Guaranteed Convergence and Distribution in Evolutionary MultiObjective Algorithms EMOAs via Achiveme

1
Guaranteed Convergence and Distribution in
Evolutionary Multi-Objective Algorithms (EMOAs)
via Achivement Scalarizing Functions
GRADUATE SCHOOL SEMINAR

• By
• Karthik Sindhyaa
• Thesis Supervisors
• Prof. Kalyanmoy Deba
• Prof. Kaisa Miettinenb
• a Kanpur Genetic Algorithms Laboratory, IIT
  Kanpur
• b Quantitative Methods in Economics, HSE Helsinki

2
Motivation

• None of the EMOAs guarentee to identify optimal
  trade-offs in finite number of generations even
  for simple problems.
• They can only generate a set of solutions whose
  objective vectors are hopefully not too far away
  from the optimal objective vectors.
• Main goal in EMO is to generate only
  representative set of Pareto solutions for
  Decision maker (DM), so that, (s)he can get an
  idea of different trade-offs.
• Hence it makes less sense to get a large number
  of points to represent pareto front, as most of
  EMOAs operate present day, instead a
  representative set of well distributed Pareto
  solutions will suffice.
• Innovization, an important post optimal analysis,
  is meaningless on hopefully near optimal
  objective vectors.
• Main Goals of this study -
• Provide EMO convergence property
• While keeping diversity within entire or on
  partial Pareto optimal set.
• Achieve both tasks in computationally efficient
  way.

3
Literature Survey

• Literature in the direction of fostering synergy
  between EMO and MCDM communities has yeilded
  differernt approaches
• Find a preferred solution to the decision maker
  from a set of non-dominated points generated by
  EMOA
• Incorporating preference information in EMOA.
• STOM in EMO by Tamura (1999), Reference point
  based EMO by Deb et al. (2006), Interactive EMO
  and decision making using reference diraction by
  Deb et al. (2007),
• First step in the direction of hybridizing EA
  with scalarizing fitness function to generate
  approximately efficient solutions was considered
  by Ishibuchi et al. (1998).
• Their idea was followed up by Jaszkiewicz (2002)
  and he proposed multi-objective genetic local
  search (MOGLS).
• Ishibuchi et. al.(2006), also proposed an idea of
  integrating Scalarizing Fitness Functions into
  EMO algorithms.The idea is to probabilistically
  using a scalarizing fitness function (weighted
  sum fitness fucntion) for parent selection and
  generation update in EMO algorithms.

4
Proposed Methodology

• In contemporary stage, methodology executes as a
  serial process and involves following stages
• Execute EMOA to get a non-dominated set which is
  near Pareto-optimal,
• The non-dominated set from EMOA is now clustered
  and a representative set is constructed choosing
  representative points from each cluster.
• Pseudo-weight vector (Deb et. al. (2001)) is
  calculated for the representative set.
• This preference information is used by means of
  changing the weights in ASFs.
• The above procedure cannot guarantee the extreme
  points of the Pareto-optimal set.

Pareto-Point
5
Initial Studies

• Two objective test problems (ZDT1,ZDT2 ZDT3)
  have been chosen.

6
Future Work Conclusion

• Investigate above approach with
• More objectives
• Interactive applications
• Compare with MOGLS
• Computational time accuracy
• Investigate the procedure with other scalarizing
  functions
• Implement concurrent integration
• Local search as a special operator within EMOA
• Application to engineering problems
• Finally, Initial Results are promising and
  methodology has the capacity to grow into strong
  rooted procedure to solve Multi-objective
  problems.

7
References

• Deb, K.(2001). Multi-Objective Optimization Using
  Evolutionary Algorithms. John Wiley Sons,
  Chichester.
• Meittinen, K. (1999). Nonlinear Multiobjective
  Optimization. Boston Kluwer.
• Srinivas, N. and Deb, K. (1994). Multi-objective
  function optimization using non-dominated sorting
  genetic algorithms. Evolutionary Computing
  Journal 2(3), 221-248.
• Tamura, H.,Shibata, T., Tomiyama, S., Hatono, I.
  (1999), A Meta-Heuristic Satisficing Tradeoff
  Method for Solving Multiobjective Combinatorial
  Optimization Problems- With Application to
  Flowshop Scheduling, In Proceedings of the IEEE
  International Conference on Systems, Man and
  Cybernetics, vol. 3, pp. 593-544.
• Deb, K., Sundar, J. (2006). Reference point based
  multi-objective optimization using evolutionary
  algorithms. In Proceedings of the Genetic and
  Evolutionary Computation Conference, pp. 635-642.
• Deb, K., Kumar, A. (2007). Interactive
  evolutionary multi-objective optimization and
  decision making using reference direction method.
  In Proceedings of the Genetic and Evolutionary
  Computation Conference, pp. 781-788
• Ishibuchi, H., Murata, T. (1998), Multi-objective
  Genetic Local search Algorithm and Its
  Application to Flowshop Scheduling. IEEE
  Transactions on Systems, Man and Cubernetics, 28,
  3, 392-403.
• Jaszkiewicz, A. (to appear), Genetic local search
  for multi-objective combinatorial optimization.
  European Journal of Operation Research.
• Ishibuchi, H., Doi, T., Nojima, Y.(2006).
  Incorporation of scalarizing fitness functions
  into evolutionary multiobjective optimization
  algorithms, Lecture Notes in Computer Science
  4193 Parallel Problem Solving from Nature - PPSN
  IX, pp. 493-502.
• Meittinen, K., Mäkelä, MM. (2002). On scalarizing
  fucntions in multiobjective optimization. OR
  spectrum, pp. 193-213.
• Luque, M., Meittinen, K., Eskelinen, P., Ruiz, F.
  (2007). Incorporating preference information in
  interactive refernce point methods for
  multiobjective optimization. Omega, (To appear).
• Deb, K., Goel, t. (2001). A hybrid
  multi-objective evolutionary approach to
  engineering shape design. In Proceedings of the
  Third International Conference on Evolutionary
  Multi-criterion Optimization (EMO-2001), pp.
  385-399.