Inheritable Genetic Algorithm for Biobjective 0/1 Combinatorial Optimization Problems and its Applications

Shinn-Ying Ho*, Jian Hung Chen, Meng Hsun Huang

*Corresponding author for this work

Research output: Contribution to journalArticle

50 Scopus citations

Abstract

In this paper, we formulate a special type of multiobjective optimization problems, named biobjective 0/1 combinatorial optimization problem BOCOP, and propose an inheritable genetic algorithm IGA with orthogonal array crossover (OAX) to efficiently find a complete set of nondominated solutions to BOCOP. BOCOP with n binary variables has two incommensurable and often competing objectives: minimizing the sum r of values of all binary variables and optimizing the system performance. BOCOP is NP-hard having a finite number C(n, r) of feasible solutions for a limited number r. The merits of IGA are threefold as follows: 1) OAX with the systematic reasoning ability based on orthogonal experimental design can efficiently explore the search space of C(n, r); 2) IGA can efficiently search the space of C(n, r± 1) by inheriting a good solution in the space of C(n, r); and 3) The single-objective IGA can economically obtain a complete set of high-quality nondominated solutions in a single run. Two applications of BOCOP are used to illustrate the effectiveness of the proposed algorithm: polygonal approximation problem (PAP) and the problem of editing a minimum reference set for nearest neighbor classification (MRSP). It is shown empirically that IGA is efficient in finding complete sets of nondominated solutions to PAP and MRSP, compared with some existing methods.

Original languageEnglish
Pages (from-to)609-620
Number of pages12
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume34
Issue number1
DOIs
StatePublished - 1 Feb 2004

Keywords

  • Combinatorial problem
  • Inheritable genetic algorithm
  • Multiobjective optimization
  • Nearest neighbor classifier
  • Pareto solutions
  • Shape approximation

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