### International Journal of Applied Mathematics and Theoretical Physics

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### An Improved Ant Colony Algorithm to Solve Prohibited Transportation Problems

Physical distribution (transportation) of goods and services from multiple supply centers to multiple demand centers is an important application of linear programming (LP). A transportation problem (TP) can also be solved using the simplex method when expressed as an LP model. However, because a TP has a large number of variables and constraints, solving it using simplex methods takes a long time. Many scientists have devised and continue to devise novel solutions to the classic TP. The prohibited route transportation problem, on the other hand, is a subset of TPs for which most scientists have yet to develop a specific TP. Certain routes may be impassable in some cases due to transportation issues. To name a few: construction projects, poor road conditions, strikes, unexpected disasters, and local traffic laws. Such limits (or prohibitions) in the TP can be managed by assigning a very high cost to the prohibited routes, ensuring that they do not appear in the optimal solution. This paper presents a heuristic algorithm and an improved ant colony optimization algorithm for achieving an initial feasible solution (IFS) to a prohibitive transportation problem (PTP). Using the PTP in the proposed method, on the other hand, produces the best IFS for a prohibited transportation problem and outperforms existing methods with less computation time and complexity. As a result, the proposed methods are an appealing alternative to traditional problem-solving approaches. In some numerical examples, the feasible solution of the proposed method is the same as the optimal solution.

Ant Colony Optimization Algorithm, Initial Feasible Solution, Optimal Solution, Prohibited Transportation Problems, Transportation Problem

APA Style

Ekanayake Mudiyanselage Uthpala Senarath Bandara Ekanayake. (2022). An Improved Ant Colony Algorithm to Solve Prohibited Transportation Problems. International Journal of Applied Mathematics and Theoretical Physics, 8(2), 43-51. https://doi.org/10.11648/j.ijamtp.20220802.12

ACS Style

Ekanayake Mudiyanselage Uthpala Senarath Bandara Ekanayake. An Improved Ant Colony Algorithm to Solve Prohibited Transportation Problems. Int. J. Appl. Math. Theor. Phys. 2022, 8(2), 43-51. doi: 10.11648/j.ijamtp.20220802.12

AMA Style

Ekanayake Mudiyanselage Uthpala Senarath Bandara Ekanayake. An Improved Ant Colony Algorithm to Solve Prohibited Transportation Problems. Int J Appl Math Theor Phys. 2022;8(2):43-51. doi: 10.11648/j.ijamtp.20220802.12