Skip to main content
SpringerLink
Log in

An innovative hybrid algorithm for bound-unconstrained optimization problems and applications

  • Published:
Journal of Intelligent Manufacturing Aims and scope Submit manuscript

Abstract

Particle swarm optimization (PSO) and differential evolution (DE) are two efficient meta-heuristic algorithms, achieving excellent performance in a wide variety of optimization problems. Unfortunately, when both algorithms are used to solve complex problems then they inevitably suffer from stagnation, premature convergence and unbalanced exploration–exploitation. Hybridization of PSO and DE may provide a platform to resolve these issues. Therefore, this paper proposes an innovative hybrid algorithm (ihPSODE) which would be more effective than PSO and DE. It integrated with suggested novel PSO (nPSO) and DE (nDE). Where in nPSO a new, inertia weight and acceleration coefficient as well as position update equation are familiarized, to escape stagnation. And in nDE a new, mutation strategy and crossover rate is introduced, to avoid premature convergence. In order to balance between global and local search capability, after calculation of ihPSODE population best half member has been identified and discard rest members. Further, in current population nPSO is employed to maintain exploration and exploitation, then nDE is used to enhance convergence accuracy. The proposed ihPSODE and its integrating component nPSO and nDE have been tested over 23 basic, 30 IEEE CEC2014 and 30 IEEE CEC2017 unconstrained benchmark functions plus 3 real life optimization problems. The performance of proposed algorithms compared with traditional PSO and DE, their existed variants/hybrids as well as some of the other state-of-the-art algorithms. The results indicate the superiority of proposed algorithms. Finally, based on overall performance ihPSODE is recommended for bound-unconstrained optimization problems in this present study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

Abbreviations

\( f \) :

Real valued function

\( D \) :

Dimension

\( l_{j} \) & \( u_{j} \) :

Lower and upper limits for jth decision vector limits

\( L \) & \( K \) :

Total number of inequality and equality constraint

\( g_{l} \) :

Inequality constraint

\( h_{k} \) :

Equality constraint

\( x_{i} \) :

Position vector of ith particle

\( v_{i} \) :

Velocity vector of ith particle

\( pbest_{i } \) :

Individual best position of ith particle

\( gbest_{j } \) :

Global best position of particle

\( t \) :

Iteration index

\( c_{1} \) & \( c_{2} \) :

Cognitive and social acceleration coefficient

\( r_{1} \) & \( r_{2} \) :

Uniform random numbers in [0, 1]

\( w \) :

Inertia weight

\( np \) :

Population size

\( x_{l} \) & \( x_{u} \) :

Lower and upper boundaries

\( x_{ij}^{t} \) :

Target vector

\( v_{ij }^{t} \) :

Mutant vector

\( u_{ ij}^{t} \) :

Trial vector

\( F \) :

Scaling vector

\( C_{r} \) :

Crossover rate

\( i \) :

\( \in \left[ {1,np} \right] \)

\( j \) :

\( \in \left[ {1,D} \right] \)

\( rand \) :

Random numbers

\( t_{max} \) :

Maximum iterations

\( n_{t} \) :

Non-linear decreasing factor

\( \tau \) :

Convergence factor

OPs:

Optimization problems

MAs:

Meta-heuristics algorithms

SIAs:

Swarm intelligence algorithms

EAs:

Evolutionary algorithms

PBAs:

Physics-based algorithms

HBAs:

Human behavior based algorithms

PSO:

Particle swarm optimization

CSA:

Clonal selection algorithm

SFLA:

Shuffled frog leaping algorithm

WSO:

Wasp swarm optimization

IWO:

Invasive weed optimization

ABC:

Artificial bee colony

BBO:

Biogeography based optimization

CS:

Cuckoo search

FA:

Firefly algorithm

BA:

Bat algorithm

KH:

Krill herd

SSO:

Social spider optimization

SMO:

Spider monkey optimization

GWO:

Grey wolf optimizer

MFO:

Moth-flame optimization

WOA:

Whale optimization algorithm

GSO:

Glowworm swarm optimization

GOA:

Grasshopper optimization algorithm

COA:

Coyote optimization algorithm

EPC:

Emperor penguins colony

GA:

Genetic algorithm

DE:

Differential evolution

CE:

Cross entropy

PLA:

Photosynthetic learning algorithm

HS:

Harmony search

SWOA:

Small-world optimization algorithm

GSA:

Gravitational search algorithm

WCA:

Water cycle algorithm

WWO:

Water wave optimization

TLBO:

Teaching–learning-based optimization

SAR:

Search and rescue optimization

PSO-DT:

Improved PSO with disturbance term

DAPSO:

Modified adaptive PSO with dynamic adaptation

KCPSO:

Knowledge-based cooperative PSO

PMPSO-TVAC:

Predicted modified PSO with time varying accelerator coefficients

CPSO:

Constrained PSO

DPSO:

Discrete PSO

QPSO:

Quantum-behaved PSO

CPSO-VQO:

Chaotic PSO-virtual quartic objective function

ELPSO:

Enhanced leader PSO

DMeSR-PSO:

Dynamic mentoring and self-regulation based PSO

MOPSO:

Multi-objective particle swarm optimization

MPSO:

Modified PSO

DMSDL-PSO:

Dynamic multi-swarm differential learning PSO

VPSO:

Vortex PSO

SHPSO:

