A Crossover in Simulated Annealing for Population Initialization of Genetic Algorithm to Optimize Distribution Cost

Asyrofa Rahmi, Wayan Firdaus Mahmudy, Syaiful Anam


Solving distribution problems have been an alluring topic for some academician. The determination of proper distribution network to provide a minimal cost is still difficult to resolve. This is because there are some difficult constraints to be addressed. As an algorithm, which typically offers a set of solutions in solving the problems, genetic algorithms (GA) has verified its power in solving complex combinatorial problems. The generation of a set of initial solutions (population) generally performed randomly in GA. In the large cases, it is becoming one of the drawbacks since the search space becomes too wide, so the probability to get stuck in a local optimum solution is also high. Therefore, simulated annealing (SA) is employed to generate the initial population for the GA. SA has been selected since it is able to avoid a local optimum solution. In this study, the process of finding new solutions using SA is improved by using the crossover process, which is commonly used in GA. This method has become novel because the crossover has the same principle of providing varied new solutions that still retain some of the properties of the parent solution. The result of the modification SA-GA proven to provide superior results than the existing algorithms.


Genetic Algorithms; Crossover; Simulated Annealing; Multi-Level Multi-Product Distribution;

Full Text:



H. Guo, X. Wang, and S. Zhou, “A Transportation Problem with Uncertain Costs and Random Supplies,” International Journal of eNavigation and Maritime Economy, vol. 2, pp. 1–11, 2015.

P. Bahrampour, M. Safari, and M. B. Taraghdari, “Modeling MultiProduct Multi-Stage Supply Chain Network Design,” in 1st International Conference on Applied Economics and Business, ICAEB 2015 Modeling, 2016, vol. 36, no. 16, pp. 70–80.

R. R. P. Langroodi and M. Amiri, “A system dynamics modeling approach for a multi-level, multi-product, multi-region supply chain under demand uncertainty,” Expert Systems with Applications, vol. 51, pp. 231–244, 2016.

C. Gicquel and M. Minoux, “Multi-product valid inequalities for the discrete lot-sizing and scheduling problem,” Computers and Operation Research, vol. 54, pp. 12–20, 2015.

S. H. Kim and Y. H. Lee, “Synchronized production planning and scheduling in semiconductor fabrication,” COMPUTERS & INDUSTRIAL ENGINEERING, vol. 96, pp. 72–85, 2016.

P. Sitek and J. Wikarek, “Mathematical programming model of cost optimization for supply chain from perspective of logistics provider,” Management and Production Engineering Review, vol. 3, no. 2, pp. 49– 61, 2012.

A. Rahmi, M. Z. Sarwani, and W. F. Mahmudy, “Genetic Algorithms for Optimization of Multi-Level Product Distribution,” Accepted to International Journal of Intelligent Engineering & Systems, 2016.

K. Boudjelaba, F. Ros, and D. Chikouche, “An efficient hybrid genetic algorithm to design finite impulse response filters,” Expert Systems with Applications, vol. 41, no. 13, pp. 5917–5937, 2014.

C. Faycal, M. E. Riffi, and B. Ahiod, “Hybrid genetic algorithm and greedy randomized adaptive search procedure for solving a nurse scheduling problem,” Journal of Theoretical and Applied Information Technology, vol. 73, no. 2, pp. 313–320, 2015.

S. Sen, P. Roy, A. Chakrabarti, and S. Sengupta, “Generator Contribution Based Congestion Management using Multiobjective Genetic Algorithm,” TELKOMNIKA, vol. 9, no. 1, pp. 1–8, 2011.

A. Kumar and P. V Tsvetkov, “Annals of Nuclear Energy Optimization of U – Th fuel in heavy water moderated thermal breeder reactors using multivariate regression analysis and genetic algorithms,” Annals of Nuclear Energy, vol. 85, pp. 885–892, 2015.

M. Mirzaali, S. M. H. Seyedkashi, G. H. Liaghat, H. Moslemi Naeini, K. Shojaee G., and Y. H. Moon, “Application of simulated annealing method to pressure and force loading optimization in tube hydroforming process,” International Journal of Mechanical Sciences, vol. 55, no. 1, pp. 78–84, 2012.

M. Z. Sarwani, A. Rahmi, and W. F. Mahmudy, “An Adaptive Genetic Algorithm for Cost Optimization of Multi-Stage Supply Chain,” Accepted to Journal of Telecommunication, Electronic and Computer Engineering, 2016.

T. Sousa, T. Soares, H. Morais, R. Castro, and Z. Vale, “Simulated annealing to handle energy and ancillary services joint management considering electric vehicles,” Electric Power Systems Research, vol. 136, pp. 383–397, 2016.

J. S. Arora and J. S. Arora, Chapter 16 – Genetic Algorithms for Optimum Design. 2012.

W. F. Mahmudy, “Optimization of Part Type Selection and Machine Loading Problems in Flexible Manufacturing System Using Variable Neighborhood Search,” IAENG International Journal of Computer Science, vol. 42, no. 3, 2015.

Z. Qiongbing, “A New Crossover Mechanism for Genetic Algorithms with Variable-length Chromosomes for Path Optimization Problems,” Expert Systems With Applications, 2016.

M. Thakur and A. Kumar, “Electrical Power and Energy Systems Optimal coordination of directional over current relays using a modified real coded genetic algorithm : A comparative study,” INTERNATIONAL JOURNAL OF ELECTRICAL POWER AND ENERGY SYSTEMS, vol. 82, pp. 484–495, 2016.

W. F. Mahmudy, R. M. Marian, and L. H. S. Luong, “Real Coded Genetic Algorithms for Solving Flexible Job-Shop Scheduling Problem - Part II: Optimization,” Advanced Materials Research, vol. 701, pp. 364–369, 2013.

R. Jiao, Z. Yang, R. Shi, and B. Lin, “A Multistage Multiobjective Substation Siting and Sizing Model Based on Operator-Repair Genetic Algorithm,” IEEJ Transactions on Electrical and Electronic Engineering, vol. 9, pp. S28--S36, 2014.

N. Soni and T. Kumar, “Study of Various Mutation Operators in Genetic Algorithms,” vol. 5, no. 3, pp. 4519–4521, 2014.

A. P. Engelbrecht, Computational Intelligence. England: John Wiley & Sons, 2007.

A. Rahmi and W. F. Mahmudy, “Regression Modelling for Precipitation Prediction Using Genetic Algorithms,” submitted TELKOMNIKA.

W. Lesmawati, A. Rahmi, and W. F. Mahmudy, “Optimization of Frozen Food Distribution using Genetic Algorithms,” Journal of Environmental Engineering & Sustainable Technology, vol. 3, no. 1, pp. 51–58, 2016.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

ISSN: 2180-1843

eISSN: 2289-8131