Abstract
Multiobjective evolutionary algorithm based on decomposition has made a great contribution to the field of evolutionary multiobjective optimization problem. The decomposition-based algorithms construct a number of scalar optimization subproblems by using a set of weight vectors, and optimize these subproblems simultaneously to approximate the Pareto front (PF). The weight vectors have a massive influence on the performance of the decomposition-based algorithm, especially for the multiobjective optimization problems (MOP) with a complex PF. To solve this, we propose a parameterless decomposition scheme to adjust the weight vectors automatically. Experiment results indicate that the proposed algorithm can obtain better uniformity solutions for the MOP with complex PF.
| Original language | English |
|---|---|
| Title of host publication | Proceedings - 2018 10th International Conference on Advanced Computational Intelligence, ICACI 2018 |
| Publisher | IEEE |
| Pages | 842-845 |
| Number of pages | 4 |
| ISBN (Electronic) | 9781538643624 |
| DOIs | |
| Publication status | Published - 8 Jun 2018 |
| Event | 10th International Conference on Advanced Computational Intelligence, ICACI 2018 - Xiamen, Fujian, China Duration: 29 Mar 2018 → 31 Mar 2018 |
Publication series
| Name | Proceedings - 2018 10th International Conference on Advanced Computational Intelligence, ICACI 2018 |
|---|
Conference
| Conference | 10th International Conference on Advanced Computational Intelligence, ICACI 2018 |
|---|---|
| Country/Territory | China |
| City | Xiamen, Fujian |
| Period | 29/03/18 → 31/03/18 |
Scopus Subject Areas
- Artificial Intelligence
- Computer Networks and Communications
- Modelling and Simulation
- Control and Optimization
User-Defined Keywords
- Evolutionary computation
- Multi-objective optimization
- Parameterless decomposition
- Uniformity solution
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Proceedings - 2018 10th International Conference on Advanced Computational Intelligence, ICACI 2018. IEEE, 2018. p. 842-845 (Proceedings - 2018 10th International Conference on Advanced Computational Intelligence, ICACI 2018).
Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review
TY - GEN
T1 - A parameterless decomposition-based evolutionary multi-objective algorithm
AU - Gu, Fangqing
AU - CHEUNG, Yiu Ming
AU - Liu, Hai Lin
AU - Lin, Zixian
N1 - Funding Information: • The number of subpopulation is set at K = 10 for MaOP1, and K = 20 for MaOP2-MaOP7 in MOEA/D-M2M. B. Experimental Results and Analysis We present the results of all compared algorithms. Table I summarizes the value of AHV-metric of the final solutions obtained by the compared algorithms. From this table, we can see that the proposed algorithm performs the best, implying that the proposed algorithm can maintain better distribution on the problems with the degraded PF. A plausible reason that the proposed algorithm outperforms NSGA-III and MOEA/D-M2M is as follows: In the proposed algorithm, the weight vectors are calculated online according to the solution and its neighboring weight vector. The weight vector gets close to its corresponding solution to avoid many subproblems obtaining the same Pareto optimal solution. Also, the weight vectors are far away from each other, thus making the proposed algorithm achieve better uniformity of solutions. Since the test instances are degraded, i.e. the true PFs are located in a reduced objective space, this means that almost all of subproblems obtained the Pareto solutions on the boundary in NSGA-III and MOEA/D-M2M with uniform reference points and weight vectors. In those degraded MOPs optimization, the weight adjustment lags behind the population evolution in MOEA/D-AWA. It may reduce the performance of the algorithm. IV. CONCLUSION In this paper, we have proposed a parameterless decomposition-based EMO algorithm for solving MOPs with the complex PF, in which the weight vectors are updated according to the solution and its neighbors online, rather than predefined in advance. We have conducted the proposed algorithm on seven test problems. Empirical results have demonstrated the effectiveness of the proposed algorithm for solving MOPs with the complex PF in comparison with the existing counterparts. