Performance assessment of the hybrid Archive-based Micro Genetic Algorithm (AMGA) on the CEC09 test problems

In this paper, the performance assessment of the hybrid Archive-based Micro Genetic Algorithm (AMGA) on a set of bound-constrained synthetic test problems is reported. The hybrid AMGA proposed in this paper is a combination of a classical gradient based single-objective optimization algorithm and an evolutionary multi-objective optimization algorithm. The gradient based optimizer is used for a fast local search and is a variant of the sequential quadratic programming method. The Matlab implementation of the SQP (provided by the fmincon optimization function) is used in this paper. The evolutionary multi-objective optimization algorithm AMGA is used as the global optimizer. A scalarization scheme based on the weighted objectives is proposed which is designed to facilitate the simultaneous improvement of all the objectives. The scalarization scheme proposed in this paper also utilizes reference points as constraints to enable the algorithm to solve non-convex optimization problems. The gradient based optimizer is used as the mutation operator of the evolutionary algorithm and a suitable scheme to switch between the genetic mutation and the gradient based mutation is proposed. The hybrid AMGA is designed to balance local versus global search strategies so as to obtain a set of diverse non-dominated solutions as quickly as possible. The simulation results of the hybrid AMGA are reported on the bound-constrained test problems described in the CEC09 benchmark suite.

[1]  Ronald L. Iman.  Latin Hypercube Sampling , 2008 .

[2]  Saúl Zapotecas Martínez,et al.  Hybridizing an evolutionary algorithm with mathematical programming techniques for multi-objective optimization , 2008, GECCO '08.

[3]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[4]  Tomoyuki Hiroyasu,et al.  NCGA: Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems , 2002, GECCO Late Breaking Papers.

[5]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[6]  M. Reza Soleymani,et al.  An Efficient Nearest Neighbor Search Method , 1987, IEEE Trans. Commun..

[7]  A. Messac,et al.  Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier , 2004 .

[8]  Kalyanmoy Deb,et al.  AMGA: an archive-based micro genetic algorithm for multi-objective optimization , 2008, GECCO '08.

[9]  Carlos A. Coello Coello,et al.  A new memetic strategy for the numerical treatment of multi-objective optimization problems , 2008, GECCO '08.

[10]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[11]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[12]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[13]  Klaus Schittkowski,et al.  NLPQL: A fortran subroutine solving constrained nonlinear programming problems , 1986 .

[14]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[15]  Kalyanmoy Deb,et al.  Hybridization of SBX based NSGA-II and sequential quadratic programming for solving multi-objective optimization problems , 2007, 2007 IEEE Congress on Evolutionary Computation.

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  Peter A. N. Bosman,et al.  Exploiting gradient information in numerical multi--objective evolutionary optimization , 2005, GECCO '05.

[18]  Xiaolin Hu,et al.  Hybridization of the multi-objective evolutionary algorithms and the gradient-based algorithms , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[19]  Jesús García,et al.  Introducing MONEDA: scalable multiobjective optimization with a neural estimation of distribution algorithm , 2008, GECCO '08.

[20]  Hamidreza Eskandari,et al.  FastPGA: A Dynamic Population Sizing Approach for Solving Expensive Multiobjective Optimization Problems , 2006, EMO.

[21]  Kalyanmoy Deb,et al.  Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization , 2008, Eur. J. Oper. Res..