Skip to main content
Top
Published in: Neural Computing and Applications 10/2019

06-03-2018 | Original Article

Quantum-behaved bat algorithm for many-objective combined economic emission dispatch problem using cubic criterion function

Authors: Fahad Parvez Mahdi, Pandian Vasant, M. Abdullah-Al-Wadud, Vish Kallimani, Junzo Watada

Published in: Neural Computing and Applications | Issue 10/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this research, a quantum computing idea based bat algorithm (QBA) is proposed to solve many-objective combined economic emission dispatch (CEED) problem. Here, CEED is represented using cubic criterion function to reduce the nonlinearities of the system. Along with economic load dispatch, emissions of SO2, NOx, and CO2 are considered as separate three objectives, thus making it a four-objective (many-objective) optimization problem. A unit-wise price penalty factor is considered here to convert all the objectives into a single objective in order to compare the final results with other previously used methods like Lagrangian relaxation (LR), particle swarm optimization, and simulated annealing. QBA is applied in six-unit power generation system for four different loads. The obtained results show QBA successfully solve many-objective CEED problem with greater superiority than other methods found in the literature in terms of quality results, robustness, and computational performance. In the end of this paper, a detailed future research direction is provided based on the simulation results and its analysis. The outcome of this research demonstrates that the inclusion of quantum computing idea in metaheuristic technique provides a useful and reliable tool for solving such many-objective optimization problem.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Wang B, Li Y, Watada J (2013) Supply reliability and generation cost analysis due to load forecast uncertainty in unit commitment problems. IEEE Trans Power Syst 28:2242–2252CrossRef Wang B, Li Y, Watada J (2013) Supply reliability and generation cost analysis due to load forecast uncertainty in unit commitment problems. IEEE Trans Power Syst 28:2242–2252CrossRef
2.
go back to reference Nanda J, Kothari D, Lingamurthy K (1988) Economic-emission load dispatch through goal programming techniques. IEEE Trans Energy Convers 3:26–32CrossRef Nanda J, Kothari D, Lingamurthy K (1988) Economic-emission load dispatch through goal programming techniques. IEEE Trans Energy Convers 3:26–32CrossRef
3.
go back to reference Granelli G, Montagna M, Pasini G, Marannino P (1992) Emission constrained dynamic dispatch. Electr Power Syst Res 24:55–64CrossRef Granelli G, Montagna M, Pasini G, Marannino P (1992) Emission constrained dynamic dispatch. Electr Power Syst Res 24:55–64CrossRef
4.
go back to reference Dhillon J, Parti S, Kothari D (1993) Stochastic economic emission load dispatch. Electr Power Syst Res 26:179–186CrossRef Dhillon J, Parti S, Kothari D (1993) Stochastic economic emission load dispatch. Electr Power Syst Res 26:179–186CrossRef
5.
go back to reference El-Keib A, Ding H (1994) Environmentally constrained economic dispatch using linear programming. Electr Power Syst Res 29:155–159CrossRef El-Keib A, Ding H (1994) Environmentally constrained economic dispatch using linear programming. Electr Power Syst Res 29:155–159CrossRef
6.
go back to reference Chen J-F, Chen S-D (1997) Multiobjective power dispatch with line flow constraints using the fast Newton–Raphson method. IEEE Trans Energy Convers 12:86–93CrossRef Chen J-F, Chen S-D (1997) Multiobjective power dispatch with line flow constraints using the fast Newton–Raphson method. IEEE Trans Energy Convers 12:86–93CrossRef
7.
go back to reference Krishnamurthy S, Tzoneva R (2012) Impact of price penalty factors on the solution of the combined economic emission dispatch problem using cubic criterion functions. In: Presented at the IEEE power and energy society general meeting Krishnamurthy S, Tzoneva R (2012) Impact of price penalty factors on the solution of the combined economic emission dispatch problem using cubic criterion functions. In: Presented at the IEEE power and energy society general meeting
8.
go back to reference Papageorgiou LG, Fraga ES (2007) A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones. Electr Power Syst Res 77:1292–1296CrossRef Papageorgiou LG, Fraga ES (2007) A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones. Electr Power Syst Res 77:1292–1296CrossRef
10.
go back to reference Pandian SMV, Thanushkodi K, Anjana PS, Dilesh D, Kiruthika B, Ramprabhu CS et al (2011) An efficient particle swarm optimization technique to solve combined economic emission dispatch problem. Eur J Sci Res 54:187–192 Pandian SMV, Thanushkodi K, Anjana PS, Dilesh D, Kiruthika B, Ramprabhu CS et al (2011) An efficient particle swarm optimization technique to solve combined economic emission dispatch problem. Eur J Sci Res 54:187–192
11.
