Abstract
In this paper, Multi-Objective Harris Hawks Optimization (MOHHO) is proposed based on strengthened dominance relation (SRD) to solve multi-objective optimization problems. Specifically, MOHHO uses an additional population archive to store the best non-dominated solutions generated so far by the exploration process at the aim to maintain the elitism concept. Moreover, the leader’s solutions are selected from the external archive to guide the main population of Hawks to interesting search regions. Furthermore, the strengthened dominance relation is adopted to provide a good compromise between coverage and convergence of the obtained Pareto set. The proposed algorithm is validated via five bi-objective and seven three-objective test functions, and it is compared with three well-known multi-objective meta-heuristics. The experimental results show that MOHHO algorithm outperforms its competitors by providing better convergence behaviour with more diversified solutions.
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Afshari H, Hare W, Tesfamariam S (2019) Constrained multi-objective optimization algorithms: review and comparison with application in reinforced concrete structures. Appl Soft Comput 83:105631
Allou L, Zouache D, Amroun K, Got A (2022) A novel epsilon-dominance Harris Hawks optimizer for multi-objective optimization in engineering design problems. Neural Comput Appl 1–30
Bader J, Zitzler E (2011) Hype: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45–76
Beume N, Naujoks B, Emmerich M (2007) SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur J Oper Res 181(3):1653–1669
Brockhoff D, Wagner T, Trautmann H (2015) 2 indicator-based multiobjective search. Evol Comput 23(3):369–395
Brockhoff D, Zitzler E (2007) Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods. In: 2007 IEEE congress on evolutionary computation, pp. 2086–2093. IEEE
Cheng Y, Jin Y, Hu J (2009) Adaptive epsilon non-dominated sorting multi-objective evolutionary optimization and its application in shortest path problem. In: 2009 ICCAS-SICE, pp. 2545–2549. IEEE
Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279
Dabba A, Tari A, Zouache D (2020) Multiobjective artificial fish swarm algorithm for multiple sequence alignment. Inf Syst Oper Res 58(1):38–59
Deb K, Jain H (2013) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601
Deb K, Pratap A, Agarwal S, Meyarivan T (2002a) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197
Deb K, Thiele L, Laumanns M, Zitzler E (2002b) Scalable multi-objective optimization test problems. In: Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No. 02TH8600), vol 1, pp 825–830. IEEE
Deb K, Mohan M, Mishra S (2005) Evaluating the \(\varepsilon\)-domination based multi-objective evolutionary algorithm for a quick computation of pareto-optimal solutions. Evol Comput 13(4):501–525
Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18
Du P, Wang J, Hao Y, Niu T, Yang W (2020) A novel hybrid model based on multi-objective Harris Hawks optimization algorithm for daily pm2.5 and pm10 forecasting. Appl Soft Comput 96:106620
Falcón-Cardona JG, Coello CAC (2020) Indicator-based multi-objective evolutionary algorithms: a comprehensive survey. ACM Comput Surv 53(2):1–35
Gölcük İ, Ozsoydan FB (2021) Quantum particles-enhanced multiple Harris Hawks swarms for dynamic optimization problems. Expert Syst Appl 167:114202
Got A, Moussaoui A, Zouache D (2020) A guided population archive whale optimization algorithm for solving multiobjective optimization problems. Expert Syst Appl 141:112972
Got A, Zouache D, Moussaoui A (2022) Momrfo: multi-objective manta ray foraging optimizer for handling engineering design problems. Knowl-Based Syst 237:107880
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872
Houssein EH, Hosney ME, Oliva D, Mohamed WM, Hassaballah M (2020) A novel hybrid Harris Hawks optimization and support vector machines for drug design and discovery. Comput Chem Eng 133:106656
Jangir P, Buch H, Mirjalili S, Manoharan P (2021) Mompa: multi-objective marine predator algorithm for solving multi-objective optimization problems. Evolut Intell 1–27
