Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32119
Investigating Feed Mix Problem Approaches: An Overview and Potential Solution

Authors: Rosshairy Abd Rahman, Chooi-Leng Ang, Razamin Ramli


Feed is one of the factors which play an important role in determining a successful development of an aquaculture industry. It is always critical to produce the best aquaculture diet at a minimum cost in order to trim down the operational cost and gain more profit. However, the feed mix problem becomes increasingly difficult since many issues need to be considered simultaneously. Thus, the purpose of this paper is to review the current techniques used by nutritionist and researchers to tackle the issues. Additionally, this paper introduce an enhance algorithm which is deemed suitable to deal with all the issues arise. The proposed technique refers to Hybrid Genetic Algorithm which is expected to obtain the minimum cost diet for farmed animal, while satisfying nutritional requirements. Hybrid GA technique with artificial bee algorithm is expected to reduce the penalty function and provide a better solution for the feed mix problem.

Keywords: Artificial bee algorithm, feed mix problem, hybrid genetic algorithm.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3035


[1] A. M. Anderson, and M. D. Earle, (1983). "Diet planning in the third world by linear and goal programming" The Journal of the Operational Research Society, vol. 34, pp. 9-16., 1983.
[2] H. A. Abbass, "Marriage in honey-bee optimization (MBO): A haplometrosis polygynous swarming approach" in Proc. The Congress on Evolutionary Computation (CEC2001), Seoul, Korea. (2001).
[3] M. O. Afolayan, and M. Afolayan, "Nigeria oriented poultry feed formulation software requirements," Journal of Applied Sciences Research, vol. 4, no. 11, pp. 1596-1602, 2008.
[4] D. L. J. Alexander, P. C. H. Morel, and G. R. Wood, "Feeding strategies for maximising gross margin in pig production," in Global optimization: Scientific and Engineering Case Studies (pp. 33-43). United State: Springer US. 2006.
[5] S. Babu and P. Sanyal, Food Security, Poverty and Nutrition Policy Analysis: Statistical Methods and Applications. Washington, DC, USA: Academic Press. 2009. pp. 304.
[6] P. J. d. Bailleul, J. Rivest, F. Dubeau, and C. Pomar, "Reducing nitrogen excretion in pigs by modifying the traditional least-cost formulation algorithm," Livestock Production Science, vol. 72, pp. 199-211. 2001.
[7] M. A., Barbieri, and G. Cuzon, "Improved nutrient specification for linear programming of penaeid rations." Aquaculture, vol. 19, pp. 313- 323, 1980.
[8] J. M. Cadenas, D. A. Pelta, H. R. Pelta, and J. L. Verdegay, "Application of fuzzy optimization to diet problems in Argentinean farms," European Journal of Operational Research, vol. 158, pp. 218- 228, 2004.
[9] W. Candler, "A "short-cut" method for the complete solution of game theory and feed-mix problems". Econometrica, vol. 28, no. 3, pp. 618- 634, 1960.
[10] C. Castrodeza, P. Lara, and T. Pe├▒a, "Multicriteria fractional model for feed formulation: Economic, nutritional and environmental criteria," Agricultural Systems, vol. 86, pp. 76-96, 2005.
[11] S. Chakeredza, F. K. Akinnifesi, O. C. Ajayi, G. Sileshi, S. Mngomba, and F. M. T. Gondwe, "A simple method of formulating least-cost diets for smallholder dairy production in sub-Saharan Africa'" African Journal of Biotechnology, vol. 7, no. 16, pp. 2925-2933, 2008.
[12] H. S. Chang, "Converging marriage in honey-bees optimization and application to stochastic dynamic programming'" Journal of Global Optimization, vol. 35, pp. 423-441, 2006.
[13] A. E. Chappell, "Linear programming cuts costs in production of animal feeds'" Operational Research Quarterly, vol 25, no. 1, pp. 19-26, 1974.
[14] J. T. Chen, "Quadratic programming for least-cost feed formulations under probabilistic protein constraints," American Journal of Agricultural Economics, vol. 55, no. 2, pp. 175-183, 1973.
[15] T. A. El-Mihoub, A. A. Hopgood, L. Nolle, and A. Battersby, "Hybrid genetic algorithms: A review," Engineering Letters, vol. 13, no. 2, 2006.
