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Inheritable genetic algorithm for biobjective 0/1 combinatorial optimization problems and its applications.

Shinn-Ying Ho1, Jian-Hung Chen, Meng-Hsun Huang

  • 1Department of Information Engineering and Computer Science, Feng Chia University, Taichung, Taiwan 407, ROC. syho@fcu.edu.tw

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|September 17, 2004
PubMed
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This study introduces a novel inheritable genetic algorithm (IGA) with orthogonal array crossover (OAX) to solve complex biobjective 0/1 combinatorial optimization problems (BOCOP). The IGA efficiently finds complete sets of optimal solutions for performance and resource minimization.

Area of Science:

  • Operations Research
  • Computer Science
  • Optimization Theory

Background:

  • Introduces the biobjective 0/1 combinatorial optimization problem (BOCOP), characterized by two competing objectives: minimizing resource usage (sum of binary variables) and optimizing system performance.
  • Highlights that BOCOP is NP-hard, with a finite number of feasible solutions C(n, r) for a given number of variables (n) and resource limit (r).
  • Addresses the challenge of efficiently finding a complete set of nondominated solutions for such complex optimization problems.

Purpose of the Study:

  • To formulate and address the biobjective 0/1 combinatorial optimization problem (BOCOP).
  • To propose an efficient inheritable genetic algorithm (IGA) incorporating orthogonal array crossover (OAX) for solving BOCOP.
  • To demonstrate the algorithm's effectiveness in finding complete sets of nondominated solutions for specific applications.

Related Experiment Videos

Main Methods:

  • Formulation of the biobjective 0/1 combinatorial optimization problem (BOCOP).
  • Development of an inheritable genetic algorithm (IGA) utilizing orthogonal array crossover (OAX) for efficient search space exploration.
  • Inheritance mechanism within IGA to leverage solutions from related problem spaces (C(n, r) to C(n, r+/-1)).

Main Results:

  • The proposed IGA with OAX systematically explores the search space of C(n, r) effectively.
  • IGA demonstrates efficient searching in related solution spaces by inheriting high-quality solutions.
  • Empirical results show IGA efficiently finds complete sets of nondominated solutions for polygonal approximation problem (PAP) and minimum reference set problem (MRSP).

Conclusions:

  • The inheritable genetic algorithm (IGA) with orthogonal array crossover (OAX) is an effective method for solving biobjective 0/1 combinatorial optimization problems (BOCOP).
  • IGA provides a computationally economical approach to obtain high-quality, complete sets of nondominated solutions in a single run.
  • The algorithm's efficiency is validated through successful applications in polygonal approximation and nearest neighbor classification.