Skip to main content
SpringerLink
Log in

A dynamic resource allocation strategy for collaborative constrained multi-objective optimization algorithm

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Infeasible solutions are helpful for finding the feasible regions, but how many feasible and infeasible solutions should be invested to achieve the optimal search efficiency remains to be further studied. Combined with the recently proposed collaborative constrained multi-objective framework, the contributions of the helper population and original population in different types of CMOPs are discussed. It is unreasonable to assign equal resources to these two populations in different CMOPs and different searching stages. This paper aims to investigate resource allocation in a constraint environment to efficiently utilize the limited resources and obtain a better performance. Therefore, the concept of return on investment (ROI) is first introduced to measure the contributions of two populations, and then guide the population size allocation (APS). To prevent the ROI from continuously declining as the population size decreases, an evolutionary resource allocation strategy (AER) is proposed to adjust their evolutionary state according to the cooperative relationship, and to further increase their ROI and again compete for population size, to maximize the evolutionary efficiency of the two populations in competition and cooperation. The proposed CCMODRA is compared with seven popular algorithms that cover three types of CMOEAs and test them on three benchmarks that cover four types of CMOPs. The comprehensive performance of CCMODRA is better than the other seven CMOEAs on 71% of the 3-objective CDTLZs, 57% of the 5-objective CDTLZs and 46% of the MWs. The effectiveness of the APS and AER strategies are verified on generating contribution solutions and DOC test problems. In addition, the total profit obtained by CCMODRA in the knapsack problem with capacity constraints is improved by 0.2% to 216% compared with the other seven algorithms.

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

Similar content being viewed by others

Data Availability

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Li Y, Lin J, Wang Z (2022) Multi-skill resource constrained project scheduling using a multi-objective discrete jaya algorithm. Appl Intell 52(5):5718–5738. https://doi.org/10.1007/s10489-021-02608-8

    Article  Google Scholar 

  2. Li X, An Q, Zhang J, Xu F, Tang R, Dong Z, Zhang X, Lai J, Mao X (2021) A novel two-stage constraints handling framework for real-world multi-constrained multi-objective optimization problem based on evolutionary algorithm. Appl Intell 51(11):8212–8229

    Article  Google Scholar 

  3. Pan X, Wang L, Qiu Q, Qiu F, Zhang G (2022) Many-objective optimization for large-scale evs charging and discharging schedules considering travel convenience. Appl Intell 52(3):2599–2620. https://doi.org/10.1007/s10489-021-02494-0

    Article  Google Scholar 

  4. Tirkolaee EB, Goli A, Hematian M, Sangaiah AK, Han T (2019) Multi-objective multi-mode resource constrained project scheduling problem using pareto-based algorithms. Computing 101(6):547–570

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhao H, Chen ZG, Zhan ZH, Kwong S, Zhang J (2021) Multiple populations co-evolutionary particle swarm optimization for multi-objective cardinality constrained portfolio optimization problem. Neurocomputing 430:58–70

    Article  Google Scholar 

  6. Li K, Wang R, Zhang T, Ishibuchi H (2018) Evolutionary many-objective optimization: a comparative study of the state-of-the-art. IEEE Access 6:26194–26214. https://doi.org/10.1109/ACCESS.2018.2832181

    Article  Google Scholar 

  7. Tian Y, Si L, Zhang X, Cheng R, He C, Tan K, Jin Y (2021) Evolutionary large-scale multi-objective optimization: a survey. ACM Comput Surv 1:1–34

    Google Scholar 

  8. Wang Y, Li JP, Xue X, Bc Wang (2020) Utilizing the correlation between constraints and objective function for constrained evolutionary optimization. IEEE Trans Evol Comput 24(1):29–43. https://doi.org/10.1109/TEVC.2019.2904900

    Article  Google Scholar 

  9. Coello CAC (2019) Constraint-handling techniques used with evolutionary algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO 2019, Prague, Czech Republic, July 13-17, 2019, ACM. https://doi.org/10.1145/3319619.3323366 , pp 485–506

