Abstract
In this paper, a novel dynamic multi-objective optimization algorithm is introduced. The proposed method is composed of three parts: change detection, response to change, and optimization process. The first step is to use Sentry solutions to detect the environmental change and advises the algorithm when a change occurs. Then, to increase the diversity of solutions, the worst solutions should be elected and removed from population and re-initialized with new solutions. The main idea is to use Borda count method which is an optimal rank aggregation technique that ranks the solutions in order of preference and nominates the worst solutions that should be removed. The last step is optimization process which is done by multi-objective Cat swarm optimization (CSO) in this paper. CSO utilizes the population that has been improved from the previous step to estimate the best solutions and converges to optimal Pareto front. The performance of the proposed algorithm is tested on dynamic multi-objective benchmarks, and the results are compared with the ones achieved by previous algorithms. The simulation results indicate that the proposed algorithm can effectively track the time-varying optimal Pareto front and achieves competitive results in comparison with traditional approaches.
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References
Avdagic Z, Konijicija K, Omanovic S (2009) Evolutionary approach to solving nonstationary dynamic multi-objective problems. Found Comput Intell 3:267–289
Camara M, Ortega J, Toto F (2009) Single front genetic algorithm for parallel multi-objective optimization in dynamic environments. Neurocomputing 72:3570–3579
Camara M, Ortega J, Toto J (2007) Parallel processing for multi-objective optimization in dynamic environments. IEEE international parallel and distributed processing symposium
Chu S, Tsai P, Pan J (2006) Cat swarm optimization. Lecture note in artificial intelligence, 4099. Springer, Berlin, pp 854–858
Coello CA, Lamont GB, Veldhuisen DA (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, New York
Dang Y, Wang C (2008) An evolutionary algorithm for dynamic multi-objective optimization. Appl Math Comput 25:6–18
Deb K (2002) Multiobjective optimization using evolutionary algorithms. Wiley, Oxford
Deb K, Rao N, Karthik S (2007). Dynamic mylti-objective optimization and decision making using modified NSGA2: a case study on hydro thermal power scheduling. LNCS, pp 803–817
Engelbrecht A (2010) Heterogeneous particle swarm optimization. In: Proceeding of the 7th international conference on swarm intelligence, pp 191–202
Farina M (2001) A minimal cost hybrid strategy for pareto optimal front approximation. Evol Optim 3(1):41–52
Farina M, Deb K, Amato P (2004) Dynamic multiobjective optimization problems: test cases, approximations, and applications. IEEE Trans Evolut Comput 8:425–442
Goh C, Tan K (2007) An investigation on noisy environments in evolutionary multiobjective optimization. IEEE Trans Evolut Comput 11:354–381
Goh C, Tan K (2009) A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization. IEEE Trans Evolut Comput 13:103–127
Hatzakis IW (2006) Dynamic multi-objective optimization with evolutionary algorithms: a forward-looking approach. In: Proceedings of the 8th annual conference on genetic and evolutionary computation, Washington, pp 1201–1208
Helbig M (2012) Solving dynamic multi-objective optimisation problems using vector evaluated particle swarm optimisation. University of Pretoria, Pretoria
Helbig M, Engelbrecht A (2011) Archive management for dynamic multi-objective optimisation problems using vector evaluated particle swarm optimization. In: IEEE congress of evolutionary computation (CEC), New Orleans, pp 2047–2054
Helbig M, Engelbrecht A (2012) Analyses of guide update approaches for vector evaluated particle swarm optimisation on dynamic multi-objective optimisation problems. WCCI 2012 IEEE world congress on computational intelligence, Australia
Helbig M, Engelbrecht A (2013) Dynamic multi-objective optimization using PSO. In: Alba E (ed) Methaheuristic for dynamic optimization. Springer, Berlin, pp 147–188
Helbig M, Engelbrecht A (2013) Performance measures for dynamic multi-objective optimisation algorithms. Inform Sci 250:61–81
Helbig M, Engelbrecht A (2014) Heterogeneous dynamic vector evaluated particle swarm optimisation for dynamic multi-objective optimisation. IEEE congress on evolutionary computation (CEC), China
