Extends MBO control object with multi-objective specific options.

  method = NULL,
  ref.point.method = NULL,
  ref.point.offset = NULL,
  ref.point.val = NULL,
  parego.s = NULL,
  parego.rho = NULL,
  parego.use.margin.points = NULL,
  parego.sample.more.weights = NULL,
  parego.normalize = NULL,
  dib.indicator = NULL,
  mspot.select.crit = NULL



Control object for mbo.


Which multi-objective method should be used? “parego”: The ParEGO algorithm. “dib”: Direct indicator-based method. Subsumes SMS-EGO and epsilon-EGO. “mspot”: Directly optimizes multicrit problem where we substitute the true objectives with model-based infill crits via an EMOA. All methods can also propose multiple points in parallel. Default is “dib”.


Method for the determination of the reference point used for S-metric. Currently used for “mspot” and “dib” with indicator “sms”. Possible Values are: “all”: In each dimension: maximum of all points + ref.point.offset. “front”: In each dimension: maximum of all non-dominated points + ref.point.offset “const”: Constant value, see ref.point.val. Default is “all”.


See ref.point.method, default is 1.


Constant value of reference point for hypervolume calculation. Used if ref.point.method = "const". Has to be specified in this case.


Parameter of parego - controls the number of weighting vectors. The default depends on n.objectives and leads to ca. 100000 different possible weight vectors. The defaults for (2, 3, 4, 5, 6) dimensions are (100000, 450, 75, 37, 23) and 10 for higher dimensions.


Parameter of parego - factor for Tchebycheff function. Default 0.05 as suggested in parego paper.


For each target function: Should the weight vector (0, ..., 0, 1, 0, ..., 0), i.e. the weight vector with only 0 and a single 1 at the i-th position for the i-th target function, be drawn with probability 1? Number of TRUE entries must be less or equal to propose.points Default is not to do this.


In each iteration parego.sample.more.weights * propose.points are sampled and the weights with maximum distance to each other are chosen. Default is 1, if only 1 point is proposed each iteration, otherwise 5.


Normalization to use. Either map the whole image space to [0, 1] (standard, the default) or just the paretofront (front).


Either “sms” (SMS-EGO like algorithm) or “eps” (epsilon-EGO like algorithm). Default is “sms”.


Which infill.crit to use in the candidate selection. After the NSGA2 proposed a set of candidates, “propose.points” are selected via the hypervolume contribution of this infill.crit. Possible values are “crit.mr” and “crit.cb” (or any other InfillCrit generated with makeMBOInfillCritCB), default is “crit.mr”.




For more information on the implemented multi-objective procedures the following sources might be helpful: Knowles, J.: ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Transactions on Evolutionary Computation, 10 (2006) 1, pp. 50-66

Wagner, T.; Emmerich, M.; Deutz, A.; Ponweiser, W.: On Expected- Improvement Criteria for Model-Based Multi-Objective Optimization. In: Proc. 11th Int. Conf. Parallel Problem Solving From Nature (PPSN XI) - Part I, Krakow, Poland, Schaefer, R.; Cotta, C.; Kolodziej, J.; Rudolph, G. (eds.), no. 6238 in Lecture Notes in Computer Science, Springer, Berlin, 2010, ISBN 978-3-642-15843-8, pp. 718-727, doi:10. 1007/978-3-642-15844-5 72

Wagner, T.: Planning and Multi-Objective Optimization of Manufacturing Processes by Means of Empirical Surrogate Models. No. 71 in Schriftenreihe des ISF, Vulkan Verlag, Essen, 2013, ISBN 978-3-8027-8775-1

Zaefferer, M.; Bartz-Beielstein, T.; Naujoks, B.; Wagner, T.; Emmerich, M.: A Case Study on Multi-Criteria Optimization of an Event Detection Software under Limited Budgets. In: Proc. 7th International. Conf. Evolutionary Multi-Criterion Optimization (EMO 2013), March 19-22, Sheffield, UK, R. Purshouse; P. J. Fleming; C. M. Fonseca; S. Greco; J. Shaw, eds., 2013, vol. 7811 of Lecture Notes in Computer Science, ISBN 978-3-642-37139-4, pp. 756770, doi:10.1007/978-3-642-37140-0 56

Jeong, S.; Obayashi, S.: Efficient global optimization (EGO) for Multi-Objective Problem and Data Mining. In: Proc. IEEE Congress on Evolutionary Computation (CEC 2005), Edinburgh, UK, Corne, D.; et.al. (eds.), IEEE, 2005, ISBN 0-7803-9363-5, pp. 2138-2145