Identifying Pareto Fronts Reliably Using a Multi-Stage Reference-vector-based Framework

Kalyanmoy Deb, Claudio Lucio do Val Lopes, Flávio Vinícius Cruzeiro Martins, Elizabeth Fialho Wanner

Research output: Contribution to journalArticlepeer-review


Evolutionary multi-objective and many-objective optimization (EMO and EMaO) algorithms are increasingly being used to identify the true shape and location of the Paretooptimal front using a few representative well-converged and welldistributed solutions. The reason for their popularity is due to their ability to provide a better understanding of objective relationships for optimal solutions, and also to facilitate the choice of a preferred solution using an interactive or postoptimal multi-criterion decision analysis. However, since EMO and EMaO algorithms are stochastic, a single application may not provide a true representative set with a desired number of Pareto solutions reliably in repetitive runs and importantly with a well-distributed set of solutions. In this paper, we propose a multistage framework involving reference-vector based evolutionary multi-and many-objective algorithms (MuSt-EMO and MuSt-EMaO) that attempts to recursively rectify shortcomings of previous stages by careful executions of subsequent stages so that a prescribed number of well-distributed and well-converged solutions are achieved at the end. The proposed multi-stage approach is implemented to a number of popular reference vector based EMO/EMaO algorithms and is applied on various multiand many-objective test and real-world problems.
Original languageEnglish
JournalIEEE Transactions on Evolutionary Computation
Early online date1 Mar 2023
Publication statusE-pub ahead of print - 1 Mar 2023


  • Convergence, Statistics, Sociology, Optimization, Reliability, Heuristic algorithms, Evolutionary computation
  • Multi-objective optimization, evolutionary algorithms, Pareto front , Gap-filling method


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