go back to reference Noman N, Iba H (2008) Differential evolution for economic load dispatch problems. Electr Power Syst Res 78:1322–1331CrossRef Noman N, Iba H (2008) Differential evolution for economic load dispatch problems. Electr Power Syst Res 78:1322–1331CrossRef
12.
go back to reference Siddaiah R, Saini RP (2016) A review on planning, configurations, modeling and optimization techniques of hybrid renewable energy systems for off grid applications. Renew Sustain Energy Rev 58:376–396CrossRef Siddaiah R, Saini RP (2016) A review on planning, configurations, modeling and optimization techniques of hybrid renewable energy systems for off grid applications. Renew Sustain Energy Rev 58:376–396CrossRef
13.
go back to reference Koridak LA, Rahli M (2010) Optimization of the emission and economic dispatch by the genetic algorithm. Prz Elektrotech 86:363–366 Koridak LA, Rahli M (2010) Optimization of the emission and economic dispatch by the genetic algorithm. Prz Elektrotech 86:363–366
14.
go back to reference Ratniyomchai T, Oonsivilai A, Pao-La-Or P, Kulworawanichpong T (2010) Particle swarm optimization for solving combined economic and emission dispatch problems. World Scientific and Engineering Acad and Soc, Athens Ratniyomchai T, Oonsivilai A, Pao-La-Or P, Kulworawanichpong T (2010) Particle swarm optimization for solving combined economic and emission dispatch problems. World Scientific and Engineering Acad and Soc, Athens
15.
go back to reference Basu M (2005) A simulated annealing-based goal-attainment method for economic emission load dispatch of fixed head hydrothermal power systems. Int J Electr Power Energy Syst 27:147–153CrossRef Basu M (2005) A simulated annealing-based goal-attainment method for economic emission load dispatch of fixed head hydrothermal power systems. Int J Electr Power Energy Syst 27:147–153CrossRef
16.
go back to reference Hota P, Barisal A, Chakrabarti R (2010) Economic emission load dispatch through fuzzy based bacterial foraging algorithm. Int J Electr Power Energy Syst 32:794–803CrossRef Hota P, Barisal A, Chakrabarti R (2010) Economic emission load dispatch through fuzzy based bacterial foraging algorithm. Int J Electr Power Energy Syst 32:794–803CrossRef
17.
go back to reference Abou El Ela AA, Abido MA, Spea SR (2010) Differential evolution algorithm for emission constrained economic power dispatch problem. Electr Power Syst Res 80:1286–1292CrossRef Abou El Ela AA, Abido MA, Spea SR (2010) Differential evolution algorithm for emission constrained economic power dispatch problem. Electr Power Syst Res 80:1286–1292CrossRef
19.
go back to reference Guvenc U, Sonmez Y, Duman S, Yorukeren N (2012) Combined economic and emission dispatch solution using gravitational search algorithm. Sci Iran 19:1754–1762CrossRef Guvenc U, Sonmez Y, Duman S, Yorukeren N (2012) Combined economic and emission dispatch solution using gravitational search algorithm. Sci Iran 19:1754–1762CrossRef
20.
go back to reference Karakonstantis I, Vlachos A (2015) Ant colony optimization for continuous domains applied to emission and economic dispatch problems. J Inf Optim Sci 36:23–42MathSciNet Karakonstantis I, Vlachos A (2015) Ant colony optimization for continuous domains applied to emission and economic dispatch problems. J Inf Optim Sci 36:23–42MathSciNet
21.
go back to reference Dixit GP, Dubey HM, Pandit M, Panigrahi B (2011) Artificial bee colony optimization for combined economic load and emission dispatch. In: International conference on sustainable energy and intelligent systems (SEISCON 2011), pp 340–345 Dixit GP, Dubey HM, Pandit M, Panigrahi B (2011) Artificial bee colony optimization for combined economic load and emission dispatch. In: International conference on sustainable energy and intelligent systems (SEISCON 2011), pp 340–345
22.
go back to reference Sapra U (2013) Solving combined economic and emission dispatch using cuckoo search. Int J Eng Trends Technol 4:2544–2549 Sapra U (2013) Solving combined economic and emission dispatch using cuckoo search. Int J Eng Trends Technol 4:2544–2549
23.
