Multiobjective optimization on a budget of 250 evaluations. In engineering and other `real-world’ applications, multiobjective optimization problems must frequently be tackled on a tight evaluation budget -- tens or hundreds of function evaluations, rather than thousands. In this paper, we investigate two algorithms that use advanced initialization and search strategies to operate better under these conditions. The first algorithm, Bin_MSOPS, uses a binary search tree to divide up the decision space, and tries to sample from the largest empty regions near `fit’ solutions. The second algorithm, ParEGO, begins with solutions in a latin hypercube and updates a Gaussian processes surrogate model of the search landscape after every function evaluation, which it uses to estimate the solution of largest expected improvement. The two algorithms are tested using a benchmark suite of nine functions of two and three objectives -- on a budget of only 250 function evaluations each, in total. Results indicate that the two algorithms search the space in very different ways and this can be used to understand performance differences. Both algorithms perform well but ParEGO comes out on top in seven of the nine test cases after 100 function evaluations, and on six after the first 250 evaluations.

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  1. Davins-Valldaura, Joan; Moussaoui, Saïd; Pita-Gil, Guillermo; Plestan, Franck: ParEGO extensions for multi-objective optimization of expensive evaluation functions (2017)
  2. Feliot, Paul; Bect, Julien; Vazquez, Emmanuel: A Bayesian approach to constrained single- and multi-objective optimization (2017)
  3. Steponavičė, Ingrida; Hyndman, Rob J.; Smith-Miles, Kate; Villanova, Laura: Dynamic algorithm selection for Pareto optimal set approximation (2017)
  4. Akhtar, Taimoor; Shoemaker, Christine A.: Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection (2016)
  5. Martínez-Frutos, Jesús; Herrero-Pérez, David: Kriging-based infill sampling criterion for constraint handling in multi-objective optimization (2016)
  6. Picheny, Victor: Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction (2015)
  7. Rakshit, Pratyusha; Konar, Amit: Differential evolution for noisy multiobjective optimization (2015)
  8. Couckuyt, Ivo; Deschrijver, Dirk; Dhaene, Tom: Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization (2014)
  9. Kaliszewski, I.; Miroforidis, J.: Two-sided Pareto front approximations (2014)
  10. Kunakote, Tawatchai; Bureerat, Sujin: Surrogate-assisted multiobjective evolutionary algorithms for structural shape and sizing optimisation (2013)
  11. Lovison, Alberto: Global search perspectives for multiobjective optimization (2013)
  12. Auger, Anne; Bader, Johannes; Brockhoff, Dimo; Zitzler, Eckart: Hypervolume-based multiobjective optimization: theoretical foundations and practical implications (2012)
  13. Charalampakis, Aristotelis E.: Registrar: a complete-memory operator to enhance performance of genetic algorithms (2012)
  14. Gorissen, Dirk; Couckuyt, Ivo; Laermans, Eric; Dhaene, Tom: Multiobjective global surrogate modeling, dealing with the 5-percent problem (2010)
  15. Jakobsson, Stefan; Patriksson, Michael; Rudholm, Johan; Wojciechowski, Adam: A method for simulation based optimization using radial basis functions (2010)
  16. Klinkenberg, Jan-Willem; Emmerich, Michael T.M.; Deutz, André H.; Shir, Ofer M.; Bäck, Thomas: A reduced-cost SMS-EMOA using kriging, self-adaptation, and parallelization (2010)
  17. Eskandari, Hamidreza; Geiger, Christopher D.: Evolutionary multiobjective optimization in noisy problem environments (2009)
  18. Knowles, Joshua; Corne, David; Reynolds, Alan: Noisy multiobjective optimization on a budget of 250 evaluations (2009)
  19. Rodríguez, Jorge E.; Medaglia, Andrés L.; Coello Coello, Carlos A.: Design of a motorcycle frame using neuroacceleration strategies in MOEAs (2009)
  20. Villemonteix, Julien; Vazquez, Emmanuel; Sidorkiewicz, Maryan; Walter, Eric: Global optimization of expensive-to-evaluate functions: An empirical comparison of two sampling criteria (2009)

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