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Incorporating user preferences in many-objective optimization using relation ε-preferred

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Abstract

During the last 10 years, many-objective optimization problems, i.e. optimization problems with more than three objectives, are getting more and more important in the area of multi-objective optimization. Many real-world optimization problems consist of more than three mutually dependent subproblems, that have to be considered in parallel. Furthermore, the objectives have different levels of importance. For this, priorities have to be assigned to the objectives. In this paper we present a new model for many-objective optimization called Prio-ε-Preferred, where the objectives can have different levels of priorities or user preferences. This relation is used for ranking a set of solutions such that an ordering of the solutions is determined. Prio-ε-Preferred is controlled by a parameter ε, that is problem specific and has to be adjusted experimentally by the developer. Therefore we also present an extension called Adapted-ε-Preferred (AEP), that determines the ε values automatically without any user interaction. To demonstrate the efficiency of our approach, experiments are performed. The method based on Prio-ε-Preferred is used to guide the search of an Evolutionary Algorithm. As optimization problem a very complex scheduling problem, i.e. a utilization planning in a hospital is used. The considered benchmarks consist of 2 up to 90 optimization objectives. First, Prio-ε-Preferred  where ε is set “by hand”, is compared to the basic method NSGA-II. It is shown that Prio-ε-Preferred clearly outperforms NSGA-II. Furthermore, it turns out that the results obtained by AEP are as good as if ε is adjusted manually.

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Notes

  1. In contrast to (Sülflow et al. 2007) benchmarks from (Benchmarks 2012) are taken. This makes the results comparable to other approaches.

  2. But indeed, the modeling of user preferences as presented here in combination with the hypervolume indicator is an interesting task for future work.

  3. If \(p \ge \#days\), the algorithm stops. But if the border of the next planning period is known, the operator can easily be extended such that it can mutate the first days of the next planning period.

  4. In all Tables Millar-2Shift is an abbreviation for benchmark Millar-2Shift-DATA1.

Abbreviations

AEP:

Adapted-ε-preferred

MOO:

Multi-objective optimization

EA:

Evolutionary algorithm

NRP:

Nurse rostering problem

SCC:

Strongly-connected components

DFS:

Depth-first-search

SC:

Satisfiability class

VM:

k-Vertical mutation

HM:

k-Horizontal mutation

SSM:

k-Set shift mutation

SPM:

Set pattern mutation

AVG:

Average value

OF:

Objective function

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Authors and Affiliations

  1. Institute of Computer Science, University of Bremen, 28359, Bremen, Germany

    Nicole Drechsler

  2. solvertec GmbH, 28359, Bremen, Germany

    André Sülflow

  3. Institute of Computer Science/DFKI Bremen, University of Bremen, 28359, Bremen, Germany

    Rolf Drechsler

Authors
  1. Nicole Drechsler
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  2. André Sülflow
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  3. Rolf Drechsler
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Correspondence to Nicole Drechsler.

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Drechsler, N., Sülflow, A. & Drechsler, R. Incorporating user preferences in many-objective optimization using relation ε-preferred. Nat Comput 14, 469–483 (2015). https://doi.org/10.1007/s11047-014-9422-0

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