<p>The Fixed Charge Transportation Problem (FCTP) is an extension of the classical Transportation Problem (TP) and is classified as NP-hard due to its high combinatorial complexity. In this work, the multi-objective neural network algorithm is redesigned to solve the multi-objective fixed charge transportation problem (MOFCTP). The proposed approach restructures vector-based candidate solutions into a matrix formulation, adapts weight matrices to align with this matrix representation, and incorporates a constraint-handling mechanism to enforce supply and demand feasibility. Additionally, it implements repair mechanisms–addressing negative and fractional entries–to ensure integral solutions, while integrating non-dominated sorting and KNN-based diversity preservation for effective multi-objective selection. An extensive experimental analysis was conducted on multiple benchmark FCTP instances to validate the proposed algorithm’s efficacy, with comparative evaluations performed against modified NSGA-II and MOEA/D. Performance was assessed using established multi-objective metrics, including the Relative Non-Dominance Index (RNI), Hypervolume (HV), and Spacing, which collectively demonstrate the algorithm’s superior convergence and solution quality relative to state-of-the-art methods. Further comparative analyses reinforce these findings, highlighting the algorithm’s robustness. The results conclusively validate the effectiveness of the proposed multi-objective neural network approach in addressing FCTP challenges and suggest its broader applicability in transportation and logistics optimization.</p>