Surrogate-assisted hierarchical PSO

PSOCO:

PSO with crossover operation

UAPSO:

Unique adaptive PSO

MTVPSO:

Modified time-varying PSO

HAFPSO:

Hunter-attack fractional-order PSO

DPSO:

Disruption PSO

IPSOA:

Improved PSO algorithm

CMPSOWV:

Constrained multi-swarm PSO without velocity

NOPSO:

Non-inertial opposition-based PSO

NMSPSO:

Novel multi-swam PSO

ANFIS-VCPSO:

Adaptive neuro fuzzy inference system-vibration and communication PSO

DEPC:

DE with preferential crossover

ODE:

Opposition based DE

JADE:

Adaptive DE with optional external archive

MDE:

Modified DE

FiADE:

Fitness adaptive DE

MDE_pBX:

Modified DE with p-best crossover

ESMDE:

Evolving surrogate model-based DE

mDE:

Modified DE

GRCDE:

Clustering-based DE with random-based sampling and gaussian sampling)

FDE:

Fuzzy DE

MMDE:

Minimax DE

εDE-LS:

Ε constrained DE-local search

NDE:

Novel DE

daDE:

Direction averaged DE

HDEMCO:

Hierarchical DE combined with multi-cross operation

MRDE:

Multi-role based DE

EJADE:

Enhanced adaptive DE

BADE:

Boltzmann annealing DE

ADE:

Accelerated DE

εDE-HP:

ΕDE-halfspace partition

CDDEA:

Co-evolutionary discrete DE algorithm

PID:

Proportional–integral–derivative

FIR:

Finite impulse response

nPSO:

Novel PSO

nDE:

Novel DE

ihPSODE:

Innovative hybrid PSODE

IEEE:

Institute of Electrical and Electronics Engineers

CEC:

Congress on evolutionary computation

TS:

Test suite

RLPs:

Real life problems

UBF:

Unconstrained benchmark functions

SD:

Standard deviation

df :

Degree of freedom

Vs:

Versus

ECD:

Empirical cumulative distribution

SP:

Success performance

CD:

Critical difference

References

  • Ali, M. (2007). Differential evolution with preferential crossover. European Journal of Operational Research, 181(3), 1137–1147.

    Article  Google Scholar 

  • Amjady, N., & Sharifzadeh, H. (2010). Solution of non-convex economic dispatch problem considering valve loading effect by a new Modified differential evolution algorithm. International Journal of Electrical Power & Energy Systems, 32(8), 893–903.

    Article  Google Scholar 

  • Ang, K. M., Lim, W. H., Isa, N. A. M., Tiang, S. S., & Wong, C. H. (2020). A constrained multi-swarm particle swarm optimization without velocity for constrained optimization problems. Expert Systems with Applications, 140, 112882.

    Article  Google Scholar 

  • Awad, N. H., Ali, M. Z., Liang, J. J., Qu, B. Y., & Suganthan, P. N. (2016). Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore.

  • Azadani, E. N., Hosseinian, S., & Moradzadeh, B. (2010). Generation and reserve dispatch in a competitive market using constrained particle swarm optimization. International Journal of Electrical Power & Energy Systems, 32(1), 79–86.

    Article  Google Scholar 

  • Babu, B. (2004). New optimization techniques in engineering. Berlin: Springer.

    Google Scholar 

  • Brest, J., Greiner, S., Boskovic, B., Mernik, M., & Zumer, V. (2006). Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation, 10(6), 646–657.

    Article  Google Scholar 

  • Cai, X. J., Cui, Y., & Tan, Y. (2009). Predicted modified PSO with time varying accelerator coefficients. International Journal of Bio-inspired Computation, 1(1/2), 50–60.

    Article  Google Scholar 

  • Chegini, S. N., Bagheri, A., & Najafi, F. (2018). A new hybrid PSO based on sine cosine algorithm and Levy flight for solving optimization problems. Applied Soft Computing, 73, 697–726.

    Article  Google Scholar 

  • Chen, Y., Li, L., Peng, H., Xiao, J., & Wu, Q. (2018a). Dynamic multi-swarm differential learning particle swarm optimizer. Swarm and Evolutionary Computation, 39, 209–221.

    Article  Google Scholar 

  • Chen, Y., Li, L., Xiao, J., Yang, Y., Liang, J., & Li, T. (2018b). Particle swarm optimizer with crossover operation. Engineering Applications of Artificial Intelligence, 70, 159–169.

    Article  Google Scholar 

  • Chen, X., Tianfield, H., Mei, C., Du, W., & Liu, G. (2017a). Biogeography-based learning particle swarm optimization. Soft Computing, 21, 7519–7541.

    Article  Google Scholar 

  • Chen, D., Zou, F., Lu, R., & Wang, P. (2017b). Learning backtracking search optimization algorithm and its application. Information Sciences, 376, 71–94.

    Article  Google Scholar 

  • Cuevas, E., Cienfuegos, M., Zaldívar, D., & Pérez-Cisneros, M. (2013). A swarm optimization algorithm inspired in the behavior of the social-spider. Expert Systems with Applications, 40(16), 6374–6384.

    Article  Google Scholar 

  • Das, K. N., & Parouha, R. P. (2015). An ideal tri-population approach for unconstrained optimization and applications. Applied Mathematics and Computation, 256, 666–701.

