An amoeboid algorithm for solving linear transportation problem

• 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.

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.