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China under Grants 61672444, 61272366 and 61673121, in part by the Natural Science Foundation of Guangdong Province under Grant 2017A030310467, and in part by the Projects of Science and Technology of Guangzhou under Grant 201508010008, and the SZSTI Grant: JCYJ20160531194006833. This work was also supported by the Faculty Research Grant of Hong Kong Baptist University (HKBU) under Project FRG2/16-17/051. TABLE I. The Minimum(Best) and Mean of AHV-metric Values Obtained by The Compared Algorithms AHV-metric Our Algorithm NSGA-III MOEA/D-AWA MOEA/D-M2M Instance best mean best mean best mean best mean MaOP1 0.802461 0.773125 0.66525 0.661352 0.489734 0.403754 0.743976 0.690142 MaOP2 0.965834 0.935647 0.879183 0.82233 0.777752 0.643808 0.258203 0.248125 MaOP3 8.987652 8.634582 7.847038 7.710055 7.188816 6.866672 1.018329 0.887693 MaOP4 0.402389 0.365814 0.255330 0.245111 0.195129 0.148368 0.313981 0.292559 MaOP5 0.985647 0.974652 0.966614 0.966306 0.931094 0.92623 0.944085 0.940865 MaOP6 0.762145 0.745321 0.650539 0.645879 0.573799 0.540439 0.684177 0.664930 MaOP7 0.367841 0.356985 0.270925 0.261672 0.211224 0.167972 0.310110 0.299639 REFERENCES [1] H.-L. Liu, Y. Wang, and Y.-M. Cheung, “A multi-objective evolutionary algorithm using min-max strategy and sphere coordinate transforma-tion,” Intelligent Automation & Soft Computing, vol. 15, no. 3, pp. 361– 384, 2009. [2] Y.-M. Cheung, F. Gu, and H.-L. Liu, “Objective extraction for many-objective optimization problems: Algorithm and test problems,” IEEE Transactions on Evolutionary Computation, vol. 20, no. 5, pp. 755–772, 2016. [3] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002. [4] Z. Eckart, L. Marco, and T. Lothar, “SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization,” in Proc. Evolutionary Methods for Design Optimization and Control with Appli-cations to Industrial Problems, 2001, pp. 95–100. [5] J. Bader and E. Zitzler, “HypE: An algorithm for fast hypervolume-based many-objective optimization,” Evolutionary Computation, vol. 19, no. 1, pp. 45–76, 2011. [6] B. Nicola, B. Naujoks, and M. Emmerich, “SMS-EMOA: Multiobjec-tive selection based on dominated hypervolume,” European Journal of Operational Research, vol. 181, no. 3, pp. 1653–1669, 2007. [7] Q. Zhang and H. Li, “MOEA/D: A multiobjective evolutionary algorithm based on decomposition,” IEEE Transactions on Evolutionary Compu-tation, vol. 11, no. 6, pp. 712–731, 2007. [8] H.-L. Liu, F. Gu, and Q. Zhang, “Decomposition of a multiobjective optimization problem into a number of simple multiobjective subprob-lems,” IEEE Transactions on Evolutionary Computation, vol. 18, no. 3, pp. 450–455, 2014. [9] H. Ishibuchi, N. Akedo, and Y. Nojima, “Behavior of multi-objective evolutionary algorithms on many-objective knapsack problems,” IEEE Transactions on Evolutionary Computation, vol. 19, no. 2, pp. 264–283, 2014. [10] O. Schütze, A. Lara, and C. A. C. Coello, “On the influence of the number of objectives on the hardness of a multiobjective optimization problem,” IEEE Transactions on Evolutionary Computation, vol. 15, no. 4, pp. 444–455, 2011. [11] K. Deb and H. Jain, “An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints,” IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, pp. 577–601, 2014. [12] H. Jain and K. Deb, “An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach,” IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, pp. 602–622, 2014. [13] K. Li, K. Deb, Q. Zhang, and S. Kwong, “An evolutionary many-objective optimization algorithm based on dominance and decomposi- tion,” IEEE Transactions on Evolutionary Computation, vol. 19, no. 5, pp. 694–716, 2015. [14] H. Ishibuchi, H. Masuda, and Y. Nojima, “Pareto fronts of many-objective degenerate test problems,” IEEE Transactions on Evolutionary Computation, 2015. [15] H. Ishibuchi, Y. Setoguchi, H. Masuda, and Y. Nojima, “Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes,” IEEE Transactions on Evolutionary Computation, Doi: 10.1109/TEVC.2016.2587749. [16] Y. Qi, X. Ma, F. Liu, L. Jiao, J. Sun, and J. Wu, “MOEA/D with adaptive weight adjustment,” Evolutionary Computation, vol. 22, no. 2, pp. 231– 264, 2014. [17] F. Gu, H.