    Article  Google Scholar 

  • Das, K. N., Parouha, R. P., & Deep, K. (2017). Design and applications of a new DE-PSO-DE algorithm for unconstrained optimisation problems. International Journal of Swarm Intelligence, 3(1), 23–57.

    Article  Google Scholar 

  • Dash, J., Dam, B., & Swain, R. (2020). Design and implementation of sharp edge FIR filters using hybrid differential evolution particle swarm optimization. AEU International Journal of Electronics and Communications, 114, 153019.

    Article  Google Scholar 

  • De Castro, L. N., & Von Zuben, F. J. (2000). The clonal selection algorithm with engineering applications. In Proceedings of GECCO (Vol. 2000, pp. 36–39).

  • Dechampai, D., Tanwanichkul, L., Sethanan, K., & Pitakaso, R. (2017). A differential evolution algorithm for the capacitated VRP with flexibility of mixing pickup and delivery services and the and the maximum duration of a route in poultry industry. Journal of Intelligent Manufacturing, 28, 1357–1376.

    Article  Google Scholar 

  • Derakhshan Asl, A., & Wong, K. Y. (2017). Solving unequal-area static and dynamic facility layout problems using modified particle swarm optimization. Journal of Intelligent Manufacturing, 28, 1317–1336.

    Article  Google Scholar 

  • Do, D. T. T., Lee, S., & Lee, J. (2016). A modified differential evolution algorithm for tensegrity structures. Composite Structures, 158, 11–19.

    Article  Google Scholar 

  • Dong, J., Zhang, L., & Xiao, T. (2018). A hybrid PSO/SA algorithm for bi-criteria stochastic line balancing with flexible task times and zoning constraints. Journal of Intelligent Manufacturing, 29, 737–751.

    Article  Google Scholar 

  • Dor, A. E., Clerc, M., & Siarry, P. (2012). Hybridization of differential evolution and particle swarm optimization in a new algorithm DEPSO-2S. Swarm and Evolutionary Computation, 7269, 57–65.

    Article  Google Scholar 

  • Du, S.-Y., & Liu, Z.-G. (2020). Hybridizing particle swarm optimization with JADE for continuous optimization. Multimedia Tools and Application, 79, 4619–4636.

    Article  Google Scholar 

  • Du, H., Wu, X., & Zhuang, J. (2006). Small-world optimization algorithm for function optimization. In L. Jao, et al. (Eds.), Advances in natural computation (pp. 264–273). Heidelberg: Springer.

    Chapter  Google Scholar 

  • Epitropakis, M. G., Plagianakos, V. P., & Vrahatis, M. N. (2012). Evolving cognitive and social experience in particle swarm optimization through differential evolution: A hybrid approach. Information Sciences, 216, 50–92.

    Article  Google Scholar 

  • Eskandar, H., Sadollah, A., Bahreininejad, A., & Hamdi, M. (2012). Water cycle algorithm—A novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures, 110–111, 151–166.

    Article  Google Scholar 

  • Espitia, H. E., & Sofrony, J. I. (2018). Statistical analysis for vortex particle swarm optimization. Applied Soft Computing, 67, 370–386.

    Article  Google Scholar 

  • Eusuff, M., & Lansey, K. E. (2003). Optimization of water distribution network design using the shuffled frog leaping algorithm. Journal of Water Resources Planning and Management, 129(3), 210–225.

    Article  Google Scholar 

  • Famelis, I. T., Alexandridis, A., & Tsitouras, C. (2017). A highly accurate differential evolution–particle swarm optimization algorithm for the construction of initial value problem solvers. Engineering Optimization, 50(8), 1364–1379.

    Article  Google Scholar 

  • Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2019). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems, 191, 105190.

    Article  Google Scholar 

  • Foumani, M., Moeini, A., Haythorpe, M., & Smith-Miles, K. (2018). A cross-entropy method for optimising robotic automated storage and retrieval systems. International Journal of Production Research, 56(19), 6450–6472.

    Article  Google Scholar 

  • Gaitonde, V. N., & Karnik, S. R. (2012). Minimizing burr size in drilling using artificial neural network (ANN)-particle swarm optimization (PSO) approach. Journal of Intelligent Manufacturing, 23, 1783–1793.

    Article  Google Scholar 

  • Gandomi, A. H., & Alavi, A. H. (2012). Krill herd: a new bio-inspired optimization algorithm. Communications in Nonlinear Science and Numerical Simulation, 17(12), 4831–4845.

    Article  Google Scholar 

  • García-Martínez, C., Lozano, M., Herrera, F., Molina, D., & Sánchez, A. M. (2008). Global and local real coded genetic algorithms based on parent centric crossover operators. European Journal of Operational Research, 185(3), 1088–1113.

    Article  Google Scholar 

  • Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: Harmony search. Simulation, 76(2), 60–68.

    Article  Google Scholar 

  • Ghosh, A., Das, S., Chowdhury, A., & Giri, R. (2011). An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Information Sciences, 181, 3749–3765.

    Article  Google Scholar 

  • Goldberg, D. E., & Holland, J. H. (1988). Genetic algorithms and machine learning. Machine Learning, 3, 95–99.

    Article  Google Scholar 

  • Gong, W., & Cai, Z. (2013). Differential evolution with ranking-based mutation operators. IEEE Transactions on Cybernetics, 43(6), 2066–2081.

