Extremized PICEA-g for Nadir Point Estimation in Many-Objective Optimization

  • Rui WangEmail author
  • Meng-jun Ming
  • Li-ning Xing
  • Wen-ying Gong
  • Ling Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10956)


Nadir point, constructed by the worst Pareto optimal objective values, plays an important role in multi-objective optimization and decision making. For example, the nadir point is often a pre-requisite in many multi-criterion decision making approaches. Along with the ideal point, the nadir point can be applied to normalize solutions so as to facilitate a comparison and aggregation of objectives. Moreover, nadir point is useful in visualization software catered for multi-objective optimization. However, the estimation of nadir point is still a challenging problem, particularly, for optimization and/or decision-making problems with many objectives. In this paper, a modified preference-inspired coevolutionary algorithm using goal vectors (PICEA-g) called extremized PICEA-g is proposed to estimate the nadir point. The extremized PICEA-g, denoted as e-PICEA-g, is an \( \left( {N + N} \right) \) elitist algorithm and employs a two-phase selection strategy. In the first-phase \( \left( {N + K} \right) \) solutions are selected out from the overall \( 2N \) solutions based on the dominance-level and an angle based closeness indicator. In the second-phase the selected \( \left( {N + K} \right) \) solutions are further filtered by removing \( K \) poor ones in terms of their fitness calculated by a slightly modified PICEA-g fitness scheme. By the two-phase selection strategy, the e-PICEA-g skillfully harnesses the advantages of edge-point-to-nadir and extreme-to-nadir principles. Experimental results demonstrate the efficiency and effectiveness of the e-PICEA-g on many-objective optimization benchmarks with up to 13 objectives.


Nadir point Evolutionary algorithm PICEA-g Extremized Many-objective optimization 



This work was supported by the National key research and development plan (2016YFB0901900), the National Natural Science Foundation of China (Nos. 61773390), National Natural Science Fund for Distinguished Young Scholars of China (61525304) and Natural Science Fund for Distinguished Young Scholars of Hunan Province (2017JJ1001).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Rui Wang
    • 1
    Email author
  • Meng-jun Ming
    • 1
  • Li-ning Xing
    • 1
  • Wen-ying Gong
    • 2
  • Ling Wang
    • 3
  1. 1.College of Systems EngineeringNational University of Defense TechnologyChangshaPeople’s Republic of China
  2. 2.School of Computer ScienceChina University of GeosciencesWuhanPeople’s Republic of China
  3. 3.Department of AutomationTsinghua UniversityBeijingPeople’s Republic of China

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