Achieving balance between proximity and diversity in multi-objective evolutionary algorithm

Ke LI, Sam KWONG, Jingjing CAO, Miqing LI, Jinhua ZHENG, Ruimin SHEN

Research output: Journal PublicationsJournal Article (refereed)peer-review

93 Citations (Scopus)


Currently, an alternative framework using the hypervolume indicator to guide the search for elite solutions of a multi-objective problem is studied in the evolutionary multi-objective optimization community very actively, comparing to the traditional Pareto dominance based approach. In this paper, we present a dynamic neighborhood multi-objective evolutionary algorithm based on hypervolume indicator (DNMOEA/HI), which benefits from both Pareto dominance and hypervolume indicator based frameworks. DNMOEA/HI is featured by the employment of hypervolume indicator as a truncation operator to prune the exceeded population, while a well-designed density estimator (i.e., tree neighborhood density) is combined with the Pareto strength value to perform fitness assignment. Moreover, a novel algorithm is proposed to directly evaluate the hypervolume contribution of a single individual. The performance of DNMOEA/HI is verified on a comprehensive benchmark suite, in comparison with six other multi-objective evolutionary algorithms. Experimental results demonstrate the efficiency of our proposed algorithm. Solutions obtained by DNMOEA/HI well approach the Pareto optimal front and are evenly distributed over the front, simultaneously. © 2011 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)220-242
JournalInformation Sciences
Issue number1
Publication statusPublished - 1 Jan 2012
Externally publishedYes

Bibliographical note

The authors thank the anonymous reviewers for their valuable comments which greatly helped them to improve the contents of this paper. The second author acknowledges support from City University Grant No. 9610025 and City University Strategic Grant No. 7002680.


  • Fitness assignment
  • Hypervolume indicator
  • Minimum spanning tree
  • Multi-objective evolutionary optimization
  • Population maintenance


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