    Article  Google Scholar 

  • Guedria, N. B. (2020). An accelerated differential evolution algorithm with new operators for multidamage detection in plate-like structures. Applied Mathematical Modelling, 80, 366–383.

    Article  Google Scholar 

  • Gui, L., Xia, X., Yu, F., Wu, H., Wu, R., Wei, B., et al. (2019). A multi-role based differential evolution. Swarm and Evolutionary Computation, 50, 100508.

    Article  Google Scholar 

  • Hakli, H., & Uğuz, H. (2014). A novel particle swarm optimization algorithm with Levy flight. Applied Soft Computating, 23, 333–345.

    Article  Google Scholar 

  • Hao, Z. -F., Gua, G. -H., & Huang, H. (2007). A particle swarm optimization algorithm with differential evolution. In Proceedings of sixth international conference on machine learning and cybernetics (pp. 1031–1035).

  • Harifi, S., Khalilian, M., Mohammadzadeh, J., & Ebrahimnejad, S. (2020). Optimization in solving inventory control problem using nature inspired Emperor Penguins Colony algorithm. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-020-01616-8.

    Article  Google Scholar 

  • He, Q., & Han, C. (2006). An improved particle swarm optimization algorithm with disturbance term. In Computational Intelligence in Bioinformatics, (Vol. 4115, pp. 100-108), Berlin, Springer.

  • Heidari, A. A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., & Chen, H. (2019). Harris hawks optimization: Algorithm and applications. Future Generation Computer Systems, 97, 849–872.

    Article  Google Scholar 

  • Hendtlass, T. (2001). A combined swarm differential evolution algorithm for optimization problems. In L. Monostori, J. Váncza, & M. Ali (Eds.), Engineering of intelligent systems, IEA/AIE 2001. Lecture Notes in Computer Science (Vol. 2070, pp. 11–18). Berlin: Springer.

  • Hosseini, S. A., Hajipour, A., & Tavakoli, H. (2019). Design and optimization of a CMOS power amplifier using innovative fractional-order particle swarm optimization. Applied Soft Computing, 85, 105831.

    Article  Google Scholar 

  • Hu, L., Hua, W., Lei, W., & Xiantian, Z. (2020). A modified Boltzmann annealing differential evolution algorithm for inversion of directional resistivity logging-while-drilling measurements. Journal of Petroleum Science and Engineering, 180, 106916.

    Google Scholar 

  • Isiet, M., & Gadala, M. (2019). Self-adapting control parameters in particle swarm optimization. Applied Soft Computing, 83, 105653.

    Article  Google Scholar 

  • Islam, S. M., Das, S., Ghosh, S., Roy, S., & Suganthan, P. N. (2012). An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 42(2), 482–500.

    Article  Google Scholar 

  • Jana, N. D., & Sil, J. (2016). Interleaving of particle swarm optimization and differential evolution algorithm for global optimization. International Journal of Computers and Applications, 38(2–3), 116–133.

    Article  Google Scholar 

  • Jie, J., Zeng, J., Han, C., & Wang, Q. (2008). Knowledge-based cooperative particle swarm optimization. Applied Mathematics and Computation, 205(2), 861–873.

    Article  Google Scholar 

  • Jordehi, A. R. (2015). Enhanced leader PSO: A new PSO variant for solving global optimisation problems. Applied Soft Computing, 26, 401–417.

    Article  Google Scholar 

  • Kang, Q., & He, H. (2011). A novel discrete particle swarm optimization algorithm for meta-task assignment in heterogeneous computing systems. Microprocessors and Microsystems, 35(1), 10–17.

    Article  Google Scholar 

  • Karaboga, D., & Basturk, B. (2007). A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (abc) algorithm. Journal of Global Optimization, 39(3), 459–471.

    Article  Google Scholar 

  • Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of the 1995 IEEE international conference on neural networks (Vol. 4, pp. 1942–1948). IEEE.

  • Küçükoğlu, İ., & Öztürk, N. (2019). A hybrid meta-heuristic algorithm for vehicle routing and packing problem with cross-docking. Journal of Intelligent Manufacturing, 30, 2927–2943.

    Article  Google Scholar 

  • Lanlan, K., Ruey, S. C., Wenliang, C., & Yeh, C. (2020). Non-inertial opposition-based particle swarm optimization and its theoretical analysis for deep learning applications. Applied Soft Computing, 88, 106038.

    Article  Google Scholar 

  • Li, S., Gu, Q., Gong, W., & Ning, B. (2020). An enhanced adaptive differential evolution algorithm for parameter extraction of photovoltaic models. Energy Conversion and Management, 205, 112443.

    Article  Google Scholar 

  • Li, C., Yang, S., & Nguyen, T. T. (2012). A self-learning particle swarm optimizer for global optimization problems. IEEE Transactions on System, Man and Cybernetics, 42(3), 627–646.

    Article  Google Scholar 

  • Li, X., & Yin, M. (2014). Modified differential evolution with self-adaptive parameters method. Journal of Combinatorial Optimization, 31(2), 546–576.

    Article  Google Scholar 

  • Liang, J. J., Qu, B. Y., & Suganthan, P.N. (2013). Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real parameter numerical optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore.

  • Lim, W. C. E., Kanagaraj, G., & Ponnambalam, S. G. (2016). A hybrid cuckoo search-genetic algorithm for hole-making sequence optimization. Journal of Intelligent Manufacturing, 27, 417–429.