go back to reference Azizipanah-Abarghooee R, Niknam T (2012) A new improved bat algorithm for fuzzy interactive multi-objective economic/emission dispatch with load and wind power uncertainty. Uncertain Model Knowl Eng Decis Mak 7:388–393CrossRef Azizipanah-Abarghooee R, Niknam T (2012) A new improved bat algorithm for fuzzy interactive multi-objective economic/emission dispatch with load and wind power uncertainty. Uncertain Model Knowl Eng Decis Mak 7:388–393CrossRef
24.
go back to reference Roy PK, Bhui S (2013) Multi-objective quasi-oppositional teaching learning based optimization for economic emission load dispatch problem. Int J Electr Power Energy Syst 53:937–948CrossRef Roy PK, Bhui S (2013) Multi-objective quasi-oppositional teaching learning based optimization for economic emission load dispatch problem. Int J Electr Power Energy Syst 53:937–948CrossRef
25.
go back to reference Abdelaziz AY, Ali ES, Abd Elazim SM (2016) Combined economic and emission dispatch solution using flower pollination algorithm. Int J Electr Power Energy Syst 80:264–274CrossRef Abdelaziz AY, Ali ES, Abd Elazim SM (2016) Combined economic and emission dispatch solution using flower pollination algorithm. Int J Electr Power Energy Syst 80:264–274CrossRef
27.
go back to reference Basu M (2013) Combined heat and power economic emission dispatch using nondominated sorting genetic algorithm-II. Int J Electr Power Energy Syst 53:135–141CrossRef Basu M (2013) Combined heat and power economic emission dispatch using nondominated sorting genetic algorithm-II. Int J Electr Power Energy Syst 53:135–141CrossRef
28.
go back to reference Osman MS, Abo-Sinna MA, Mousa AA (2009) An epsilon-dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem. Electr Power Syst Res 79:1561–1567CrossRef Osman MS, Abo-Sinna MA, Mousa AA (2009) An epsilon-dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem. Electr Power Syst Res 79:1561–1567CrossRef
29.
go back to reference Guvenc U (2010) Combined economic emission dispatch solution using genetic algorithm based on similarity crossover. Sci Res Essays 5:2451–2456MathSciNet Guvenc U (2010) Combined economic emission dispatch solution using genetic algorithm based on similarity crossover. Sci Res Essays 5:2451–2456MathSciNet
30.
go back to reference Wang LF, Singh C (2009) Reserve-constrained multiarea environmental/economic dispatch based on particle swarm optimization with local search. Eng Appl Artif Intell 22:298–307CrossRef Wang LF, Singh C (2009) Reserve-constrained multiarea environmental/economic dispatch based on particle swarm optimization with local search. Eng Appl Artif Intell 22:298–307CrossRef
31.
go back to reference Lu S, Sun C, Lu Z (2010) An improved quantum-behaved particle swarm optimization method for short-term combined economic emission hydrothermal scheduling. Energy Convers Manag 51:561–571CrossRef Lu S, Sun C, Lu Z (2010) An improved quantum-behaved particle swarm optimization method for short-term combined economic emission hydrothermal scheduling. Energy Convers Manag 51:561–571CrossRef
32.
go back to reference Chen P-H, Kuo C-C (2011) Economic-emission load dispatch by refined particle swarm optimization and interactive bi-objective programming. Int Rev Electr Eng Iree 6:2584–2595 Chen P-H, Kuo C-C (2011) Economic-emission load dispatch by refined particle swarm optimization and interactive bi-objective programming. Int Rev Electr Eng Iree 6:2584–2595
33.
go back to reference Bahmanifirouzi B, Farjah E, Niknam T (2012) Multi-objective stochastic dynamic economic emission dispatch enhancement by fuzzy adaptive modified theta particle swarm optimization. J Renew Sustain Energy 4:023105CrossRef Bahmanifirouzi B, Farjah E, Niknam T (2012) Multi-objective stochastic dynamic economic emission dispatch enhancement by fuzzy adaptive modified theta particle swarm optimization. J Renew Sustain Energy 4:023105CrossRef
34.
go back to reference Zhang Y, Gong D-W, Ding Z (2012) A bare-bones multi-objective particle swarm optimization algorithm for environmental/economic dispatch. Inf Sci 192:213–227CrossRef Zhang Y, Gong D-W, Ding Z (2012) A bare-bones multi-objective particle swarm optimization algorithm for environmental/economic dispatch. Inf Sci 192:213–227CrossRef
35.
