Soft Computing

, Volume 21, Issue 17, pp 5003–5024 | Cite as

An r-dominance-based preference multi-objective optimization for many-objective optimization

  • Ruochen Liu
  • Xiaolin Song
  • Lingfen Fang
  • Licheng Jiao
Methodologies and Application


Evolutionary multi-objective optimization (EMO) algorithms have been used in finding a representative set of Pareto-optimal solutions in the past decade and beyond. However, most of Pareto domination-based multi-objective optimization evolutionary algorithms (MOEAs) are not suitable for many-objective optimization, in which, a good trade-off among many objectives becomes very difficult. In real-world applications, the fact is that the decision-maker is not interested in the overall Pareto-optimal front since the final decision is a unique or several solutions. So the decision-maker can incorporate his/her preferences into the search process of MOEAs to guide the search toward the preferred parts of the Pareto region rather than the whole Pareto-optimal region. In this paper, we hybridize the classical Pareto dominance principle with reference-based dominance and propose a reference-dominance-based preference multi-objective optimization algorithm (r-PMOA). The proposed method has been extensively compared with other recently proposed preference-based EMO approaches over several benchmark problems of multi-objective optimization having 2–10 objectives. The results of the experiment indicate that r-PMOA achieves competitive results.


Preference multi-objective optimization Artificial immune system Preference rank Many-objective problem 



This work was supported by the National Natural Science Foundation of China (Nos. 61373111, 61272279, 61103119 and 61203303); the Fundamental Research Funds for the Central Universities (Nos. K50511020014, K50510020011, K5051302049, and K5051302023); and the Provincial Natural Science Foundation of Shaanxi of China (No. 2014JM8321).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ruochen Liu
    • 1
  • Xiaolin Song
    • 1
  • Lingfen Fang
    • 1
  • Licheng Jiao
    • 1
  1. 1.Laboratory of Intelligent Perception and Image Understanding of Ministry of EducationXidian UniversityXi’anChina

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