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On Utilizing Infeasibility in Multiobjective Evolutionary Algorithms

In: Multiobjective Programming and Goal Programming

Author

Listed:
  • Thomas Hanne

    (University of Applied Sciences Northwestern Switzerland)

Abstract
In this article, we consider the problem of infeasible solutions (i.e. solutions which violate one or several restrictions of an optimization problem) which can hardly be avoided when new solutions are generated by stochastic and other means during the run of an optimization algorithm. Since typical approaches for dealing with infeasibility such as using a repair mechanism, a punishment approach, or a simple recalculation of solutions are not fully satisfying in many problems, we suggest a new approach of tolerating and actively using infeasible solutions within the framework of multiobjective evolutionary algorithms. The novel evolutionary algorithm allows solving a multiobjective optimization problem (MOP) with continuous variables by approximating the efficient set. The algorithm uses populations of variable size and new rules for selecting solutions for the subsequent generations. In particular, some of the selected solutions may be infeasible such that the Pareto front is approached at the same time from two “sides”, the feasible set and a subset of the infeasible set. Since the considered in feasible solutions correspond to a dual optimization problem, we call the new algorithm primal—dual multiobjective optimization algorithm, or PDMOEA. The algorithm is demonstrated by considering a numerical test problem and is compared with two other approaches for dealing with infeasibility. The example shows a specific strength of the new approach: By tunneling through infeasible regions, the population may more easily extent to new separated parts of the Pareto set.

Suggested Citation

  • Thomas Hanne, 2009. "On Utilizing Infeasibility in Multiobjective Evolutionary Algorithms," Lecture Notes in Economics and Mathematical Systems, in: Vincent Barichard & Matthias Ehrgott & Xavier Gandibleux & Vincent T'Kindt (ed.), Multiobjective Programming and Goal Programming, pages 113-122, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-85646-7_11
    DOI: 10.1007/978-3-540-85646-7_11
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    Cited by:

    1. Felipe, Angel & Teresa Ortuño, M. & Tirado, Gregorio, 2011. "Using intermediate infeasible solutions to approach vehicle routing problems with precedence and loading constraints," European Journal of Operational Research, Elsevier, vol. 211(1), pages 66-75, May.

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