A hybrid particle swarm with velocity mutation for constraint optimization problems

Two approaches for solving numerical continuous domain constrained optimization problems are proposed and experimented with. The first approach is based on particle swarm optimization algorithm with a new mutation operator in its velocity updating rule. Also, a gradient mutation is proposed and incorporated into the algorithm. This algorithm uses ε-level constraint handling method. The second approach is based on covariance matrix adaptation evolutionary strategy with the same method for handling constraints. It is experimentally shown that the first approach needs less number of function evaluations than the second one to find a feasible solution while the second approach is more effective in optimizing the objective value. Thus, a hybrid approach is proposed (third approach) which uses the first approach for locating potentially different feasible solutions and the second approach for further improving the solutions found so far. Also, a multi-swarm mechanism is used in which several instances of the first approach are run to locate potentially different feasible solutions. The proposed hybrid approach is applied to 18 standard constrained optimization benchmarks with up to 30 dimensions. Comparisons with two other state-of-the-art approaches show that the hybrid approach performs better in terms of finding feasible solutions and minimizing the objective function.

[1]  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.

[2]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

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

[4]  Michael N. Vrahatis,et al.  Particle Swarm Optimization Method for Constrained Optimization Problems , 2002 .

[5]  Andries Petrus Engelbrecht,et al.  Particle Swarms for Linearly Constrained Optimisation , 2007, Fundam. Informaticae.

[6]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[7]  Raymond Chiong,et al.  Why Is Optimization Difficult? , 2009, Nature-Inspired Algorithms for Optimisation.

[8]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[9]  Zhigang Shang,et al.  Coevolutionary Comprehensive Learning Particle Swarm Optimizer , 2010, IEEE Congress on Evolutionary Computation.

[10]  S. Halgamuge,et al.  A comparison of constraint-handling methods for the application of particle swarm optimization to constrained nonlinear optimization problems , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[11]  Zbigniew Michalewicz,et al.  A Survey of Constraint Handling Techniques in Evolutionary Computation Methods , 1995 .

[12]  P. Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2010 Competition on Constrained Real- Parameter Optimization , 2010 .

[13]  C. D. Meyer,et al.  Generalized inverses of linear transformations , 1979 .

[14]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[15]  T. Takahama,et al.  Solving Constrained Optimization Problems by the ε Constrained Particle Swarm Optimizer with Adaptive Velocity Limit Control , 2006, 2006 IEEE Conference on Cybernetics and Intelligent Systems.

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

[17]  Hyun Myung,et al.  Preliminary Investigations into a Two-State Method of Evolutionary Optimization on Constrained Problems , 1995, Evolutionary Programming.

[18]  Zbigniew Michalewicz,et al.  GENOCOP: a genetic algorithm for numerical optimization problems with linear constraints , 1996, CACM.

[19]  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.