Cost optimization of feed mixes by genetic algorithms

Abstract

The cost optimization is a key element to determine the least-cost feed mixture according to animals’ nutrient requirements and the effective use of the sources. In this paper, the cost optimization of feeds is performed by genetic algorithm, considering the growing style and type, age, nutritional requirement and feedstuff costs for poultry and different types of animals. The proposed method is compared with linear programming approach to measure its performance. The obtained results show that Genetic algorithms could be applicable to the cost optimization of the feed mixtures. In addition, a software program is developed by using Delphi environment, which provides flexible, extensible and user-friendly framework for tuning the heuristic relevant parameters and improving the solution quality.

Introduction

The problems related to inadequate nutrition that arise from rapid population growth are more prevalent in the world. Although there has been production growth, the problems could not be solved both quantitatively and qualitatively. On the contrary, the unequal income distribution creates more problems for the low income section of the population [1]. For human beings to grow up and to live a healthy life, they need to include some protein to their diet. Poultry meat and eggs are the primary supplies of the mentioned protein sources.

Balanced and adequate nutrition is required for animals to be healthy and productive. Also considering the animals’ consumption, to meet their nutritional requirements, feed mixes should be prepared. The feeding is most important factor affecting the production cost in animal breeding industry such that it is about 70–75% of the total production cost. This is also for only if one applies a scientific feeding program, otherwise the cost will be more than the aforementioned percentages. The feeding requirements change according to the animals’ kind, age, and the productivity expected from the animals. Consequently feeding cost is so important for the feed industry that it is only possible to meet the nutritional requirements of the animals if the stockbreeders have a scientific approach to the problem [2].

When the feed mixes are prepared, it is desired that it should both meet the animals’ nutritional needs and be low cost. In such cases, it is necessary to utilize optimization techniques. Linear and non-linear programming techniques have been used for over two decade in many studies: the allocation of milk resources for cheese making [3], animal diet formulation [4], life cycle assessment [5], evaluation of nitrogen taxation scenario [6], optimization of the performance response to energy density in broiler feed formulation [7], cost and benefits for the segregation of compound feed [8].

The present studies have demonstrated advantage of utilizing the optimization procedures to meet the mentioned objectives. However in determining least-cost feed mixes, the linear/non-linear constraints are increasingly complex and difficult to handle. In such conditions, application of standard linear or non-linear programming techniques are both time consuming and insufficient.

In recent years, Genetic Algorithms, therefore, have wide application in various fields of science and technology such as bioinformatics, manufacturing, engineering, economics, mathematics, chemistry, physics and etc. One of the advantages of the genetic algorithms (GA) over standard non-linear programming techniques is that GA can find global minimum instead of local minimum. The other advantage is that GA does not need derivative calculation of the function that may not be readily available or very hard to calculate [9]. GA can reach to solutions quickly and be applied on the complex optimization problems easily and plainly [10].

In this study, an approach finding least-cost feed mixes, which satisfy the nutritional requirements for poultry and different types of animals (cattle, sheep and rabbits, etc.), is proposed by using genetic algorithms. So the complex constraints are handled taking into account relationships between ingredients and the nutritional value of the feed mixes. The results obtained are compared to linear programming model. The overall results show that the genetic algorithms can be used for determining least-cost feed mixes. Furthermore, a software program is developed by using object oriented visual Delphi environment for poultry animals and domestic animals (cattle, sheep and rabbits). It has ability to illustrate visually the optimization results and to analysis the relevant parameters in simulation.