Helbig M, Engelbrecht A (2015) Using headless chicken crossover for local guide selection when solving dynamic multi-objective optimization. In: Proceedings of the 7th world congress on nature and biologically inspired computing (NaBIC2015) in Pietermaritzburg, South Africa, pp 381–392
Helbig M, Deb K, Engelbrecht A (2016) Key challenges and future directions of dynamic multi-objective optimization. IEEE world congress on computational intelligence, Canada
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948
Koo W, Goh C, Tan K (2010) A predictive gradient strategy for multiobjective evolutionary algorithms in a fast changing environment. Memetic Comp:87–110
Li X, Branke J, Blackwel T (2006) Particle swarm with speciation and adaptation in a dynamic environment. In: Proceedings of 8th conference on genetic and evolutionary computation (GECCO 2006), pp 51–58
Liang J, Qin A, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE trans evol comput 10(3):281–295
Liu M, Liu Y (2016) A dynamic evolutionary multi-objective optimization algorithm based on decomposition and adaptive diversity introduction. 12th international conference on natural computation, fuzzy systems and knowledge discovery (ICNC-FSKD)
Liu R, Chen Y, Ma W, Mu C, Jiao L (2013) A novel cooperative coevolutionary dynamic multi-objective optimization algorithm using a new predictive model. Soft Comput 18(10):1913–1929
Liu R, Fan J, Jiao L (2015) Integration of improved predictive model and adaptive differential evolution based dynamic multi-objective evolutionary optimization algorithm. Appl Intell 43:192–207
Liu R, Nui X, Fan J, Mu C, Jiao L (2014) An orthogonal predictive model-based dynamic multi-objective optimization algorithm. Soft Comput 19:3083–3107
Mantysaari J, Hamalainen R (2001) A dynamic interval goal programming approach to the regulation of a lake-river system. J Multi-Criteria Decis Anal 10(2):75–86
Mantysaari J, Hamalainen R (2002) Dynamic multi-objective heating optimization. Eur J Oper Res 142:1–15
Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler, maybe better. IEEE Trans Evolut Comput 8:204–210
Muruganantham A, Zhao Y, Gee S, Qiu X (2013) Dynamic multiobjective optimization using evolutionary algorithm with Kalman Filter. 17th Asia Pacific symposium on intelligent and evolutionary systems, IES2013
Qiao J, Zhang W (2016) Dynamic multi-objective optimization control for wastewater treatment process. J Neural Comput Appl. doi:10.1007/s00521-016-2642-8
Saari D (1985) The optimal ranking method is the Borda Count. International institute for applied systems analysis, IIASA collaborative paper
Shang R, Jiao L, Ren Y, Li L, Wang L (2014) Quantum immune clonal coevolutionary algorithm for dynamic multiobjective optimization. Soft Comput 18:743–756
Tizhoosh H (2005) Opposition-based learning: a new scheme for machine intelligence. CIMCA/IAWTIC
Wu Y, Jin Y, Liu X (2014) A directed search strategy for evolutionary dynamic multiobjective optimization. Soft Comput 19(11):3221–3235
Xu B, Zhang Y, Gong D, Rong M (2016) Cooperative co-evolutionary algorithm for dynamic multi-objective optimization based on environmental variable grouping. 7th international conference, ICSI 2016, Bali, pp 564–570
Yang X, Yuan J, Mao H (2007) A modified particle swarm optimizer with dynamic adaptation. Appl Math Comput 189:1205–1213
Zheng Y, Ling H, Xue J, Chen S (2014) Population classification in fire evacuation: a multi-objective particle swarm optimization approach. IEEE Trans Evol Comput 18(1):70–81
Zheng Y, Song Q, Chen S (2013) Multi-objective fireworks optimization for variable-rate fertilization in oil crop production. Appl Soft Comput 13(11):4253–4263
Zhou X, Liu Y, Li B, Sun G (2015) Multi-objective biogeography based optimization algorithm with decomposition for community detection in dynamic networks. Phys A Stat Mech Appl 436:430–442
Zhou A, Zhang Q (2014) A population prediction strategy for evolutionary dynamic multiobjective optimization. IEEE Trans Cybern 44(1):40–53
Zhou A, Zhang Q, Sendhoff B, Tsang E (2007) Prediction-based population re-initialization for evolutionary dynamic multi-objective optimization. The 4th international conference on evolutionary multi-criterion optimization. Springer, Berlin
Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Swiss Federal Institute of Technology (ETH), Zurich
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Orouskhani, M., Teshnehlab, M. & Nekoui, M.A. Evolutionary dynamic multi-objective optimization algorithm based on Borda count method. Int. J. Mach. Learn. & Cyber. 10, 1931–1959 (2019). https://doi.org/10.1007/s13042-017-0695-3
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DOI: https://doi.org/10.1007/s13042-017-0695-3