[16] E. Engelbrecht, Optimising animal diets at the Johannesburg zoo. Unpublished Bachelor degree thesis, University of Pretoria, Pretoria, 2008.
[17] L. Fa-Chao, and J. Chen-Xia, "Study on fuzzy optimization methods based on principal operation and inequity degree," Computers and Mathematics with Applications, vol. 56, pp. 1545-1555, 2008.
[18] D. B. Fogel, "The advantages of evolutionary computation," Biocomputing and Emergent Computation, pp. 1-11, 1997.
[19] D. M. Forsyth, "Chapter 5: Computer programming of beef cattle diet," in Beef cattle feeding and nutrition, 2nd ed., T. W. Perry and M. J. Cecava, Academic Press, Inc, 1995. pp. 68.
[20] T. Furuya, T. Satake, and Y. Minami, "Evolutionary programming for mix design," Computers and Electronics in Agriculture, vol. 18, pp. 129-135, 1997.
[21] J. R. Gillespie, and F. B. Flanders, Modern Livestock and Poultry Production, 8 ed., Clifton Park, New York: Cengage Learning, 2009, pp. 104-187.
[22] J. J. Glen, "A Mathematical Programming Approach to Beef Feedlot Optimization," Management Science, vol. 26, no. 5, pp. 524-535, 1980.
[23] J. J. Glen, "A linear programming model for an intensive beef production enterprise," The Journal of the Operational Research Society, vol. 37, no. 5, pp. 487-494, 1986.
[24] D. E. Goldberg, Genetic Algorithms in search, optimization, and machine learning, Canada: Addison-Wesley Publishing Company, Inc., 1989, pp. 1-379.
[25] V. R. Guevara, "Use the nonlinear programming to optimize performance response to energy density in broiler feed formulation," Poultry Science, vol. 83, pp. 147-151, 2004.
[26] D. Haibin, X. Zhihui, and X. Chunfang, "An improved quantum evolutionary algorithm based on artificial bee colony optimization," in W. Yu & E. N. Sanchez, Advances in Computational intelligence, New York: Springer-Verlag Berlin Heidelberg, 2009.
[27] F. S. Hillier, and G. J. Lieberman, Introduction to operations research, 8th ed. New York: Mc Graw-Hill International Edition, 2005, pp. 617- 654.
[28] Holland, J. H. (1998). Adaptation in Natural and Artificial Systems: An introductory analysis with applications to biology, control, and artificial intelligence, 5th Ed, United States of America: MIT Press.
[29] M. S. Htun, T. T. Thein, and P. Tin, "Linear Programming Approach to Diet Problem for Black Tiger Shrimp in Shrimp Aquaculture," in Proc. Information and Telecommunication Technologies, 2005.
[30] Ismail Abu Hassan; Hambal Hj. Hanafi; Che Utama Che Musa; and S. Pathmasothy. 1988. "Status of Shrimp and Finfish Feeds in Malaysia," Report of The Workshop on Shrimp and Finfish Feed Development, Johor Bahru, Malaysia. 25-29 October 1988.
[31] P. Kaelo, & M.M. Ali, "Integrated crossover rules in real coded genetic algorithms," European Journal of Operational Research, vol. 176, no. 1, pp. 60-76. 2007.
[32] D. Karaboga, "An idea based on honey bee swarm for numerical optimization," Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005.
[33] N. Karaboga, "A new design method based on artificial bee colony algorithm for digital IIR filters," Journal of The Franklin Institute, vol. 346, pp. 328-348, 2009.
[34] H. C. D. Kock, and M. Sinclair, "Multi-Mix Feedstock Problems on Microcomputers," The Journal of the Operational Research Society, vol. 38, no. 7, pp. 585-590, 1987.
[35] J. S. H. Kornbluth, and R. E. Steuer, "Multiple objective linear fractional programming," Management Science, vol. 27, no. 9, pp. 1024- 1039, 1981.
[36] P. Lara, "Multiple objective fractional programming and livestock ration formulation: A case study for dairy cow diets in Spain," Agricultural Systems, vol. 41, pp. 321-334, 1993.
[37] P. Lara, and C. Romero, "An interactive multigoal programming model for determining livestock rations: An application to dairy cows in Andalusia, Spain," The Journal of the Operational Research Society, vol. 43, no. 10, pp. 945-953, 1992.