go back to reference Jadoun VK, Gupta N, Niazi KR, Swamkar A (2015) Modulated particle swarm optimization for economic emission dispatch. Int J Electr Power Energy Syst 73:80–88CrossRef Jadoun VK, Gupta N, Niazi KR, Swamkar A (2015) Modulated particle swarm optimization for economic emission dispatch. Int J Electr Power Energy Syst 73:80–88CrossRef
36.
go back to reference Jadoun VK, Gupta N, Niazi KR, Swarnkar A, Bansal RC (2015) Multi-area environmental economic dispatch with reserve constraints using enhanced particle swarm optimization. Electr Power Compon Syst 43:1667–1679CrossRef Jadoun VK, Gupta N, Niazi KR, Swarnkar A, Bansal RC (2015) Multi-area environmental economic dispatch with reserve constraints using enhanced particle swarm optimization. Electr Power Compon Syst 43:1667–1679CrossRef
37.
go back to reference Jiang S, Ji Z, Wang Y (2015) A novel gravitational acceleration enhanced particle swarm optimization algorithm for wind-thermal economic emission dispatch problem considering wind power availability. Int J Electr Power Energy Syst 73:1035–1050CrossRef Jiang S, Ji Z, Wang Y (2015) A novel gravitational acceleration enhanced particle swarm optimization algorithm for wind-thermal economic emission dispatch problem considering wind power availability. Int J Electr Power Energy Syst 73:1035–1050CrossRef
38.
go back to reference Mandal KK, Mandal S, Bhattacharya B, Chakraborty N (2015) Non-convex emission constrained economic dispatch using a new self-adaptive particle swarm optimization technique. Appl Soft Comput J 28:188–195CrossRef Mandal KK, Mandal S, Bhattacharya B, Chakraborty N (2015) Non-convex emission constrained economic dispatch using a new self-adaptive particle swarm optimization technique. Appl Soft Comput J 28:188–195CrossRef
39.
go back to reference Gopalakrishnan R, Krishnan A (2013) An efficient technique to solve combined economic and emission dispatch problem using modified Ant colony optimization. Sadhana Acad Proc Eng Sci 38:545–556MathSciNetMATH Gopalakrishnan R, Krishnan A (2013) An efficient technique to solve combined economic and emission dispatch problem using modified Ant colony optimization. Sadhana Acad Proc Eng Sci 38:545–556MathSciNetMATH
40.
go back to reference Basu M (2004) An interactive fuzzy satisfying-based simulated annealing technique for economic emission load dispatch with nonsmooth fuel cost and emission level functions. Electr Power Compon Syst 32:163–173CrossRef Basu M (2004) An interactive fuzzy satisfying-based simulated annealing technique for economic emission load dispatch with nonsmooth fuel cost and emission level functions. Electr Power Compon Syst 32:163–173CrossRef
41.
go back to reference Shaw B, Mukherjee V, Ghoshal SP (2012) A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems. Int J Electr Power Energy Syst 35:21–33CrossRef Shaw B, Mukherjee V, Ghoshal SP (2012) A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems. Int J Electr Power Energy Syst 35:21–33CrossRef
42.
go back to reference Mohy-ud-din G (2017) Hybrid dynamic economic emission dispatch of thermal, wind, and photovoltaic power using the hybrid backtracking search algorithm with sequential quadratic programming. J Renew Sustain Energy 9:29CrossRef Mohy-ud-din G (2017) Hybrid dynamic economic emission dispatch of thermal, wind, and photovoltaic power using the hybrid backtracking search algorithm with sequential quadratic programming. J Renew Sustain Energy 9:29CrossRef
43.
go back to reference Gherbi YA, Bouzeboudja H, Gherbi FZ (2016) The combined economic environmental dispatch using new hybrid metaheuristic. Energy 115:468–477CrossRef Gherbi YA, Bouzeboudja H, Gherbi FZ (2016) The combined economic environmental dispatch using new hybrid metaheuristic. Energy 115:468–477CrossRef
44.
go back to reference Azizipanah-Abarghooee R, Dehghanian P, Terzija V (2016) Practical multi-area bi-objective environmental economic dispatch equipped with a hybrid gradient search method and improved Jaya algorithm. IET Gener Trans Distrib 10:3580–3596CrossRef Azizipanah-Abarghooee R, Dehghanian P, Terzija V (2016) Practical multi-area bi-objective environmental economic dispatch equipped with a hybrid gradient search method and improved Jaya algorithm. IET Gener Trans Distrib 10:3580–3596CrossRef
45.
