Multi-objective optimization based reverse strategy with differential evolution algorithm for constrained optimization problems

We rebuilt the model of constrained optimization problems, called reversed model.We developed a comparison strategy based on origin and new model.Difference between usual algorithm and proposed one is discussed.Experimental results show the effectiveness of the proposed algorithm. Solving constrained optimization problems (COPs) has been gathering attention from many researchers. In this paper, we defined the best fitness value among feasible solutions in current population as gbest. Then, we converted the original COPs to multi-objective optimization problems (MOPs) with one constraint. The constraint set the function value f(x) should be less than or equal to gbest; the objectives are the constraints in COPs. A reverse comparison strategy based on multi-objective dominance concept is proposed. Compared with usual strategies, the innovation strategy cuts off the worse solutions with smaller fitness value regardless of its constraints violation. Differential evolution (DE) algorithm is used as a solver to search for the global optimum. The method is called multi-objective optimization based reverse strategy with differential evolution algorithm (MRS-DE). The experimental results demonstrate that MRS-DE can achieve better performance on 22 classical benchmark functions compared with several state-of-the-art algorithms.

[1]  R. Haftka,et al.  Constrained particle swarm optimization using a bi-objective formulation , 2009 .

[2]  Ling Wang,et al.  An effective hybrid genetic algorithm with flexible allowance technique for constrained engineering design optimization , 2012, Expert Syst. Appl..

[3]  Yong Wang,et al.  Constrained Evolutionary Optimization by Means of ( + )-Differential Evolution and Improved Adaptive Trade-Off Model , 2011, Evolutionary Computation.

[4]  Ponnuthurai N. Suganthan,et al.  Diversity enhanced Adaptive Evolutionary Programming for solving single objective constrained problems , 2009, 2009 IEEE Congress on Evolutionary Computation.

[5]  Wenyin Gong,et al.  A multiobjective differential evolution algorithm for constrained optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[6]  Dexuan Zou,et al.  A novel modified differential evolution algorithm for constrained optimization problems , 2011, Comput. Math. Appl..

[7]  Tetsuyuki Takahama,et al.  Constrained optimization by the ε constrained differential evolution with an archive and gradient-based mutation , 2010, IEEE Congress on Evolutionary Computation.

[8]  Tetsuyuki Takahama,et al.  Constrained Optimization by ε Constrained Differential Evolution with Dynamic ε-Level Control , 2008 .

[9]  Wenjian Luo,et al.  Differential evolution with dynamic stochastic selection for constrained optimization , 2008, Inf. Sci..

[10]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[11]  Yuren Zhou,et al.  Multiobjective Optimization and Hybrid Evolutionary Algorithm to Solve Constrained Optimization Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Xavier Blasco Ferragud,et al.  Multiobjective optimization algorithm for solving constrained single objective problems , 2010, IEEE Congress on Evolutionary Computation.

[13]  Kalyanmoy Deb,et al.  Multiobjective Problem Solving from Nature: From Concepts to Applications (Natural Computing Series) , 2008 .

[14]  Carlos A. Coello Coello,et al.  Constrained Optimization via Multiobjective Evolutionary Algorithms , 2008, Multiobjective Problem Solving from Nature.

[15]  Tetsuyuki Takahama,et al.  Constrained Optimization by the epsilon Constrained Hybrid Algorithm of Particle Swarm Optimization and Genetic Algorithm , 2005, Australian Conference on Artificial Intelligence.

[16]  Yong Wang,et al.  Combining Multiobjective Optimization With Differential Evolution to Solve Constrained Optimization Problems , 2012, IEEE Transactions on Evolutionary Computation.

[17]  Yafei Huang,et al.  A hybrid differential evolution augmented Lagrangian method for constrained numerical and engineering optimization , 2013, Comput. Aided Des..

[18]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[19]  Efrén Mezura-Montes,et al.  Differential evolution in constrained numerical optimization: An empirical study , 2010, Inf. Sci..

[20]  Kevin M. Passino,et al.  Biomimicry of bacterial foraging for distributed optimization and control , 2002 .

[21]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[22]  Ruhul A. Sarker,et al.  A self-adaptive combined strategies algorithm for constrained optimization using differential evolution , 2014, Appl. Math. Comput..

[23]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[24]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

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

[26]  Masao Fukushima,et al.  Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization , 2006, J. Glob. Optim..

[27]  Tetsuyuki Takahama,et al.  Constrained Optimization by the ε Constrained Differential Evolution with Gradient-Based Mutation and Feasible Elites , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[28]  A. Kai Qin,et al.  Self-adaptive Differential Evolution Algorithm for Constrained Real-Parameter Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[29]  Wenjian Luo,et al.  A Novel Search Biases Selection Strategy for Constrained Evolutionary Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[30]  T. Takahama,et al.  Constrained Optimization by α Constrained Genetic Algorithm (αGA) , 2003 .

[31]  Janez Brest,et al.  Constrained Real-Parameter Optimization with ε -Self-Adaptive Differential Evolution , 2009 .

[32]  Wenyin Gong,et al.  Engineering optimization by means of an improved constrained differential evolution , 2014 .

[33]  Rainer Storn,et al.  System design by constraint adaptation and differential evolution , 1999, IEEE Trans. Evol. Comput..

[34]  Patrice Joyeux,et al.  Particle swarm optimization for solving engineering problems: A new constraint-handling mechanism , 2013, Eng. Appl. Artif. Intell..

[35]  Tetsuyuki Takahama,et al.  Efficient constrained optimization by the ε constrained differential evolution with rough approximation using kernel regression , 2013, 2013 IEEE Congress on Evolutionary Computation.

[36]  Liang Gao,et al.  An improved electromagnetism-like mechanism algorithm for constrained optimization , 2013, Expert Syst. Appl..

[37]  Yong Wang,et al.  An improved (μ + λ)-constrained differential evolution for constrained optimization , 2013, Inf. Sci..

[38]  Yong Wang,et al.  A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization , 2006, IEEE Transactions on Evolutionary Computation.

[39]  Tapabrata Ray,et al.  An Improved Self-Adaptive Constraint Sequencing approach for constrained optimization problems , 2015, Appl. Math. Comput..

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

[41]  Ben Niu,et al.  Bacterial-inspired algorithms for solving constrained optimization problems , 2015, Neurocomputing.

[42]  Jing Liu,et al.  An Organizational Evolutionary Algorithm for Numerical Optimization , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[43]  Efrn Mezura-Montes,et al.  Constraint-Handling in Evolutionary Optimization , 2009 .

[44]  Tapabrata Ray,et al.  Infeasibility Driven Evolutionary Algorithm for Constrained Optimization , 2009 .

[45]  N. Jawahar,et al.  An effective hybrid cuckoo search and genetic algorithm for constrained engineering design optimization , 2014 .