A domain-specific crossover and a helper objective for generating minimum weight compliant mechanisms

ABSTRACT

While designing the Compliant Mechanisms (CM), an equal attention is required on both the problem formulation and the optimization algorithm used. Authors of this paper have successfully proposed the formulation of CM tracing user-defined paths based on the precision points. In this paper, authors modify the NSGA-II algorithm by incorporating (i) a helper objective and (ii) a domain specific crossover which assist in generating a diverse set of non-dominated solutions. First, the single-objective optimization problem of minimizing the weight of structure is solved and named the topology as a reference design. Thereafter, a bi-objective optimization problem is dealt to evolve 'trade-off' solutions for a primary objective of minimizing the weight and a secondary objective of maximizing the diversity with respect to the reference design. Both the optimization problems are solved using a local search based NSGA-II procedure. This study has further compared its results with another GA implementation having a different crossover operator.

REFERENCES

• 1: K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2):182--197, 2002.
• 2: K. Deb and S. Chaudhuri. Automated discovery of innovative designs of mechanical components using evolutionary multiobjective algorithms. In N. Nedjah and L. de Macedo M, editors, Evolutionary Machine Design: Methodology and Applications, chapter 6, pages 143--168. Nova Science Publishers, Inc, New York, 2005.
• 3: D. Sharma, K. Deb, and N. N. Kishore. Evolving path generation compliant mechanisms (PGCM) using local-search based multi-objective genetic algorithm. In International Conference on Trends in Product Life Cycle, Modeling, Simulation and Synthesis (PLMSS), pages 227--238, December 2006.
• 4: D. Sharma, K. Deb, and N. N. Kishore. A domain-specific crossover and a helper objective for generating minimum weight compliant mechanisms. Technical Report KanGAL Report No.2008001., Indian Institute of Technology Kanpur, India, 2008.
• 5: D. Sharma, K. Deb, and N. N. Kishore. Towards generating diverse topologies of path tracing compliant mechanisms using a local search based multi-objective genetic algorithm procedure. Accepted in 2008 IEEE World Congress on Computational Intelligence (WCCI) Conference, 2008.

INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Engineering

General Terms:
Design

Keywords:
GA, compliant mechanisms, helper objective