) is an optimization problem which aims at obtaining the optimal pattern of the distribution of units of a product from several supply points of original to several destinations [1–8], which plays an important role in many complex systems [2,9,10]. By considering various facts, such as varying costs, product type constraint and uncertain environment, TP has been extended into Fixed Charge Transportation Problem (FCTP) [3,11], and Solid Transportation Problem (STP) [5,12,13]. Due to the uncertainty in real environment [14–17], Fuzzy Solid Transportation Problem (FSTP) [18–20] and other optimization problems under uncertain environment [21–26] have been heavily studied. In the classical transportation model, there is n demand points and m supply points. The supply points try to meet the demand of the demand points. To be more specific, let m sources be supply points that produce the commodity, and n sinks be demand points that need ∗ Corresponding author. Tel.: +86 23 68254555; fax: +86 23 68254555. E-mail addresses: ydeng@swu.edu.cn, professordeng@163.com (Y. Deng). 0378-4371/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physa.2013.12.023