A Metaheuristic Framework For The Pooling Problem: Application Of The Firefly Algorithm

Abstract

This paper investigates the optimization of pooling problems, especially the use of the Firefly Algorithm (FA), including a Proposed FA with self-adaptive properties, to solve the Haverly Pooling Problem in three distinct contexts. Using MATLAB simulations, the study evaluates the effectiveness of FA and Proposed FA in comparison to traditional optimization methods, including MSLP, MALT, and VNS. Pooling problems involve the combination of raw materials with various qualities to create final products that meet specific quality criteria, a task made more difficult by the non-linear complexity of the issue. Experiments on Haverly's pooling issues used the algorithms, and their results were contrasted with the exact answers. While the Proposed FA gets a near-optimal value of 400.25 for Haverly 1, making it almost undetectable from the exact solution, the exact answer is 400. Haverly 2's exact answer is 600; the Proposed FA, which shows a small overestimation of 0.87%, produces 605.23. With the exact answer of 750, Haverly 3 shows strong performance with the Proposed FA, which produces 748.96, only 0.14% lower than the accurate solution. The findings show that in every case the Proposed FA either exceeds or closely matches the exact solution, outperforming rival algorithms like MSLP, MALT, and VNS, which showed more variation. The Proposed FA's use of a self-adaptive step size improves the exploitation and exploration of the search space, hence producing very precise outcomes. This study finds that the Proposed FA is an effective optimization tool for solving pooling issues, showing improved performance compared to traditional optimization methods.