Kahloul S, Zouache D, Brahmi B, Got A (2022) A multi-external archive-guided henry gas solubility optimization algorithm for solving multi-objective optimization problems. Eng Appl Artif Intell 109:104588
Laumanns M, Thiele L, Deb K, Zitzler E (2002) Combining convergence and diversity in evolutionary multiobjective optimization. Evol Comput 10(3):263–282
Li H, Zhang Q (2008) Multiobjective optimization problems with complicated pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 13(2):284–302
Li K, Deb K, Zhang Q, Kwong S (2014) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19(5):694–716
Liang J, Ban X, Yu K, Qu B, Qiao K, Yue C, Chen K, Tan KC (2022) A survey on evolutionary constrained multi-objective optimization. IEEE Trans Evolut Comput
Liu HL, Gu F, Zhang Q (2013) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18(3):450–455
Mirjalili S, Saremi S, Mirjalili SM, Coelho LDS (2016) Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst. Appl. 47:106–119
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191
Najafzadeh M (2015) Neuro-fuzzy GMDH systems based evolutionary algorithms to predict scour pile groups in clear water conditions. Ocean Eng 99:85–94
Najafzadeh M, Niazmardi S (2021) A novel multiple-kernel support vector regression algorithm for estimation of water quality parameters. Nat Resour Res 30(5):3761–3775
Najafzadeh M, Tafarojnoruz A (2016) Evaluation of neuro-fuzzy GMDH-based particle swarm optimization to predict longitudinal dispersion coefficient in rivers. Environ Earth Sci 75(2):1–12
Saini N, Saha S (2021) Multi-objective optimization techniques: a survey of the state-of-the-art and applications. Eur Phys J Spec Topics 230(10):2319–2335
Savsani V, Tawhid MA (2017) Non-dominated sorting moth flame optimization (NS-MFO) for multi-objective problems. Eng Appl Artif Intell 63:20–32
Sierra MR, Coello CAC (2004) A new multi-objective particle swarm optimizer with improved selection and diversity mechanisms. Technical Report of CINVESTAV-IPN
Sun Y, Yen GG, Yi Z (2018) IGD indicator-based evolutionary algorithm for many-objective optimization problems. IEEE Trans Evol Comput 23(2):173–187
Tian Y, Cheng R, Zhang X, Su Y, Jin Y (2018) A strengthened dominance relation considering convergence and diversity for evolutionary many-objective optimization. IEEE Trans Evol Comput 23(2):331–345
Wagner M, Neumann F (2013) A fast approximation-guided evolutionary multi-objective algorithm. In: Proceedings of the 15th annual conference on Genetic and evolutionary computation, pp 687–694
Wang S, Jia H, Liu Q, Zheng R (2021) An improved hybrid aquila optimizer and Harris Hawks optimization for global optimization. Math Biosci Eng 18:7076–7109
While L, Hingston P, Barone L, Huband S (2006) A faster algorithm for calculating hypervolume. IEEE Trans Evol Comput 10(1):29–38
Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731
Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257–271
Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195
Zitzler E, Laumanns M, Thiele L (2001) Spea2: improving the strength pareto evolutionary algorithm. TIK-report 103
Zouache D, Abdelaziz FB (2022) Guided manta ray foraging optimization using epsilon dominance for multi-objective optimization in engineering design. Expert Syst Appl 189:116126
Zouache D, Moussaoui A, Abdelaziz FB (2018) A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem. Eur J Oper Res 264(1):74–88
Zouache D, Arby YO, Nouioua F, Abdelaziz FB (2019) Multi-objective chicken swarm optimization: a novel algorithm for solving multi-objective optimization problems. Comput Ind Eng 129:377–391
Zouache D, Abdelaziz FB, Lefkir M, Chalabi NEH (2021) Guided moth-flame optimiser for multi-objective optimization problems. Ann Oper Res 296(1):877–899
Zouache D, Ben Abdelaziz F (2022) MGDE: a many-objective guided differential evolution with strengthened dominance relation and bi-goal evolution. Ann Oper Res 1–38
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Zouache, D., Got, A. & Drias, H. An external archive guided Harris Hawks optimization using strengthened dominance relation for multi-objective optimization problems. Artif Intell Rev 56, 2607–2638 (2023). https://doi.org/10.1007/s10462-022-10235-z
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DOI: https://doi.org/10.1007/s10462-022-10235-z