An Innovative Genetic Algorithms-Based Inexact Non-Linear Programming Problem Solving Method

Weihua  Jin; Zhiying  Hu; Christine  Chan

doi:10.4236/jep.2017.83018

Weihua Jin, Zhiying Hu^*, Christine Chan

Abstract: In this paper, an innovative Genetic Algorithms (GA)-based inexact non-linear programming (GAINLP) problem solving approach has been proposed for solving non-linear programming optimization problems with inexact information (inexact non-linear operation programming). GAINLP was developed based on a GA-based inexact quadratic solving method. The Genetic Algorithm Solver of the Global Optimization Toolbox (GASGOT) developed by MATLAB^TM was adopted as the implementation environment of this study. GAINLP was applied to a municipality solid waste management case. The results from different scenarios indicated that the proposed GA-based heuristic optimization approach was able to generate a solution for a complicated nonlinear problem, which also involved uncertainty.

Keywords: Genetic Algorithms, Inexact Non-Linear Programming (INLP), Economy of Scale, Numeric Optimization, Solid Waste Management

Cite this paper: Jin, W. , Hu, Z. and Chan, C. (2017) An Innovative Genetic Algorithms-Based Inexact Non-Linear Programming Problem Solving Method. Journal of Environmental Protection, 8, 231-249. doi: 10.4236/jep.2017.83018.

References

[1] Anderson, L. (1968) A Mathematical Model for the Optimization of a Waste Management System. Technical Report 68-1, Sanitary Engineering Research Laboratory, University of California, Berkely.

[2] Christensen, H. and Haddix, G. (1974) A Model for Sanitary Landfill Management and Decision. Computers and Operation Research, 1, 275-281.
https://doi.org/10.1016/0305-0548(74)90052-5

[3] Fuertes, L., Hundson, J. and Mark, D. (1974) Solid Waste Management: Equity Trade-Off Models. Journal of Urban Planning and Development, 100, 155-171.

[4] Jenkins, L. (1982) Parametric Mixed Integer Programming: An Application to Solid Waste Management. Management Science, 28, 1271-1284.
https://doi.org/10.1287/mnsc.28.11.1270

[5] Jacobs, T. and Everett, J. (1992) Optimal Scheduling of Landfill Operations Incorporating Recycling. Journal of Environmental Engineering, 118, 420-429.
https://doi.org/10.1061/(ASCE)0733-9372(1992)118:3(420)

[6] Badran, M. and El-Haggar, S. (2006) Optimization of Municipal Solid Waste Management in Port Said-Egypt. Waste Management, 26, 534-545.
https://doi.org/10.1016/j.wasman.2005.05.005

[7] Sushi, A. and Vart, P. (1989) Waste Management Policy Analysis and Growth Monitoring: An Integrated Approach to Perspective Planning. International Journal of Systems Science, 20, 907-926. https://doi.org/10.1080/00207728908910180

[8] Chang, N. (1996) A Grey Fuzzy Multiobjective Programming Approach for the Optimal Planning of a Reservoir Watershed, Part A: Theoretical Development. Water Research, 30, 2329-2340. https://doi.org/10.1016/0043-1354(96)00124-8

[9] Chang, N., Shoemaker, C. and Schuler, R. (1996) Solid Waste Management System Analysis with Air Pollution and Leachate Impact Limitations. Waste Management and Research, 14, 463-481. https://doi.org/10.1177/0734242X9601400505

[10] Huang, G., Baetz, B. and Patry, G. (1995) Grey Integer Programming: An Application to Waste Management Planning under Uncertainty. European Journal of Operational Research, 83, 594-620. https://doi.org/10.1016/0377-2217(94)00093-R

[11] Huang, G., Baetz, B. and Patry, G. (1995) Grey Quadratic Programming and Its Application to Municipal Waste Management Planning under Uncertainty. Engineering Optimization, 23, 201-223. https://doi.org/10.1080/03052159508941354

[12] Li, Y. and Huang, G. (2009) Dynamic Analysis for Solid Waste Management Systems: An Inexact Multistage Integer Programming Approach. Journal of the Air and Waste Management Association, 59, 279-292.
https://doi.org/10.3155/1047-3289.59.3.279

[13] Huang, G. and Cai, Y. (2010) A Superiority-Inferiority-Based Inexact Fuzzy Stochastic Programming Approach for Solid Waste Management under Uncertainty. Environmental Modeling and Assessment, 15, 381-396.
https://doi.org/10.1007/s10666-009-9214-6

