A Modified Firefly Algorithm Adaptive to the Single-Stage Fixed Charge Transportation Problem

The transportation problem is primarily concerned with the ways in which resources can be transported from supply centers to final customers with minimum total transportation costs. In addition to variable transportation costs, the single-stage fixed charge transportation problem (FCTP) has become a more challenging and complex optimization problem due to the inclusion of fixed route activation costs. Therefore, since it is difficult to obtain optimal solutions for these problems in a reasonable time, heuristic algorithms are used to obtain more qualitative and accurate solutions. This study proposes a modified firefly optimization algorithm to efficiently obtain high-quality near-optimal solutions. The enhanced algorithm improves convergence behavior and robustness and is implemented in Python for computational efficiency. The performance is observed and evaluated on numerical experiments across different problem scales. Here, the solutions of the proposed algorithm are compared with other existing heuristic algorithms through numerical experiment analysis. The numerical experiments conducted across different problem scales show that the proposed method performs competitively with existing heuristics and provides superior results for large-scale cases.