    Article  Google Scholar 

  • Lin, J. T., & Chiu, C. (2018). A hybrid particle swarm optimization with local search for stochastic resource allocation problem. Journal of Intelligent Manufacturing, 29, 481–495.

    Article  Google Scholar 

  • Liu, H., Cai, Z., & Wang, Y. (2010). Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Applied Soft Computing, 10(2), 629–640.

    Article  Google Scholar 

  • Liu, G., & Guo, Z. (2016). A clustering-based differential evolution with random-based sampling and Gaussian sampling. Neurocomputing, 205, 229–246.

    Article  Google Scholar 

  • Liu, Z.-G., Ji, X.-H., & Yang, Y. (2019a). Hierarchical differential evolution algorithm combined with multi-cross operation. Expert Systems with Applications, 130, 276–292.

    Article  Google Scholar 

  • Liu, H., Wang, Y., Tu, L., Ding, G., & Hu, Y. (2019b). A modified particle swarm optimization for large-scale numerical optimizations and engineering design problems. Journal of Intelligent Manufacturing, 30, 2407–2433.

    Article  Google Scholar 

  • Lynn, N., & Suganthan, P. N. (2015). Heterogeneous comprehensive learning particle swarm optimization with enhanced exploration and exploitation. Swarm Evolutionary Computation, 24, 11–24.

    Article  Google Scholar 

  • Lynn, N., & Suganthan, P. N. (2017). Ensemble particle swarm optimizer. Applied Soft Computing, 55, 533–548.

    Article  Google Scholar 

  • Ma, W., Wang, M., & Zhu, X. (2015). Hybrid particle swarm optimization and differential evolution algorithm for bi-level programming problem and its application to pricing and lot-sizing decisions. Journal of Intelligent Manufacturing, 26, 471–483. https://doi.org/10.1007/s10845-013-0803-5.

    Article  Google Scholar 

  • Mahmoodabadi, M. J., Mottaghi, Z. S., & Bagheri, A. (2014). High exploration particle swarm optimization. Journal of Information Science, 273, 101–111.

    Article  Google Scholar 

  • Mallipeddi, R., & Lee, M. (2015). An evolving surrogate model-based differential evolution algorithm. Applied Soft Computing, 34, 770–787.

    Article  Google Scholar 

  • Mao, B., Xie, Z., Wang, Y., Handroos, H., & Wu, H. (2018). A hybrid strategy of differential evolution and modified particle swarm optimization for numerical solution of a parallel manipulator. Mathematical Problems in Engineering, 2018, 9815469.

    Article  Google Scholar 

  • Mehrabian, A. R., & Lucas, C. (2006). A novel numerical optimization algorithm inspired from weed colonization. Ecological Informatics, 1(4), 355–366.

    Article  Google Scholar 

  • Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 89, 228–249.

    Article  Google Scholar 

  • Mirjalili, S., Gandomi, A. H., Mirjalili, S. Z., Saremi, S., Faris, H., & Mirjalili, S. M. (2017). Salp swarm algorithm: Bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163–191.

    Article  Google Scholar 

  • Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in Engineering Software, 95, 51–67.

    Article  Google Scholar 

  • Mirjalili, S. A., Lewis, A., & Sadiq, A. S. (2014a). Autonomous particles groups for particle swarm optimization. Arabian Journal Science Engineering, 39, 4683–4697.

    Article  Google Scholar 

  • Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014b). Grey wolf optimizer. Advances in Engineering Software, 69, 46–61.

    Article  Google Scholar 

  • Mladenović, N., Petrović, J., Kovačević-Vujčić, V., & Čangalović, M. (2003). Solving spread spectrum radar poly phase code design problem by tabu search and variable neighborhood search. European Journal of Operational Research, 151(2), 389–399.

    Article  Google Scholar 

  • Moeini, A., Jenab, K., Mohammadi, M., & Foumani, M. (2013). Fitting the three-parameter Weibull distribution with cross entropy. Applied Mathematical Modelling, 37(9), 6354–6363.

    Article  Google Scholar 

  • Mohamed, A. W. (2018). A novel differential evolution algorithm for solving constrained engineering optimization problems. Journal of Intelligent Manufacturing, 29, 659–692.

    Article  Google Scholar 

  • Mohanty, C. P., Mahapatra, S. S., & Singh, M. R. (2016). A particle swarm approach for multi-objective optimization of electrical discharge machining process. Journal of Intelligent Manufacturing, 27, 1171–1190.

    Article  Google Scholar 

  • Mokhtari, H., & Noroozi, A. (2018). An efficient chaotic based PSO for earliness/tardiness optimization in a batch processing flow shop scheduling problem. Journal of Intelligent Manufacturing, 29, 1063–1081.

    Article  Google Scholar 

  • Mousavi, S. M., Alikar, N., Tavana, M., & Caprio, D. D. (2019). An improved particle swarm optimization model for solving homogeneous discounted series-parallel redundancy allocation problems. Journal of Intelligent Manufacturing, 30, 1175–1194.

    Article  Google Scholar 

  • Mousavi, S. M., Bahreininejad, A., Musa, S. N., & Yusof, F. (2017). modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network. Journal of Intelligent Manufacturing, 28, 191–206.

    Article  Google Scholar 

  • Murase, H., & Wadano, A. (1988). Photosynthetic algorithm for machine learning and TSP. IFAC Proceedings Volumes, 31(12), 19–24.