[38] P. Lara, and C. Romero, "Relaxation of nutrient requirements on livestocks rations through interactive multigoal programming," Agricultural Systems, vol. 45, pp. 443-453, 1994.
[39] J. P. Lazo, and D. A. Davis, "Ingredient and feed evaluation," in Encyclopedia of Aquaculture, R. R. Stickney, Texas: Wiley-Interscience Publication, 2000, pp. 453-463.
[40] J. McCall, "Genetic algorithms for modelling and optimisation," Journal of Computational and Applied Mathematics, vol. 184, pp. 205-222, 2005.
[41] K. Mitani, and H. Nakayama, "A multiobjective diet planning support system using the satisficing trade-off method," Journal of Multi-Criteria Decision Analysis, vol. 6, pp. 131-139, 1997.
[42] G. M. Mohr, "The bulk constraint and computer formulations of leastcost feed mixes," Review of Marketing and Agricultural Economics, vol. 40, no. 1, pp. 15-28, 1972.
[43] A. G. Munford, "A microcomputer system for formulating animal diets which may involve liquid raw materials," European Journal of Operational Research, vol. 41, pp. 270-276, 1989.
[44] A. G. Munford, "The use of iterative linear programming in practical applications of animal diet formulation," Mathematics and Computers in Simulation, vol. 42, pp. 255-261, 1996.
[45] National Academy Press, United States-Canadian tables of feed composition, 3rd Edition, Washington, D.C: National Academic Press, 1982.
[46] J. D. O'Connor, C. J. Sniffen, D. G. Fox, and R. A. Miligan, "Least cost dairy cattle ration formulation model based on the degradable protein system," Journal of Dairy Science, vol. 72, pp. 2733-2745, 1989.
[47] C. V. D. Panne, and W. Popp, "Minimum-cost cattle feed under probabilistic protein constraints," Management Science, vol. 9, no. 3, pp. 405-430, 1963.
[48] G. M. Pesti, and A. F. Seila, "The Use of an electronic spreadsheet to solve linear and non-linear "stochastic" feed formulation problems," Journal of Applied Poultry Research, vol. 8(1), pp. 110-121, 1999.
[49] F. Polimeno, T. Rehman, H. Neal, and C. M. Yates, "Integrating the use of Linear and Dynamic Programming Methods for Dairy Cow Diet Formulation," The Journal of the Operational Research Society, vol. 50, no. 9, pp. 931-942, 1999.
[50] C. Pomar, F. Dubeau, M. P. Létourneau-Montminy, C. Boucher, and P.- O. Julien, "Reducing phosphorus concentration in pig diets by adding an environmental objective to the traditional feed formulation algorithm," Livestock Science, vol. 111, pp. 16-27, 2007.
[51] C. A. Poojari, and B. Varghese, "Genetic algorithm based technique for solving chance constrained problems," European Journal of Operational Research, vol. 185, pp. 1128-1154, 2008.
[52] A. Prékopa, "Probabilistic programming," in Handbooks in OR and MS, vol. 10, Elsevier Science, 2003, pp. 267-351.
[53] S. A. Rahman, and F. E. Bender, "Linear programming approximation of least-cost feed mixes with probability restrictions," Amer. J. Ag. Econ, vol. 53, pp. 612-618, 1971.
[54] T. Rehman, and C. Romero, "Multiple-criterion decision making techniques and their role in livestock ration formulation," Agricultural Systems, vol. 15, pp. 1, 23-49, 1984.
[55] T. Rehman, and C. Romero, "Goal programming with penalty functions and livestock ration formulation," Agricultural Systems, vol. 23, pp. 117-132, 1987.
[56] B. Render, J. R. M. Stair, and M. E. Hanna, Quantitative analysis for management, 9th ed., New Jersey: Pearson Education, Inc, 2006, pp. 315-317.
[57] C. Romero, and T. Rehman, "Livestock ration formulation via goal programming with penalty functions," in Multiple Criteria Analysis for Agricultural Decisions, vol. 11, 2003, pp. 149-161.
[58] W. B. Roush, and T. L. Cravener, "Stochastic true digestible amino acid values," Animal Feed Science and Technology, vol. 102, pp. 225-239, 2002.