[14] Ekmekçioglu, M., Kaya, T. and Kahraman, C. (2010) Fuzzy Multicriteria Disposal Method and Site Selection for Municipal Solid Waste. Waste Management, 30, 1729-1737. https://doi.org/10.1016/j.wasman.2010.02.031

[15] Piresa, A., Martinho, G. and Chang, N. (2001) Solid Waste Management in European Countries: A Review of Systems Analysis Techniques. Journal of Environmental Management, 92, 1033-1050. https://doi.org/10.1016/j.jenvman.2010.11.024

[16] Beliën, J., De Boeck, L. and Van Ackere, J. (2012) Municipal Solid Waste Collection and Management Problems: A Literature Review. Transportation Science, 48, 78-102. https://doi.org/10.1287/trsc.1120.0448

[17] Or, I. and Curi, K. (1993) Improving the Efficiency of the Solid Waste Collection System in Izmir, Turkey, through Mathematical Programming. Waste Management & Research, 11, 297-311. https://doi.org/10.1177/0734242X9301100404

[18] Sun, W., Huang, G., Lv, Y. and Li, G. (2013) Inexact Joint-Probabilistic Chance-Constrained Programming with Left-Hand-Side Randomness: An Application to Solid Waste Management. European Journal of Operational Research, 228, 217-225.
https://doi.org/10.1016/j.ejor.2013.01.011

[19] Chang, N., Schuler, R. and Shoemaker, C. (1993) Environment and Economic Optimization of an Integrated Solid Waste Management System. Journal of Resource Management and Technology, 21, 87-100.

[20] Huang, G., Baetz, B. and Patry, G. (1993) A Grey Fuzzy Linear Programming Approach for Municipal Solid Waste Management Planning under Uncertainty. Civil Engineering Systems, 10, 123-146. https://doi.org/10.1080/02630259308970119

[21] Huang, G., Baetz, B. and Patry, G. (1994) Grey Dynamic Programming for Solid Waste Management Planning Under Uncertainty. Journal of Urban Planning and Development, 120, 132-156.
https://doi.org/10.1061/(ASCE)0733-9488(1994)120:3(132)

[22] Huang, G., Baetz, B. and Patry, G. (1994) Waste Flow Allocation Planning through a Grey Fuzzy Quadratic Programming Approach. Civil Engineering Systems, 11, 209-243. https://doi.org/10.1080/02630259408970147

[23] Jin, W., Hu, Z. and Chan, C. (2013) A Genetic-Algorithms-Based Approach for Programming Linear and Quadratic Optimization Problems with Uncertainty. Mathematical Problems in Engineering, 2013, Article ID: 272491.
http://www.hindawi.com/journals/mpe/2013/272491/
https://doi.org/10.1155/2013/272491

[24] Chen, M. and Huang, G. (2001) A Derivative Algorithm for Inexact Quadratic Program-Application to Environmental Decision-Making under Uncertainty. European Journal of Operational Research, 128, 570-586.
https://doi.org/10.1016/S0377-2217(99)00374-4

[25] Callan, S. and Thomas. J. (2001) Economies of Scale and Scope: A Cost Analysis of Municipal Solid Waste Services. Land Economics, 77, 548-560.
https://doi.org/10.2307/3146940

[26] Melanie. M. (1998) An Introduction of Genetic Algorithms, The MIT Press, Cambridge.

[27] Houck, C., Joines, J. and Kay, M. (1995) A Genetic Algorithm for Function Optimization: A Matlab Implementation. NCSU-IE TR 95.09.

[28] Winston, W. (2003) Operation Research: Applications and Algorithms. Duxbury Press, Boston.

[29] Michalewicz, Z. (1998) Genetic Algorithm + Data Structures = Evolution Programs. 3rd Revised and Extended Edition, Springer, Berlin.

[30] Gen, M. and Cheng, R. (1997) Genetic Algorithm and Engineering Design. Wiley, New York.

[31] Joines, J. and Houck, C. (1994) On the Use of Non-Stationary Penalty Functions to Solve Constrained Optimization Problems with Genetic Algorithms. Proceedings of the 1st IEEE Conference on Evolutionary Computation, Orlando, 27-29 June 1994, 579-584.