    Article  Google Scholar 

  • Nasir, M., Das, S., Maity, D., Sengupta, S., Halder, U., & Suganthan, P. N. (2012). A dynamic neighborhood learning based particle swarm optimizer for global numerical optimization. Information Sciences, 209, 16–36.

    Article  Google Scholar 

  • Nenavath, H., Jatoth, R. K., & Das, S. (2018). A synergy of the sine-cosine algorithm and particle swarm optimizer for improved global optimization and object tracking. Swarm and Evolutionary Computation, 43, 1–30.

    Article  Google Scholar 

  • Niu, B., & Li, L. (2008). A novel PSO-DE-based hybrid algorithm for global optimization. Lecture Notes in Computer Science (Vol. 5227, pp. 156–163).

  • Nwankwor, E., Nagar, A. K., & Reid, D. C. (2012). Hybrid differential evolution and particle swarm optimization for optimal well placement. Computational Geosciences, 17(2), 249–268.

    Article  Google Scholar 

  • Pant, M., Thangaraj, R., & Abraham, A. (2011). DE-PSO: a new hybrid meta-heuristic for solving global optimization problems. New Mathematics and Natural Computation, 7(3), 363–381.

    Article  Google Scholar 

  • Parouha, R. P. (2019). Nonconvex/nonsmooth economic load dispatch using modified time-varying particle swarm optimization. Computational Intelligence. https://doi.org/10.1111/coin.12210.

    Article  Google Scholar 

  • Parouha, R. P., & Das, K. N. (2015). An efficient hybrid technique for numerical optimization and applications. Computers & Industrial Engineering, 83, 193–216.

    Article  Google Scholar 

  • Parouha, R. P., & Das, K. N. (2016a). A robust memory based hybrid differential evolution for continuous optimization problem. Knowledge-Based Systems, 103, 118–131.

    Article  Google Scholar 

  • Parouha, R. P., & Das, K. N. (2016b). DPD: An intelligent parallel hybrid algorithm for economic load dispatch problems with various practical constraints. Expert Systems with Applications, 63, 295–309.

    Article  Google Scholar 

  • Patel, V. K., & Savsani, V. J. (2015). Heat transfers search a novel optimization algorithm. Information Sciences, 324, 217–246.

    Article  Google Scholar 

  • Pierezan, J., & Coelho, L. D. S. (2018). Coyote optimization algorithm: A new metaheuristic for global optimization problems. In 2018 IEEE congress on evolutionary computation (CEC) (pp. 1–8), IEEE.

  • Pinto, P., Runkler, T. A., & Sousa, J. M. (2005). Wasp swarm optimization of logistic systems. In B. Ribeiro, R. F. Albrecht, A. Dobnikar, D. W. Pearson, & N. C. Steele (Eds.), Adaptive and natural computing algorithms (pp. 264–267). Vienna: Springer.

    Chapter  Google Scholar 

  • Qin, A. K., Huang, V. L., & Suganthan, P. N. (2009). Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Transactions on Evolutionary Computation, 13(2), 398–417.

    Article  Google Scholar 

  • Qin, A. K., & Suganthan, P. N. (2005). Self-adaptive differential evolution algorithm for numerical optimization. In IEEE congress on evolutionary computation (Vol. 1782, pp. 1785–1791).

  • Qiu, X., Tan, K. C., & Xu, J.-X. (2017). Multiple exponential recombination for differential evolution. IEEE Transactions on Cybernetics, 47(4), 995–1006.

    Article  Google Scholar 

  • Qiu, X., Xu, J.-X., Xu, Y., & Tan, K. C. (2018). A new differential evolution algorithm for minimax optimization in robust design. IEEE Transactions on Cybernetics, 48(5), 1355–1368.

    Article  Google Scholar 

  • Rahnamayan, S., Tizhoosh, H., & Salama, M. (2008). Opposition-based differential evolution. IEEE Transactions on Evolutionary Computation, 12(1), 64–79.

    Article  Google Scholar 

  • Raju, M., Gupta, M. K., Bhanot, N., & Sharma, V. S. (2019). A hybrid PSO–BFO evolutionary algorithm for optimization of fused deposition modelling process parameters. Journal of Intelligent Manufacturing, 30, 2743–2758.

    Article  Google Scholar 

  • Rao, R. V., Savsani, V. J., & Vakharia, D. P. (2011). Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems. Computer-Aided Design, 43(3), 303–315.

    Article  Google Scholar 

  • Rashedi, E., Nezamabadi-pour, H., & Saryazdi, S. (2009). A gravitational search algorithm. Information Sciences, 179(13), 2232–2248.

    Article  Google Scholar 

  • Sahu, B. K., Pati, S., & Panda, S. (2014). Hybrid differential evolution particle swarm optimisation optimised fuzzy proportional–integral derivative controller for automatic generation control of interconnected power system. IET Generation, Transmission and Distribution, 8(11), 1789–1800.

    Article  Google Scholar 

  • Salehpour, M., Jamali, A., Bagheri, A., & Nariman-zadeh, N. (2017). A new adaptive differential evolution optimization algorithm based on fuzzy inference system. Engineering Science and Technology, 20(2), 587–597.

    Google Scholar 

  • Saremi, S., Mirjalili, S., & Lewis, A. (2017). Grasshopper optimisation algorithm: Theory and application. Advances in Engineering Software, 105, 30–47.

