This study considers chain-topology networks, which has certain inherent limitations, and presents an optimization model that augments the network by the addition of a new link, with the objective of minimizing Average Path Length (APL).We built up a mathematical model for APL, and formulated our problem as Integer Programming. Then, we solved the problem experimentally by brute-force, trying all possible topologies, and found the optimal solutions that minimize APL for certain network sizes up to 1000 nodes. Later on, we derived analytical solution of the problem by applying Linear Regression method on the experimental results obtained.We showed that APL on a chain-topology network is decreased by the proposed optimization model, at a gradually increasing rate from 24.81 % to asymptotic value of 41.4 % as network grows. Additionally, we found that normalized length of the optimal solutions decreases logarithmically from 100 % to 58.6048 % as network size gets larger.