Grouper fish feed formulation using enhanced evolutionary algorithm with fibonacci rabbit initialization and binary-standard deviation tournament selection

Fish is one of the main meals among people in many countries. Due to that, the problems of insufficient wild-caught fish and the high market demand have driven the effort for fish farming, especially for grouper since its high commercial value. However, fish feed is costly, while the nutrients’ quality needs to be prioritized. Thus, a formulation for grouper fish feed is essential involving appropriate combination of ingredients to optimize nutritional balance with minimal cost. Therefore, this research focused on feed formulation for grouper fish taking into consideration suitable 14 ingredients and 15 nutrients. A set of hard and soft constraints was involved with certain penalties given in ensuring grouper’s healthy growth. The main contribution of this research is the development of feed formulation using Evolutionary Algorithm (EA) with four variations of EA, which are Semi-Random Initialization – Binary Tournament Selection - EA (SR-BT-EA), Fibonacci Rabbit Initialization – Binary Tournament Selection - EA (FR-BT-EA), Semi-Random Initialization - Binary- Standard Deviation Tournament Selection - EA (SR-SD-EA) and Fibonacci Rabbit Initialization - Binary-Standard Deviation Tournament Selection - EA (FR-SD-EA). These variations include the enhanced SD Tournament Selection, novel FR Initialization and newly introduced Z-score expression in the fitness value function. The results show that the fitness function of the EA is able to minimize the penalty values related to weight of ingredients and nutrients’ quality. Among the four EA variations, the FR-SD-EA is the most significant formulation achieving lowest cost of RM 407.09 for a 100 kg feed with the best-so-far fitness value of 407.090 and zero penalty. Thus, this research offers a new approach of formulating the right amount of ingredients to produce a high-quality feed containing essential nutrients for the growth of grouper fish at a minimal cost. Moreover, industrial practitioners can take advantage of the flexibility of the EA methodology to readjust the bulk weight of 100 kg to user-preferred weights, with minor modifications to the EA.