AMGA2: improving the performance of the archive-based micro-genetic algorithm for multi-objective optimization

In this article, an improved Archive-based Micro Genetic Algorithm (referred to as AMGA2) for constrained multi-objective optimization is proposed. AMGA2 is designed to obtain fast and reliable convergence on a wide variety of optimization problems. AMGA2 benefits from the existing literature in that it borrows and improves upon several concepts from existing multi-objective optimization algorithms. Improvements and modifications to the existing diversity assessment techniques and genetic variation operators are also proposed. AMGA2 employs a new kind of selection strategy that attempts to reduce the probability of exploring less desirable search regions. The proposed AMGA2 is a steady-state genetic algorithm that maintains an external archive of best and diverse solutions and a very small working population. AMGA2 has been designed to facilitate the decoupling of the working population, the external archive, and the number of solutions desired as the outcome of the optimization process. Comprehensive benchmarking and comparison of AMGA2 with the current state-of-the-art multi-objective optimization algorithms demonstrate its improved search capability.

[1]  Tapabrata Ray,et al.  Golinski's speed reducer problem revisited , 2003 .

[2]  N. Eldredge Macroevolutionary Dynamics: Species, Niches, and Adaptive Peaks , 1989 .

[3]  Xin Yao,et al.  Parallel Problem Solving from Nature PPSN VI , 2000, Lecture Notes in Computer Science.

[4]  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..

[5]  Shapour Azarm,et al.  A Kriging Metamodel Assisted Multi-Objective Genetic Algorithm for Design Optimization , 2008, DAC 2006.

[6]  Christopher R. Stephens,et al.  Rank based variation operators for genetic algorithms , 2008, GECCO '08.

[7]  Kalyanmoy Deb,et al.  A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization , 2002, Evolutionary Computation.

[8]  Kalyanmoy Deb,et al.  A Fast and Effective Method for Pruning of Non-dominated Solutions in Many-Objective Problems , 2006, PPSN.

[9]  Y. Censor Pareto optimality in multiobjective problems , 1977 .

[10]  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.

[11]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[12]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[13]  Shigenobu Kobayashi,et al.  A Real-Coded Genetic Algorithm for Function Optimization Using the Unimodal Normal Distribution Crossover , 1999 .

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

[15]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

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

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

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

[19]  Qingfu Zhang,et al.  A Multiobjective Differential Evolution Based on Decomposition for Multiobjective Optimization with Variable Linkages , 2006, PPSN.

[20]  Rafail Ostrovsky,et al.  Efficient search for approximate nearest neighbor in high dimensional spaces , 1998, STOC '98.

[21]  Kalyanmoy Deb,et al.  Interactive evolutionary multi-objective optimization and decision-making using reference direction method , 2007, GECCO '07.

[22]  B. Babu,et al.  Differential evolution for multi-objective optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[23]  A.F. Gomez-Skarmeta,et al.  An evolutionary algorithm for constrained multi-objective optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[24]  Kalyanmoy Deb,et al.  Improved Pruning of Non-Dominated Solutions Based on Crowding Distance for Bi-Objective Optimization Problems , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[25]  Kalyanmoy Deb,et al.  Performance assessment of the hybrid Archive-based Micro Genetic Algorithm (AMGA) on the CEC09 test problems , 2009, 2009 IEEE Congress on Evolutionary Computation.

[26]  Wei-Liem Loh,et al.  Fixed-domain asymptotics for a subclass of Matern-type Gaussian random fields , 2005, math/0602302.

[27]  R. Lewontin ‘The Selfish Gene’ , 1977, Nature.

[28]  H. Lindman Analysis of variance in complex experimental designs , 1974 .

[29]  Yun Li,et al.  Optimization and robustness for crashworthiness of side impact , 2001 .

[30]  Carlos A. Coello Coello,et al.  A Micro-Genetic Algorithm for Multiobjective Optimization , 2001, EMO.

[31]  Carlos A. Coello Coello,et al.  The Micro Genetic Algorithm 2: Towards Online Adaptation in Evolutionary Multiobjective Optimization , 2003, EMO.

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

[33]  Jan Golinski,et al.  Optimal synthesis problems solved by means of nonlinear programming and random methods , 1970 .

[34]  C. A. Coello Coello,et al.  Evolutionary multi-objective optimization: a historical view of the field , 2006, IEEE Computational Intelligence Magazine.

[35]  Donald E. Knuth,et al.  Big Omicron and big Omega and big Theta , 1976, SIGA.

[36]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .

[37]  Jouni Lampinen,et al.  GDE3: the third evolution step of generalized differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[38]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[39]  Shapour Azarm,et al.  Optimality and Constrained Derivatives in Two-Level Design Optimization , 1990 .

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

[41]  Kaisa Miettinen,et al.  Interactive multiobjective optimization system WWW-NIMBUS on the Internet , 2000, Comput. Oper. Res..

[42]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

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

[44]  Kalyanmoy Deb,et al.  Evaluating the -Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions , 2005, Evolutionary Computation.

[45]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

[46]  Francisco Luna,et al.  jMetal: a Java Framework for Developing Multi-Objective Optimization Metaheuristics , 2006 .

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

[48]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[49]  Shinn-Ying Ho,et al.  Intelligent evolutionary algorithms for large parameter optimization problems , 2004, IEEE Transactions on Evolutionary Computation.

[50]  Laurie J. Heyer,et al.  Exploring expression data: identification and analysis of coexpressed genes. , 1999, Genome research.

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

[52]  Kaushik Sinha,et al.  Reliability-based multiobjective optimization for automotive crashworthiness and occupant safety , 2007 .

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

[54]  C. A. Coello Coello,et al.  A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques , 1999, Knowledge and Information Systems.

[55]  Gary G. Yen,et al.  Dynamic multiobjective evolutionary algorithm: adaptive cell-based rank and density estimation , 2003, IEEE Trans. Evol. Comput..

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

[57]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[58]  Kyung K. Choi,et al.  Reliability-based design optimization for crashworthiness of vehicle side impact , 2004 .

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