Optimization of Star Pomfret Feed Production as a Linear Programming Problem Using a Hybrid Wolfe-Differential Evolution Algorithm

Abstract

Star pomfret (Trachinotus blochii) is one of the most sought-after types of marine fish in Indonesia. The production of feed for star pomfret fish is an important factor because it is related to their survival and ability to grow well.  Therefore, formulating the feed formulation for star pomfret (Trachinotus blochii) is very important to minimize feed production costs and ensure the nutritional adequacy of the fish. Therefore, we change the feed for star pomfret fish as a linear programming (LP) problem and solve it using the Hybrid Differential Evolution-Wolfe Algorithm (HWDEA).  HWDEA combines the Wolfe method, which efficiently transforms constraints into a system of linear equations, with the use of the Differential Evolution Algorithm (DEA) to find a global optimization solution, which is a solution that is not trapped in a local minimum.  We improve accuracy and efficiency by using HWDEA to find the optimal solution for this fish feed production. Our HWDEA can also overcome the limitations of traditional methods such as the simplex algorithm.  Thus, we can show that HWDEA successfully reduced feed production costs from 12,353 IDR to 9,035 IDR per kg while maintaining nutritional balance.  We can conclude that the HWDEA method successfully adapted to price fluctuations and raw material availability, allowing it to produce an optimal raw material composition in feed production.  Therefore, HWDEA can be used as an efficient tool to provide significant cost savings for supporting sustainable and profitable fish farming.