A Modified Emperor Penguin Optimizer Algorithm for Solving Fixed-Charged Transshipment Problem

Abstract

This paper introduces a novel optimization problem termed the Fixed Charged Transshipment Problem (FCTP), which incorporates fixed charges for selected routes. A new formulation for this problem is presented, aiming to address the combinatorial nature of the challenge. The study further introduces a Modified Emperor Penguin Optimizer (EPO) algorithm designed to enhance the solution approach. To evaluate the performance of the Modified EPO, a comparative analysis is conducted against the classical EPO and Particle Swarm Optimization (PSO) algorithms. 19 problems, including various multi-modal test optimization functions, serve as the testing ground. Results demonstrate the efficacy of the Modified EPO, establishing its superiority over the classical EPO and PSO. Additionally, a heuristic procedure is proposed for solving the combinatorial aspect of the FCTP. This heuristic is hybridized with both the Modified EPO and PSO algorithms. 30 FCTP problems are generated using a code available at https://github.com/MZakaraia/EPO_Transshipment/. Taguchi's orthogonal arrays are employed to optimize parameter levels for both algorithms. The study concludes with the comparison of the Modified Hybrid EPO and Hybrid PSO in solving the 30 generated FCTP problems. Remarkably, the Modified Hybrid EPO algorithm outperforms the Hybrid PSO, showing its effectiveness in addressing the Fixed Charged Transshipment Problem in terms of means and robustness.Povzetek: Članek predstavlja spremenjeni algoritem cesarskega pingvina za reševanje problema s fiksnimi stroški prenosa, ki kaže premoč nad klasičnimi metodami z robustnostjo in učinkovitostjo rešitev.