  10. Jiao R, Zeng S, Li C, Jiang Y (2018) Dynamic constrained multi-objective evolutionary algorithms with a novel selection strategy for constrained optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO 2018, Kyoto, Japan, July 15-19, 2018, ACM. https://doi.org/10.1145/3205651.3205653, pp 213–214

  11. Li K, Chen R, Fu G, Yao X (2019) Two-archive evolutionary algorithm for constrained multiobjective optimization. IEEE Trans Evol Comput 23(2):303–315. https://doi.org/10.1109/TEVC.2018.2855411

    Article  Google Scholar 

  12. Ming M, Trivedi A, Wang R, Srinivasan D, Zhang T (2021) A dual-population-based evolutionary algorithm for constrained multiobjective optimization. IEEE Trans Evol Comput 25 (4):739–753. https://doi.org/10.1109/TEVC.2021.3066301

    Article  Google Scholar 

  13. Tian Y, Zhang T, Xiao J, Zhang X, Jin Y (2021) A coevolutionary framework for constrained multiobjective optimization problems. IEEE Trans Evol Comput 25(1):102–116. https://doi.org/10.1109/TEVC.2020.3004012

    Article  Google Scholar 

  14. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6(2):182–197. https://doi.org/10.1109/4235.996017

    Article  Google Scholar 

  15. Cheng R, Jin Y, Olhofer M, Sendhoff B (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20 (5):773–791. https://doi.org/10.1109/TEVC.2016.2519378

    Article  Google Scholar 

  16. Jan MA, Tairan N, Khanum RA (2013) Threshold based dynamic and adaptive penalty functions for constrained multiobjective optimization. In: 2013 1st International conference on artificial intelligence, modelling and simulation. https://doi.org/10.1109/AIMS.2013.16, pp 49–54

  17. Jiao R, Zeng S, Li C, Yang S, Ong YS (2021) Handling constrained many-objective optimization problems via problem transformation. IEEE Trans Cybern 51(10):4834–4847. https://doi.org/10.1109/TCYB.2020.3031642

    Article  Google Scholar 

  18. Fan Z, Fang Y, Li W, Cai X, Wei C, Goodman E (2018) Moea/d with angle-based constrained dominance principle for constrained multi-objective optimization problems. Applied Soft Computing, p 74. https://doi.org/10.1016/j.asoc.2018.10.027

  19. Ying WQ, He WP, Huang YX, Li DT, Wu Y (2016) An adaptive stochastic ranking mechanism in moea/d for constrained multi-objective optimization. In: 2016 International Conference on Information System and Artificial Intelligence (ISAI). https://doi.org/10.1109/ISAI.2016.0115, pp 514–518

  20. Ning W, Guo B, Yan Y, Wu X, Wu J, Zhao D (2017) Constrained multi-objective optimization using constrained non-dominated sorting combined with an improved hybrid multi-objective evolutionary algorithm. Eng Optim 49(10):1–20. https://doi.org/10.1080/0305215X.2016.1271661

    Article  MathSciNet  Google Scholar 

  21. Strauch M, Cord AF, Patzold C, Lautenbach S, Kaim A, Schweitzer C, Seppelt R, Volk M (2019) Constraints in multi-objective optimization of land use allocation repair or penalize? Environ Model Softw 118:241–251

    Article  Google Scholar 

  22. Samanipour F, Jelovica J (2020) Adaptive repair method for constraint handling in multi-objective genetic algorithm based on relationship between constraints and variables. Appl Soft Comput 90:106143. https://doi.org/10.1016/j.asoc.2020.106143

    Article  Google Scholar 

  23. Fan Z, Li W, Cai X, Li H, Wei C, Zhang Q, Deb K, Goodman ED (2019) Push and pull search for solving constrained multi-objective optimization problems. Swarm Evol Comput 44:665–679. https://doi.org/10.1016/j.swevo.2018.08.017

    Article  Google Scholar 

  24. Liu ZZ, Wang Y (2019) Handling constrained multiobjective optimization problems with constraints in both the decision and objective spaces. IEEE Trans Evol Comput 23(5):870–884. https://doi.org/10.1109/TEVC.2019.2894743