    Article  Google Scholar 

  • Shabani, A., Asgarian, B., Gharebaghi, S. A., Salido, M. A., & Giret, A. (2019). A new optimization algorithm based on search and rescue operations. Mathematical Problems in Engineering, 2019, 2482543.

    Article  Google Scholar 

  • Simon, D. (2008). Biogeography-based optimization. IEEE Transactions on Evolutionary Computation, 12(6), 702–713.

    Article  Google Scholar 

  • Simpson, A. R., Dandy, G. C., & Murphy, L. J. (1994). Genetic algorithms compared to other techniques for pipe optimization. Journal of Water Resources Planning and Management, 120(4), 423–443.

    Article  Google Scholar 

  • Storn, R., & Price, K. (1997). Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11, 341–359.

    Article  Google Scholar 

  • Sun, J., Fang, W., Wu, X., Palade, V., & Xu, W. (2012). Quantum behaved particle swarm optimization: Analysis of individual particle behavior and parameter selection. Evolutionary Computation, 20(3), 349–393.

    Article  Google Scholar 

  • Talbi, H., & Batouche, M. (2004). Hybrid particle swarm with differential evolution for multimodal image registration. In Proceedings of the IEEE international conference on industrial technology (Vol. 3, pp. 1567–1573).

  • Tanabe, R., & Fukunaga, A. (2013). Success-history based parameter adaptation for differential evolution. In 2013 IEEE Congress on evolutionary computation (pp. 71–78).

  • Tang, B., Xiang, K., & Pang, M. (2018). An integrated particle swarm optimization approach hybridizing a new self-adaptive particle swarm optimization with a modified differential evolution. Neural Computing and Applications, 32, 4849–4883.

    Article  Google Scholar 

  • Tang, B., Zhu, Z., & Luo, J. (2016). Hybridizing particle swarm optimization and differential evolution for the mobile robot global path planning. International Journal of Advanced Robotic Systems, 13(3), 1–17.

    Article  Google Scholar 

  • Tanweer, M. R., Suresh, S., & Sundararajan, N. (2016). Dynamic mentoring and self-regulation based particle swarm optimization algorithm for solving complex real-world optimization problems. Information Sciences, 326, 1–24.

    Article  Google Scholar 

  • Tatsumi, K., Ibuki, T., & Tanino, T. (2013). A chaotic particle swarm optimization exploiting a virtual quartic objective function based on the personal and global best solutions. Applied Mathematics and Computation, 219(17), 8991–9011.

    Article  Google Scholar 

  • Tian, M. N., & Gao, X. B. (2019). Differential evolution with neighborhood-based adaptive evolution mechanism for numerical optimization. Information Sciences, 478, 422–448.

    Article  Google Scholar 

  • Too, J., Abdullah, A. R., & Saad, N. M. (2019). Hybrid binary particle swarm optimization differential evolution-based feature selection for EMG signals classification. Axioms, 8(3), 79.

    Article  Google Scholar 

  • Vahdani, B., Tavakkoli-Moghaddam, R., Zandieh, M., & Razmi, J. (2012). Vehicle routing scheduling using an enhanced hybrid optimization approach. Journal of Intelligent Manufacturing, 23, 759–774.

    Article  Google Scholar 

  • Vijay Chakaravarthy, G., Marimuthu, S., & Sait, A. N. (2013). Performance evaluation of proposed differential evolution and particle swarm optimization algorithms for scheduling m-machine flow shops with lot streaming. Journal of Intelligent Manufacturing, 24, 175–191.

    Article  Google Scholar 

  • Wang, Y., & Cai, Z. (2009). A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems. Frontiers of Computer Science, 3, 38–52.

    Article  Google Scholar 

  • Wang, Y., Cai, Z. Z., & Zhang, Q. F. (2011). Differential evolution with composite trial vector generation strategies and control parameters. IEEE Transactions on Evolutionary Computation, 15(1), 55–66.

    Article  Google Scholar 

  • Wedde, H. F., Farooq, M., & Zhang, Y. (2004). BeeHive: An efficient fault-tolerant routing algorithm inspired by honey bee behavior. In M. Dorigo, M. Birattari, C. Blum, L. M. Gambardella, F. Mondada, & T. Stützle (Eds.), Ant colony optimization and swarm intelligence (Vol. 3172, pp. 83–94). Berlin: Springer.

    Chapter  Google Scholar 

  • Wolpert, D. H., & Macready, W. G. (1997). No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1), 67–82.

    Article  Google Scholar 

  • Xia, X., Gui, L., He, G., Xie, C., Wei, B., Xing, Y., et al. (2018). A hybrid optimizer based on firefly algorithm and particle swarm optimization algorithm. Journal of Computational Science, 26, 488–500.

    Article  Google Scholar 

  • Xiong, H., Qiu, B., & Liu, J. (2020). An improved multi-swarm particle swarm optimizer for optimizing the electric field distribution of multichannel transcranial magnetic stimulation. Artificial Intelligence in Medicine, 104, 101790.

    Article  Google Scholar 

  • Xu, L., Huang, C., Li, C., Wang, J., Liu, H., & Wang, X. (2020). Estimation of tool wear and optimization of cutting parameters based on novel ANFIS-PSO method toward intelligent machining. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-020-01559-0.

    Article  Google Scholar 

  • Xuewen, X., Ling, G., & Hui, Z. Z. (2018). A multi-swarm particle swarm optimization algorithm based on dynamical topology and purposeful. Applied Soft Computing, 67, 126–140.

