Bayesian Multiobjective Optimisation with Mixed Analytical and Black-Box Functions: Application to Tissue Engineering

Research output: Contribution to journalResearch articleContributedpeer-review


  • Simon Olofsson - , Imperial College London (Author)
  • Mohammad Mehrian - , University of Liege, KU Leuven (Author)
  • Roberto Calandra - , University of California at Berkeley (Author)
  • Liesbet Geris - , University of Liege, KU Leuven (Author)
  • Marc Peter Deisenroth - , Imperial College London (Author)
  • Ruth Misener - , Imperial College London (Author)


Tissue engineering and regenerative medicine looks at improving or restoring biological tissue function in humans and animals. We consider optimising neotissue growth in a three-dimensional scaffold during dynamic perfusion bioreactor culture, in the context of bone tissue engineering. The goal is to choose design variables that optimise two conflicting objectives, first, maximising neotissue growth and, second, minimising operating cost. We make novel extensions to Bayesian multiobjective optimisation in the case of one analytical objective function and one black-box, i.e. simulation based and objective function. The analytical objective represents operating cost while the black-box neotissue growth objective comes from simulating a system of partial differential equations. The resulting multiobjective optimisation method determines the tradeoff between neotissue growth and operating cost. Our method exhibits better data efficiency than genetic algorithms, i.e. the most common approach in the literature, on both the tissue engineering example and standard test functions. The multiobjective optimisation method applies to real-world problems combining black-box models with easy-to-quantify objectives such as cost.


Original languageEnglish
Pages (from-to)727-739
Number of pages13
JournalIEEE transactions on biomedical engineering
Issue number3
Publication statusPublished - Mar 2019
Externally publishedYes

External IDs

PubMed 30028684
ORCID /0000-0001-9430-8433/work/146646286


ASJC Scopus subject areas


  • Bayesian optimisation, black-box optimisation, multi-objective optimisation, tissue engineering