-L. Liu, and K. C. Tan, “A multiobjective evolutionary algorithm using dynamic weight design method,” International Journal of Innovative Computing Information and Control, vol. 8, no. 5B, pp. 3677–3688, 2012. [18] F. Gu and Y.-M. Cheung, “Self-organizing map-based weight design for decomposition-based many-objective evolutionary algo-rithm,” IEEE Transactions on Evolutionary Computation, DOI: 10.1109/TEVC.2017.2695579. [19] H. Li and D. Landa-Silva, “An adaptive evolutionary multi-objective approach based on simulated annealing,” Evolutionary Computation, vol. 19, no. 4, pp. 561–595, 2011. [20] H. L. Liu, L. Chen, Q. Zhang, and K. Deb, “Adaptively al-locating search effort in challenging many-objective optimization problems,” IEEE Transactions on Evolutionary Computation, DOI: 10.1109/TEVC.2017.2725902. [21] S. Jiang, Z. Cai, J. Zhang, and Y.-S. Ong, “Multiobjective optimization by decomposition with pareto-adaptive weight vectors,” in Proc. 2011 Seventh International Conference on Natural Computation, 2011, pp. 1260–1264. [22] K. Deb, Multiobjective Optimization using Evolutionary Algorithms. New York: Wiley, 2001. [23] Y. Qi, X. Ma, F. Liu, L. Jiao, J. Sun, and J. Wu, “MOEA/D with adaptive weight adjustment,” Evolutionary Computation, vol. 22, no. 2, pp. 231– 264, 2014. [24] M. Emmerich, N. Beume, and B. Naujoks, “An EMO algorithm using the hypervolume measure as selection criterion,” in Proc. Evolutionary multi-criterion optimization, 2005, pp. 62–76. Funding Information: ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China under Grants 61672444, 61272366 and 61673121, in part by the Natural Science Foundation of Guangdong Province under Grant 2017A030310467, and in part by the Projects of Science and Technology of Guangzhou under Grant 201508010008, and the SZSTI Grant: JCYJ20160531194006833. This work was also supported by the Faculty Research Grant of Hong Kong Baptist University (HKBU) under Project FRG2/16-17/051.
PY - 2018/6/8
Y1 - 2018/6/8
N2 - Multiobjective evolutionary algorithm based on decomposition has made a great contribution to the field of evolutionary multiobjective optimization problem. The decomposition-based algorithms construct a number of scalar optimization subproblems by using a set of weight vectors, and optimize these subproblems simultaneously to approximate the Pareto front (PF). The weight vectors have a massive influence on the performance of the decomposition-based algorithm, especially for the multiobjective optimization problems (MOP) with a complex PF. To solve this, we propose a parameterless decomposition scheme to adjust the weight vectors automatically. Experiment results indicate that the proposed algorithm can obtain better uniformity solutions for the MOP with complex PF.
AB - Multiobjective evolutionary algorithm based on decomposition has made a great contribution to the field of evolutionary multiobjective optimization problem. The decomposition-based algorithms construct a number of scalar optimization subproblems by using a set of weight vectors, and optimize these subproblems simultaneously to approximate the Pareto front (PF). The weight vectors have a massive influence on the performance of the decomposition-based algorithm, especially for the multiobjective optimization problems (MOP) with a complex PF. To solve this, we propose a parameterless decomposition scheme to adjust the weight vectors automatically. Experiment results indicate that the proposed algorithm can obtain better uniformity solutions for the MOP with complex PF.
KW - Evolutionary computation
KW - Multi-objective optimization
KW - Parameterless decomposition
KW - Uniformity solution
UR - http://www.scopus.com/inward/record.url?scp=85049773635&partnerID=8YFLogxK
U2 - 10.1109/ICACI.2018.8377572
DO - 10.1109/ICACI.2018.8377572
M3 - Conference proceeding
AN - SCOPUS:85049773635
T3 - Proceedings - 2018 10th International Conference on Advanced Computational Intelligence, ICACI 2018
SP - 842
EP - 845
BT - Proceedings - 2018 10th International Conference on Advanced Computational Intelligence, ICACI 2018
PB - IEEE
T2 - 10th International Conference on Advanced Computational Intelligence, ICACI 2018
Y2 - 29 March 2018 through 31 March 2018
ER -