    Article  Google Scholar 

  25. Vodopija A, Oyama A, Filipic B (2019) Ensemble-based constraint handling in multiobjective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO 2019, Prague, Czech Republic, July 13-17, 2019, ACM. https://doi.org/10.1145/3319619.3326909, pp 2072–2075

  26. Rahi KH, Singh HK, Ray T (2019) Investigating the use of sequencing and infeasibility driven strategies for constrained optimization. In: 2019 IEEE Congress on Evolutionary Computation (CEC), pp 1642–1649. https://doi.org/10.1109/CEC.2019.8790239

  27. Zhou A, Zhang Q (2016) Are all the subproblems equally important? resource allocation in decomposition-based multiobjective evolutionary algorithms. IEEE Trans Evolutionary Computation 20(1):52–64

    Article  Google Scholar 

  28. Lin Q, Jin G, Ma Y, Wong K, Coello CAC, Li J, Chen J, Zhang J (2018) A diversity-enhanced resource allocation strategy for decomposition-based multiobjective evolutionary algorithm. IEEE Trans Cybernetics 48(8):2388–2401

    Article  Google Scholar 

  29. Wang L, Pan X, Shen X, Zhao P, Qiu Q (2021) Balancing convergence and diversity in resource allocation strategy for decomposition-based multi-objective evolutionary algorithm. Appl Soft Comput 100:106968. https://doi.org/10.1016/j.asoc.2020.106968

    Article  Google Scholar 

  30. Cai X, Li Y, Fan Z, Zhang Q (2015) An external archive guided multiobjective evolutionary algorithm based on decomposition for combinatorial optimization. IEEE Trans Evolutionary Computation 19 (4):508–523

    Article  Google Scholar 

  31. Zhang N, Huang Y, Cai X (2015) A two-phase external archive guided multiobjective evolutionary algorithm for the software next release problem. In: Bio-Inspired Computing - Theories and Applications - 10th International Conference, BIC-TA 2015, Hefei, China, September 25-28, 2015, Proceedings, pp 664–675

  32. Jain H, Deb K (2014) An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: Handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput 18(4):602–622. https://doi.org/10.1109/TEVC.2013.2281534

    Article  Google Scholar 

  33. Ma Z, Wang Y (2019) Evolutionary constrained multiobjective optimization: Test suite construction and performance comparisons. IEEE Trans Evol Comput 23(6):972–986. https://doi.org/10.1109/TEVC.2019.2896967

    Article  MathSciNet  Google Scholar 

  34. 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

    Article  Google Scholar 

Download references

Funding

This work was supported in part by Natural Science Foundation of Zhejiang Province (LQ20F020014), in part by the Key projects of Zhejiang Joint Fund (LZJWZ22E090001), in part by Key Projects of Science and Technology Development Plan of Zhejiang Province (2018C01080).

Author information

Authors and Affiliations

  1. Zhejiang University of Finance and Economics, School of Information Management and Artificial Intelligence, Hangzhou, 310018, China

    Xiaotian Pan

  2. College of Computer Science and Technology, College of Software, Zhejiang University of Technology, Hangzhou, 310023, China

    Liping Wang & Menghui Zhang

  3. Zhejiang Lab, Hangzhou, 310023, China

    Qicang Qiu

Authors
  1. Xiaotian Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liping Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Menghui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qicang Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Xiaotian Pan: Methodology, Writing, Experiments. Liping Wang: Supervision. Menghui Zhang: Experiments. Qicang Qiu: Data curation, Editing.

Corresponding author

Correspondence to Liping Wang.

Ethics declarations

Conflict of Interests

The authors declare that they have no conflict of interest.

Additional information

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed Consent

All authors agreed with the content and gave explicit consent to submit and also obtained consent from the responsible authorities at the institute.

Publisher’s note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pan, X., Wang, L., Zhang, M. et al. A dynamic resource allocation strategy for collaborative constrained multi-objective optimization algorithm. Appl Intell 53, 10176–10201 (2023). https://doi.org/10.1007/s10489-022-03820-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-022-03820-w

Keywords

Search

Navigation