[59] W. B. Roush, T. L. Cravener, and F. Zhang, "Computer formulation observations and caveats," Journal of Applied Poultry Science, vol. 5, pp. 116-125, 1996.
[60] W. B. Roush, R. H. Stock, T. L. Cravener, & T. H. D'Alfonso, "Using chance-constrained programming for animal feed formulation at Agway," Interfaces, The Institute of Management Sciences, vol. 24, pp. 53-58, 1994.
[61] M. A. ┼×ahman, M. ├çunka┼ƒ, ┼×. ─░nal, F. ─░nal, B. Co┼ƒkun, and U. Ta┼ƒkiran, "Cost optimization of feed mixes by genetic algorithms," Advances in Engineering Software, vol. 40, pp. 965-974, 2009.
[62] S. Salcedo-Sanz, "A survey of repair methods used as constraint handling techniques in evolutionary algorithm," Computer Science Review, vol. 3, pp. 175-192, 2009.
[63] D. Sirisatien, G. R. Wood, M. Dong, and P. C. H. Morel, "Two aspects of optimal diet determination for pig production: efficiency of solution and incorporation of cost variation," Journal of Global Optimum, vol. 43, pp. 249-261, 2009.
[64] S. N. Sivanandam, and S. N.Deepa, Introduction to genetic algorithms. New York: Springer, 2008, pp. 10-14.
[65] J. A. Suárez, G. Gaxiola, R. Mendoza, S. Cadavid, G. Garcia, G. Alanis, et al., "Substitution of fish meal with plant protein sources and energy budget for white shrimp Litopenaeus vannamei (Boone, 1931)," Aquaculture, vol. 289, pp. 118-123, 2009.
[66] S. K. Sung, K. ΙΙ-Hwan, V. Mani, and J. K. Hyung, "Real-coded genetic algorithm for machining condition optimization," Int J Adv Manuf Technol, vol. 38, 884-895, 2008.
[67] L. W. Swanson, and J. G. Woodruff, "A Sequential Approach to the Feed-Mix Problem," Operations Research, vol. 12, no. 1, pp. 89-109, 1964.
[68] E. Thomson, & J. Nolan, "UNEForm: A powerful feed formulation spreadsheet suitable for teaching or on-farm formulation," Animal Feed Science and Technology, vol. 91, pp. 233-240, 2001.
[69] J. M. Torres-Rojo, "Risk management in the design of a feeding ration: A portfolio theory approach," Agricultural Systems, vol. 68, pp. 1-20, 2001.
[70] P. R. Tozer, & J. R. Stokes, "A multi-objective programming approach to feed ration balancing and nutrient management" Agricultural Systems, vol. 67, no. 3, pp. 201-215, 2001.
[71] F. V. Waugh, "The minimum-cost dairy feed," Journal of Farm Economics, vol. 33, pp. 299-310, 1951.
[72] T. Yigit, "Constraint-based school timetabling using hybrid genetic algorithm," in AI*IA 2007: Artificial Intelligence and Human-Oriented Computing, vol. 4733, Springer Berlin / Heidelberg, 2007, pp. 848-855.
[73] J. Žgajnar, L. Juvan─ìi─ì, & S. Kav─ìi─ì, "Spreadsheet tool for least-cost and nutrition balanced beef ration formulation," in Proc. The 16th Int. Symp. Animal Science Days, Strunjan, Slovenia, 2008.
[74] J. Žgajnar, L. Juvan─ìi─ì, & S. Kav─ìi─ì, "Combination of linear and weighted goal programming with penalty function in optimisation of a daily dairy cow ration," Agric. Econ. -czech, vol. 55, no. 10, pp. 492- 500, 2009a.
[75] J. Žgajnar, L. Juvan─ìi─ì, & S. Kav─ìi─ì, "Multi-goal pig ration formulation; mathematical optimization approach," Agronomy Research, vol. 7, no. 2, pp. 775-782, 2009b.
[76] F. Zhang, and W. B. Roush, "Multiple-objective (goal) programming model for feed formulation: An example for reducing nutrient variation," Poultry Science, vol. 81, pp. 182-192, 2002.
[77] C. Zioganas, The determination of viable, parity and optimum sizes of family-type sheep farms in the Epirus Region of Greece. Unpublished PhD Thesis, Wye College-University of London, 1981.