Constrained multi-objective optimization algorithm with an ensemble of constraint handling methods

Different constraint handling techniques have been used with multi-objective evolutionary algorithms (MOEA) to solve constrained multi-objective optimization problems. It is impossible for a single constraint handling technique to outperform all other constraint handling techniques always on every problem irrespective of the exhaustiveness of the parameter tuning. To overcome this selection problem, an ensemble of constraint handling methods (ECHM) is used to tackle constrained multi-objective optimization problems. The ECHM is integrated with a multi-objective differential evolution (MODE) algorithm. The performance is compared between the ECHM and the same single constraint handling methods using the same MODE (using codes available from http://www3.ntu.edu.sg/home/EPNSugan/index.htm). The results show that ECHM overall outperforms the single constraint handling methods.

[1]  R. Courant Variational methods for the solution of problems of equilibrium and vibrations , 1943 .

[2]  David E. Goldberg,et al.  ENGINEERING OPTIMIZATION VIA GENETIC ALGORITHM, IN WILL , 1986 .

[3]  Michael M. Skolnick,et al.  Using Genetic Algorithms in Engineering Design Optimization with Non-Linear Constraints , 1993, ICGA.

[4]  Kalyanmoy Deb,et al.  MULTI-OBJECTIVE FUNCTION OPTIMIZATION USING NON-DOMINATED SORTING GENETIC ALGORITHMS , 1994 .

[5]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[6]  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.

[7]  Masahiro Tanaka,et al.  GA-based decision support system for multicriteria optimization , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[8]  A. Osyczka,et al.  A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm , 1995 .

[9]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[10]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

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

[12]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[13]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[14]  K. Deb An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[15]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

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

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

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

[19]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[20]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

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

[22]  Jonathan A. Wright,et al.  Self-adaptive fitness formulation for constrained optimization , 2003, IEEE Trans. Evol. Comput..

[23]  Tomoyuki Hiroyasu,et al.  SPEA2+: Improving the Performance of the Strength Pareto Evolutionary Algorithm 2 , 2004, PPSN.

[24]  U. Aickelin,et al.  The Application of Bayesian Optimization and Classifier Systems in Nurse Scheduling , 2004, PPSN.

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

[26]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[27]  Carlos A. Coello Coello,et al.  An Algorithm Based on Differential Evolution for Multi-Objective Problems , 2005 .

[28]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[29]  Jouni Lampinen,et al.  An easy‐to‐implement differential evolution approach for multi‐objective optimizations , 2006 .

[30]  Gary G. Yen,et al.  A Self Adaptive Penalty Function Based Algorithm for Constrained Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[31]  P. N. Suganthan,et al.  Multiobjective Differential Evolution with External Archive and Harmonic Distance-Based Diversity Measure , 2007 .

[32]  Carlos A. Coello Coello,et al.  Applications of multi-objective evolutionary algorithms in economics and finance: A survey , 2007, 2007 IEEE Congress on Evolutionary Computation.

[33]  Gary G. Yen,et al.  Constraint handling in multi-objective evolutionary optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[34]  Rainer Laur,et al.  Differential evolution with adaptive parameter setting for multi-objective optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[35]  Zhou Chun-guang,et al.  A Multi-Objective Differential Evolution Algorithm Based on Max-Min Distance Density , 2007 .

[36]  Ji Shan-Fan,et al.  IMODE: Improving Multi-Objective Differential Evolution Algorithm , 2008, 2008 Fourth International Conference on Natural Computation.

[37]  Yuren Zhou,et al.  An Adaptive Tradeoff Model for Constrained Evolutionary Optimization , 2008, IEEE Transactions on Evolutionary Computation.

[38]  Arthur C. Sanderson,et al.  Self-adaptive multi-objective differential evolution with direction information provided by archived inferior solutions , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[39]  H. Zhong-xi,et al.  Multi-objective Optimization with Modified Pareto Differential Evolution , 2008, 2008 International Conference on Intelligent Computation Technology and Automation (ICICTA).

[40]  John T. Langton,et al.  Applications of multi-objective evolutionary algorithms to air operations mission planning , 2008, GECCO '08.

[41]  Jasbir S. Arora,et al.  Use of multi-objective optimization for digital human posture prediction , 2009 .

[42]  Kyriakos C. Giannakoglou,et al.  A multi-objective metamodel-assisted memetic algorithm with strength-based local refinement , 2009 .

[43]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[44]  Ponnuthurai N. Suganthan,et al.  Multi-objective optimization using self-adaptive differential evolution algorithm , 2009, 2009 IEEE Congress on Evolutionary Computation.

[45]  Amit Konar,et al.  Differential Evolution Using a Neighborhood-Based Mutation Operator , 2009, IEEE Transactions on Evolutionary Computation.

[46]  Ponnuthurai N. Suganthan,et al.  Multi-objective evolutionary programming without non-domination sorting is up to twenty times faster , 2009, 2009 IEEE Congress on Evolutionary Computation.

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

[48]  Mehmet Fatih Tasgetiren,et al.  An ensemble of discrete differential evolution algorithms for solving the generalized traveling salesman problem , 2010, Appl. Math. Comput..

[49]  P. N. Suganthan,et al.  Ensemble of niching algorithms , 2010, Inf. Sci..

[50]  Ponnuthurai Nagaratnam Suganthan,et al.  Two-lbests based multi-objective particle swarm optimizer , 2011 .