Abstract:
The transportation problem is a well-known optimization challenge that aims at minimizing the
total costs for distributing resources from different sources to numerous destinations. In complicated
logistical situations, many objectives such as cost, time, and distance are optimized
together. This leads to the multi objective transportation problem where a productive compromise
solution is sought. Although literature has established various methods like goal and fuzzy
programming, these approaches often fall short for large-scale instances due to high computational
demands. In this study, an innovative heuristic algorithm is established using an Improved
Ant Colony Optimization approach combined with a harmonic cost matrix to aggregate
conflicting goals. The incremental novelty of this work is distinguished by the introduction of
a static probabilistic penalty mechanism. Unlike traditional methods requiring dynamic recalculations,
this deterministic approach utilizes a desirability matrix to simplify decision-making.
Furthermore, this research eliminates the standard reliance on dummy variables, maintaining
the original problem dimensionality and saving significant computational resources. The efficiency
of this technique is validated through benchmarks comparing the Improved ant colony
optimization method to other methods. Performance results demonstrate superior outcomes:
Example 1 achieves a 3.8% reduction in distance; Examples 2 and 5 yield identical optimal solutions;
Example 3 reduces time by 5.8%; and Example 4 achieves a 28.6% cost improvement.
It can definitely be concluded that the algorithm could be a highly powerful, flexible, and efficient
tool for dealing with large classes of optimization problems likely to occur in real-world
logistics.