    Article  Google Scholar 

  • Yan, B., Zhao, Z., Zhou, Y., Yuan, W., Li, J., Wu, J., et al. (2017). A particle swarm optimization algorithm with random learning mechanism and Levy flight for optimization of atomic clusters. Computer Physics Communication, 219, 79–86.

    Article  Google Scholar 

  • Yang, X.-S. (2009). Firefly algorithms for multimodal optimization. In O. Watanabe & T. Zeugmann (Eds.), Stochastic algorithms: Foundations and applications. Lecture notes in computer science (Vol. 5792, pp. 169–178). Berlin: Springer.

    Chapter  Google Scholar 

  • Yang, X.-S. (2010). A new metaheuristic bat-inspired algorithm. In J. González, D. Pelta, C. Cruz, G. Terrazas, & N. Krasnogor (Eds.), Nature inspired cooperative strategies for optimization (NICSO 2010), Studies in Computational Intelligence (Vol. 284, pp. 65–74). Berlin: Springer.

    Google Scholar 

  • Yang, X. S., & Deb, S. (2009). Cuckoo search via lévy flights. In IEEE world congress on nature & biologically inspired computing 2009 (NaBIC 2009) (pp. 210–214).

  • Yang, X., Li, J., & Peng, X. (2019). An improved differential evolution algorithm for learning high-fidelity quantum controls. Science Bulletin, 64(19), 1402–1408.

    Article  Google Scholar 

  • Yang, X., Yuan, J., & Mao, H. (2007). A modified particle swarm optimizer with dynamic adaptation. Applied Mathematics and Computation, 189(2), 1205–1213.

    Article  Google Scholar 

  • Yi, W., Gao, L., Pei, Z., Lu, J., & Chen, Y. (2020). ε Constrained differential evolution using halfspace partition for optimization problems. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-020-01565-2.

    Article  Google Scholar 

  • Yi, W., Zhou, Y., Gao, L., Li, X., & Zhang, C. (2018). Engineering design optimization using an improved local search based epsilon differential evolution algorithm. Journal of Intelligent Manufacturing, 29, 1559–1580.

    Article  Google Scholar 

  • Yu, H., Tan, Y., Zeng, J., Sun, C., & Jin, Y. (2018). Surrogate-assisted hierarchical particle swarm optimization. Information Sciences, 454–455, 59–72.

    Article  Google Scholar 

  • Yuan, S., Li, T., & Wang, B. (2020). A discrete differential evolution algorithm for flow shop group scheduling problem with sequence-dependent setup and transportation times. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-020-01580-3.

    Article  Google Scholar 

  • Zainal, N., Zain, A. M., Radzi, N. H. M., & Othman, M. R. (2016). Glowworm swarm optimization (GSO) for optimization of machining parameters. Journal of Intelligent Manufacturing, 27, 797–804.

    Article  Google Scholar 

  • Zar, J. H. (1999). Biostatistical analysis. Englewood Cliffs: Prentice Hall.

    Google Scholar 

  • Zhang, W., Ma, D., Wei, J.-J., & Liang, H.-F. (2014). A parameter selection strategy for particle swarm optimization based on particle positions. Expert Systems with Applications, 41(7), 3576–3584.

    Article  Google Scholar 

  • Zhang, J., & Sanderson, C. (2009). JADE: Adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation, 13(5), 945–958.

    Article  Google Scholar 

  • Zhang, W. J., & Xie, X. F. (2003). DEPSO: hybrid particle swarm with differential evolution operator. In Proceedings of the IEEE international conference on systems, man and cybernetics Washington DC, USA (pp. 3816–3821).

  • Zhao, X., Zhang, Z., Xie, Y., & Meng, J. (2020). Economic-environmental dispatch of microgrid based on improved quantum particle swarm optimization. Energy, 195, 117014.

    Article  Google Scholar 

  • Zheng, Y. J. (2015). Water wave optimization: a new nature-inspired metaheuristic. Computers & Operations Research, 55, 1–11.

    Article  Google Scholar 

  • Zheng, L. M., Zhang, S. X., Tang, K. S., & Zheng, S. Y. (2017). Differential evolution powered by collective information. Information Sciences, 399, 13–29.

    Article  Google Scholar 

  • Zhu, A., Xu, C., Li, Z., Wu, J., & Liu, Z. (2015). Hybridizing grey Wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC. Journal of Systems Engineering and Electronics, 26, 317–328.

    Article  Google Scholar 

Download references

Acknowledgements

Authors, heartfelt thanks to the Editor and the Reviewers for their thoughtful comments and constructive suggestions, as these comments and suggestions led us to an improvement of the work.

Author information

Authors and Affiliations

  1. Department of Mathematics, IGNTU, Amarkantak, M.P., India

    Raghav Prasad Parouha & Pooja Verma

Authors
  1. Raghav Prasad Parouha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pooja Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raghav Prasad Parouha.

Ethics declarations

Conflict of interest

The authors declared that they had no conflicts of interest with respect to their authorship or the publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Parouha, R.P., Verma, P. An innovative hybrid algorithm for bound-unconstrained optimization problems and applications. J Intell Manuf 33, 1273–1336 (2022). https://doi.org/10.1007/s10845-020-01691-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10845-020-01691-x

Keywords

Search

Navigation