go back to reference Zhang H, Yue D, Xie X, Hu S, Weng S (2015) Multi-elite guide hybrid differential evolution with simulated annealing technique for dynamic economic emission dispatch. Appl Soft Comput 34:312–323CrossRef Zhang H, Yue D, Xie X, Hu S, Weng S (2015) Multi-elite guide hybrid differential evolution with simulated annealing technique for dynamic economic emission dispatch. Appl Soft Comput 34:312–323CrossRef
46.
go back to reference Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010), Springer, Berlin. pp 65–74 Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010), Springer, Berlin. pp 65–74
47.
go back to reference Yang X-S, Hossein Gandomi A (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29:464–483CrossRef Yang X-S, Hossein Gandomi A (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29:464–483CrossRef
48.
go back to reference Schnitzler H-U, Kalko EK (2001) Echolocation by insect-eating bats we define four distinct functional groups of bats and find differences in signal structure that correlate with the typical echolocation tasks faced by each group. Bioscience 51:557–569CrossRef Schnitzler H-U, Kalko EK (2001) Echolocation by insect-eating bats we define four distinct functional groups of bats and find differences in signal structure that correlate with the typical echolocation tasks faced by each group. Bioscience 51:557–569CrossRef
49.
go back to reference Shi Y, Eberhart RC (1998) Parameter selection in particle swarm optimization. In: Porto VW, Saravanan N, Waagen D, and Eiben AE (eds) Proceedings evolutionary programming VII: 7th international conference, EP98 San Diego, California, USA, March 25–27, 1998. Springer, Berlin, pp 591–600 Shi Y, Eberhart RC (1998) Parameter selection in particle swarm optimization. In: Porto VW, Saravanan N, Waagen D, and Eiben AE (eds) Proceedings evolutionary programming VII: 7th international conference, EP98 San Diego, California, USA, March 25–27, 1998. Springer, Berlin, pp 591–600
51.
go back to reference Ziane I, Benhamida F, Graa A (2016) Simulated annealing algorithm for combined economic and emission power dispatch using max/max price penalty factor. Neural Comput Appl 28(1):197–205 Ziane I, Benhamida F, Graa A (2016) Simulated annealing algorithm for combined economic and emission power dispatch using max/max price penalty factor. Neural Comput Appl 28(1):197–205
52.
go back to reference Tozer B, Mazzuchi T, Sarkani S (2017) Many-objective stochastic path finding using reinforcement learning. Exp Syst Appl 72:371–382CrossRef Tozer B, Mazzuchi T, Sarkani S (2017) Many-objective stochastic path finding using reinforcement learning. Exp Syst Appl 72:371–382CrossRef
53.
go back to reference Zou X, Chen Y, Liu M, Kang L (2008) A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans Syst Man Cybernet Part B (Cybernetics) 38:1402–1412CrossRef Zou X, Chen Y, Liu M, Kang L (2008) A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans Syst Man Cybernet Part B (Cybernetics) 38:1402–1412CrossRef
54.
go back to reference Deb K, Saxena DK (2005) On finding pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. KanGAL Report No. 2005006 Deb K, Saxena DK (2005) On finding pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. KanGAL Report No. 2005006
55.
go back to reference Fister Jr. I, Fister I, Yang X-S (2015) Towards the development of a parameter-free bat algorithm. In: Proceedings of the 2015 2nd student computer science research conference StuCoSReC. pp 31–34 Fister Jr. I, Fister I, Yang X-S (2015) Towards the development of a parameter-free bat algorithm. In: Proceedings of the 2015 2nd student computer science research conference StuCoSReC. pp 31–34
56.
go back to reference Fister I, Mlakar U, Yang X-S, Fister I (2016) Parameterless bat algorithm and its performance study. In: Yang X-S (ed) Nature-inspired computation in engineering. Springer, Berlin, pp 267–276CrossRef Fister I, Mlakar U, Yang X-S, Fister I (2016) Parameterless bat algorithm and its performance study. In: Yang X-S (ed) Nature-inspired computation in engineering. Springer, Berlin, pp 267–276CrossRef
Metadata
Title
Quantum-behaved bat algorithm for many-objective combined economic emission dispatch problem using cubic criterion function
Authors
Fahad Parvez Mahdi
Pandian Vasant
M. Abdullah-Al-Wadud
Vish Kallimani
Junzo Watada
Publication date
06-03-2018
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 10/2019
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-018-3399-z

Other articles of this Issue 10/2019

Neural Computing and Applications 10/2019 Go to the issue

Premium Partner